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Study sets matching "calculus derivatives"

22 terms
Calculus Derivatives and Integrals
(d/dx) sin(x)
(d/dx) cos(x)
(d/dx) tan(x)
(d/dx) cot(x)
cos(x)
- sin(x)
sec²(x)
- csc²(x)
(d/dx) sin(x)
cos(x)
(d/dx) cos(x)
- sin(x)
Calculus Derivatives Review
(d/dx)constant=
(d/dx)kx=
(d/dx)ab=
(d/dx)lnx=
0
k
a'b+b'a
x'/x
(d/dx)constant=
0
(d/dx)kx=
k
13 terms
Calculus Terms (derivatives)
derivative
conditions of continuity
average rate of change
derivative of a constant
slope of the tangent
function defined, limit exists, fcn=limit
f(b)-f(a)/b-a
zero
derivative
slope of the tangent
conditions of continuity
function defined, limit exists, fcn=limit
16 terms
AP Calculus: Derivatives
derivative
what is the Difference Quotient Equati…
What is the Alternate Difference Quoti…
What is the product rule?
slope of the tangent line
f'(x) = limit of (f(x+changex)-f(x))/(changex) as the ... change…
limit of (f(x)-f(c))/(x-c) as x-->c... It is finding the slope o…
h(x)=f(x)*g(x)... derivative of h(x)=[f(x)deriv of g(x)]+[g(x)
derivative
slope of the tangent line
what is the Difference Quotient Equati…
f'(x) = limit of (f(x+changex)-f(x))/(changex) as the ... change…
14 terms
Calculus midterm derivatives
(d/dx) (f(x)/g(x)) (Quotient Rule)
(d/dx) a^x
(d/dx) ln x
(d/dx) sin x
a^x * ln(a)
1/x
cos x
(d/dx) (f(x)/g(x)) (Quotient Rule)
(d/dx) a^x
a^x * ln(a)
Trig Calculus Derivatives and intergrals
d/dx sinx
d/dx cosx
d/dx tanx
d/dx cotx
cosx
-sinx
sec²x
-csc²x
d/dx sinx
cosx
d/dx cosx
-sinx
23 terms
Derivatives for Calculus 1
f(x)=sinx
f(x)=cosx
f(x)=tanx
f(x)=cotx
f'(x)=cosx
f'(x)=-sinx
f'(x)=sec^2x
f'(x)=-csc^2x
f(x)=sinx
f'(x)=cosx
f(x)=cosx
f'(x)=-sinx
12 terms
Calculus - Derivatives of Trig. Funtions
sin'(x)
cos'(x)
tan'(x)
sec'(x)
cos(x)
-sin(x)
sec^2(x)
sec(x)tan(x)
sin'(x)
cos(x)
cos'(x)
-sin(x)
24 terms
Calculus Derivatives and Integrals
-cos x + c
sin x + c
tan x + c
-cot x + c
∫ sin x dx
∫ cos x dx
∫ sec2 x dx
∫ csc2 x dx
-cos x + c
∫ sin x dx
sin x + c
∫ cos x dx
32 terms
AP Calculus Derivatives
sin²x + cos²x
1 + tan²x
1 + cot²x
tan x
1
sec²x
csc²x
1/cot x
sin²x + cos²x
1
1 + tan²x
sec²x
21 terms
AP Calculus - Derivatives
uv (product rule)
u/v (quotient rule)
c (constant)
u^n (chain rule)
uv'+vu'
(vu'-uv')/v^2 ... hodhi-hidho/hoho
0 (zero)
uv (product rule)
uv'+vu'
u/v (quotient rule)
(vu'-uv')/v^2 ... hodhi-hidho/hoho
17 terms
BC Calculus Derivatives
(d/dx) uⁿ
(d/dx) e^u
(d/dx) b^u
(d/dx) sin(u)
The derivative of base to the n.
(d/dx) uⁿ
The derivative of base to the n.
