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Calculus Unit 2 Derivatives Essentials
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Terms in this set (29)
Formula for the Derivative by the Limit Process
f'(x)=lim ∆x→0[(f(x+∆x)-f(x))/(∆x)]
Point-Slope Formula
y - y₁=m(x - x₁)
The derivative of a constant is always = _____
0
Sum Rule: d/dx[f(x) + g(x)]=
f'(x) + g'(x)
Difference Rule: d/dx[f(x) - g(x)]=
f'(x) - g'(x)
Power Rule: d/dx[ xⁿ]=
nx^(n-1)
The derivative of position is
Velocity
The derivative of velocity is
Acceleration
s(t) usually represents
Position
s'(t) usually represents
Velocity
s''(t) usually represents
Acceleration
v₀ represents
Initial velocity (starting velocity)
s₀
Initial height (starting height)
d/dx[sin(x)]=
cos(x)
d/dx[cos(x)]=
-sin(x)
d/dx[tan(x)]=
sec²(x)
d/dx[sec(x)]=
sec(x)tan(x)
d/dx[csc(x)]=
-csc(x)cot(x)
d/dx[cot(x)]=
-csc²(x)
Product Rule (Mnemonic)
1D2+2D1
d/dx[f(x)g(x)]=
f(x)g'(x)+g(x)f'(x)
Quotient Rule (Mnemonic)
LowDHi-HiDLow over the square of what's below
d/dx[f(x)/g(x)]=
[g(x)f'(x)-f(x)g'(x)]/g(x)²
Chain Rule: d/dx[f(u)]=
f'(u)u'
Chain Rule: d/dx[f(g(x))]=
f'(g(x))g'(x)
As you take a derivative of y with respect to x, you have to multiply the derivative by ________
dy/dx
In implicit differentiation, we multiply by dy/dx because of the _________ rule
Chain
d²y/dx² means to find the __________ ____________
Second Derivative
If a graph of an equation has a horizontal tangent line (slope of zero), then the graph of its derivative should cross the ___-_______ at that point
x-axis
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