(d/dx) e^u
27 terms
Calculus - Derivatives and Applications
derivative informal
graphic representation of derivative
derivative of a point (formal)
derivative of a line (formal)
a representation of the instantaneous rate of change of f at…
the slope of the graph y=f(x) at x=c
derivative informal
a representation of the instantaneous rate of change of f at…
graphic representation of derivative
the slope of the graph y=f(x) at x=c
11 terms
Calculus Derivatives Ch 4
d/dx(sin^-1x)=
d/dx(cos^-1x)=
d/dx(tan^-1x)=
d/dx(cot^-1x)=
1/SR(1-x^2)
-1/SR(1-x^2)
1/1+x^2
1/1-x^2
d/dx(sin^-1x)=
1/SR(1-x^2)
d/dx(cos^-1x)=
-1/SR(1-x^2)
Calculus Unit 2: Derivatives
Derivative of sin(x)
Derivative of cos(x)
Derivative of tan(x)
Derivative of cot(x)
Cos(x)
-Sin(x)
Sec(x)sec(x)
-Csc(x)csc(x)
Derivative of sin(x)
Cos(x)
Derivative of cos(x)
-Sin(x)
11 terms
AP Calculus - Derivatives
Def: Derivative of sin(x)
Def: Derivative of cos(x)
Def: Derivative of tan(x)
Def: Derivative of cot(x)
Def: Derivative of sin(x)
Def: Derivative of cos(x)
23 terms
Calculus Derivatives and Integrals
-cos x + c
sin x + c
tan x + c
-cot x + c
∫ sin x dx
∫ cos x dx
∫ sec2 x dx
∫ csc2 x dx
-cos x + c
∫ sin x dx
sin x + c
∫ cos x dx
16 terms
AP Calculus BC - Derivatives
(c)
(u)
(sinu)
(cosu)
0
1
cosu * u'
(c)
0
(u)
1
20 terms
AP Calculus Derivatives Formulas
Product Rule
Quotient Rule
Chain Rule
y=c
y'= fg' + gf'
y'= (f' g - g' f )/ g^2
y'= f'(g(x)) * g'(x)
y'=0
Product Rule
y'= fg' + gf'
Quotient Rule
y'= (f' g - g' f )/ g^2
16 terms
AP Calculus AB - Chapter 3 Derivatives
Derivative of sin(x)
Derivative of cos(x)
Derivative of tan(x)
Derivative of csc(x)
Derivative of sin(x)
Derivative of cos(x)
13 terms
AP Calculus AB - Derivatives
cos x
-sin x
sec2 x
sec x tan x
d/dx sin x
d/dx cos x
d/dx tan x
d/dx sec x
cos x
d/dx sin x
-sin x
d/dx cos x
19 terms
Calculus AB- Derivatives
First Definition of a Derivative
Second Definition of a Derivative
Specific Form of Derivative
Does differentiability imply continuity?
- Can be replaced by ∆X... - Slope of a tangent line
lim (x+h)^2 - (x-h)^2... h -> 0 2h
- If f(x) is differentiable at x=c if f(x) is continuous
First Definition of a Derivative
- Can be replaced by ∆X... - Slope of a tangent line
Second Definition of a Derivative
lim (x+h)^2 - (x-h)^2... h -> 0 2h
26 terms
Calculus Derivatives Study Guide
Limit Definition
Finding points where tangent line to f…
Equation of line normal to function at…
Evaluating Trig Functions: Sin
d/dx = lim(∆x→0) f(∆x+x) - f(x) / ∆x
1. Take derivative... 2. Derivative=0... 3. Solve for x... 4. Plug x i…
1. Take derivative... 2. Plug given x value into derivative (for…
sin0 = 0... sin(π/6) = 1/2... sin(π/4) = √2/2... sin(π/3) = √3/2... sin(π…
Limit Definition
d/dx = lim(∆x→0) f(∆x+x) - f(x) / ∆x
Finding points where tangent line to f…
1. Take derivative... 2. Derivative=0... 3. Solve for x... 4. Plug x i…
32 terms
AP Calculus derivatives
f'(x)
Alternate form of derivative ... f'(a)=
1
d/dx c
1
0
f'(x)
Alternate form of derivative ... f'(a)=
16 terms
AP Calculus: Special Derivatives
sin x
cos x
tan x
csc x
cosx
-sinx
sec²x
−cscxcotx
sin x
cosx
cos x
-sinx
17 terms
Calculus 1 Derivatives
e^(Kx)
sin(x)
cos(x)
tan(x)
K*e^(Kx)
cos(x)
-sin(x)
sec^2(x)
e^(Kx)
K*e^(Kx)
sin(x)
cos(x)
27 terms
Calculus Derivatives and Integrals
-cos x + c
sin x + c
tan x + c
-cot x + c
∫ sin x dx
∫ cos x dx
∫ sec2 x dx
∫ csc2 x dx
-cos x + c
∫ sin x dx
sin x + c
∫ cos x dx
19 terms
AP Calculus AB- Derivatives
(d/dx) c
(d/dx) x
(d/dx) uⁿ
(d/dx) e^u
The derivative of base to the n.
(d/dx) c
(d/dx) x
32 terms
AP Calculus derivatives
Definition of the Derivative f'(x)
Alternate form of derivative ... f'(a)=
1
d/dx c
1
0
Definition of the Derivative f'(x)
Alternate form of derivative ... f'(a)=
32 terms
Kriegl AP Calculus derivatives
f'(x)
Alternate form of derivative ... f'(a)=
1
d/dx c
1
0
f'(x)
Alternate form of derivative ... f'(a)=
11 terms
Calculus 1: Derivatives Chart
Constant
X
X^n
e^X
0
1
nX^(n-1)
e^X
Constant
0
X
1
12 terms
Calculus Derivatives of Trig stuff
arcsinx
arccosx
arctanx
arcsecx
arcsinx
arccosx
16 terms
AP Calculus - Derivative Rules
Def: Derivative of sin(x)
Def: Derivative of cos(x)
Def: Derivative of tan(x)
Def: Derivative of cot(x)
Def: Derivative of sin(x)
Def: Derivative of cos(x)
9 terms
Calculus Derivative Applications Practice
If f'(c)=0, f''(c) > 0, then what is t…
If f'(c)=0, f''(c) < 0, then what is t…
If f'(c) < 0, then what is true for f…
If f'(c) > 0, then what is true for f…
f has a relative minimum at x=c
f has a relative maximum at x=c
f is decreasing at x=c
f is increasing at x=c
If f'(c)=0, f''(c) > 0, then what is t…
f has a relative minimum at x=c
If f'(c)=0, f''(c) < 0, then what is t…
f has a relative maximum at x=c
Calculus Derivatives of Trig stuff
arcsinx
arccosx
arctanx
arcsecx
arcsinx
arccosx
44 terms
AP Calculus Limits and Derivatives
Area of a Triangle
Area of a Circle
Circumference of a Circle
lne
A=1/2bh
A=pir^2
A=2pir
1
Area of a Triangle
A=1/2bh
Area of a Circle
A=pir^2
Calculus Trig Derivatives
d/dx (sinx)
d/dx (cosx)
d/dx (cscx)
d/dx (tanx)
cosx
-sinx
-cscx cotx
sec²x
d/dx (sinx)
cosx
d/dx (cosx)
-sinx
8 terms
Calculus AB Trig Derivatives
Sinx
Cosx
tanx
cotx
F'(x) = (Cosx)x'
F'(x) = -(sinx)x'
F'(x) = (sec^2x)x'
F'(x) = -(csc^2x)x'
Sinx
F'(x) = (Cosx)x'
Cosx
F'(x) = -(sinx)x'
11 terms
Calculus Trig Derivatives
Sin-1
Tan-1
Sec-1
Cos-1
1/ SR(1-u^2)
1/1+u^2
1/ABS(u) SR(u^2-1)
-1/SR(1-u^2)
Sin-1
1/ SR(1-u^2)
Tan-1
1/1+u^2
17 terms
Calculus theorems, definitions, derivatives
limit
infinite limit @ infinity
extreme value theorem
rolle's theorem
limit lim x-->c f(x) = L means that for all epsilon > 0 there…
lim x--> inf f(x) = inf means that for all m >0 there exists…
if f is continuous on a closed interval [a,b] there exist val…
if f is continuous on [a,b] and differentiable on (a,b) there…
limit
limit lim x-->c f(x) = L means that for all epsilon > 0 there…
infinite limit @ infinity
lim x--> inf f(x) = inf means that for all m >0 there exists…
20 terms
Derivatives - Calculus 1
d/dx (sinu)
d/dx (cosu)
d/dx (tanu)
d/dx (cotu)
cosu × du/dx
-sinu × du/dx
sec²u × du/dx
-csc²u × du/dx
d/dx (sinu)
cosu × du/dx
d/dx (cosu)
-sinu × du/dx
11 terms
Calculus ( Derivatives rules)
(d/dx)constant
(d/dx) x^n
(d/dx) e^x
(d/dx) lnx
0
nx^(n-1)
e^x
1/x
(d/dx)constant
0
(d/dx) x^n
nx^(n-1)
9 terms
Calculus: 3.9 derivatives
e^x
e^u(x)
a^x
a^u(x)
e^x
e^u(x)(du/dx)
a^x(ln a)
a^u(x)(ln a)(du/dx)
e^x
e^x
e^u(x)
e^u(x)(du/dx)
14 terms
Common Derivatives (AB Calculus)
derivative of sin(x)
derivative of cos(x)
derivative of tan(x)
derivative of cot(x)
cos(x)
-sin(x)
sec^2(x)
-csc^2(x)
derivative of sin(x)
cos(x)
derivative of cos(x)
-sin(x)
8 terms
Calculus: Derivatives of Trigonometry
d/dx(sin(x))
d/dx(sec(x))
d/dx(tan(x))
d/dx(cos(x))
cosx
secxtanx
sec^2x
-sinx
d/dx(sin(x))
cosx
d/dx(sec(x))
secxtanx
8 terms
Calculus Trig Derivatives
Cos(x)
Sin(x)
Tan(x)
Cot(x)
-Sin(x)
Cos(x)
Sec^2(x)
-Csc^2(x)
Cos(x)
-Sin(x)
Sin(x)
Cos(x)
12 terms
Calculus Trigonometry derivatives
sinx
tanx
secx
cosx
cosx
sec²x
secxtanx
-sinx
sinx
cosx
tanx
sec²x
12 terms
Calculus Trigonometric Derivatives
cosx
-sinx
sec^2x
-cscxcotx
sinx
cosx
tanx
cscx
cosx
sinx
-sinx
cosx
16 terms
AP Calculus: Derivatives
derivative
what is the Difference Quotient Equati…
What is the Alternate Difference Quoti…
What is the product rule?
slope of the tangent line
f'(x) = limit of (f(x+changex)-f(x))/(changex) as the ... change…
limit of (f(x)-f(c))/(x-c) as x-->c... It is finding the slope o…
h(x)=f(x)*g(x)... derivative of h(x)=[f(x)deriv of g(x)]+[g(x)
derivative
slope of the tangent line
what is the Difference Quotient Equati…
f'(x) = limit of (f(x+changex)-f(x))/(changex) as the ... change…
12 terms
Calculus: Differentials and Derivatives
Graphing Derivatives
Interior Derivatives
Power Rule
Constant Multiple Rule
Rules:... -If f(x) is increasing, then f'(x) is positive... -If f(x…
Rules:... -The left and right side derivatives are the same... -The…
y=xⁿ... y'=(n)(xⁿ⁻¹)
y=(h)(xⁿ)... y'=(h)(n)(xⁿ⁻¹)
Graphing Derivatives
Rules:... -If f(x) is increasing, then f'(x) is positive... -If f(x…
Interior Derivatives
Rules:... -The left and right side derivatives are the same... -The…
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