# Calc 1

### 29 terms by hindsnis

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Derivatives

= cos(x)

= -sin(x)

= sec^2(x)

= sec(x) tan(x)

= -csc(x) cot(x)

= -csc^2(x)

### derivative of trig functions reminders

...tan & cot have squares
...sec & csc are themselves x tan & cot respectively

### derivative of a^x

= (a^x) (ln a)

where "a" is a constant

### y = ln x = log_e_x

y' = 1/(x ln e) <------ln e = 1

ex: y = log_10_4x u= 4x y=log_10_u
y' = 1/(u ln 10) x (4)
y' = 4/(4x ln 10) = 1/(x ln 10)

### velocity

is the first derivative of a position function
s(t) = position function
s'(t) = velocity, v(t)

### acceleration

is the second derivative of a position function
s(t) = position function
s'(t) = v(t), velocity
s''(t) = v'(t) = acceleration, a(t)

### marginal cost

is the first derivative of a cost function and tell us the cost to produce one more item

### rate of change of population

first derivative of a population equation/function

### derivative of arccosine x (inverse cosine)

= -1/(sqrt 1-x^2)

= 1/(sqrt 1-x^2)

= 1/(1+x^2)

= (e^u)(u')

### derivative of a^u

= (ln a)(a^u)(u')

### derivative of a function (fixed #)

f(a+h) - f(a)
f'(a) = lim h-->0 --------------------
h

### derivative of a function (number varies)

f(x+h) - f(x)
f'(x) = lim h-->0 --------------------
h

1/sin

1/cos

cos/sin

### 3 requirements for a function to becontinuous at x=a

f(x) must be defined at x=a
lim x-->a f(x) must exist
f(a) = lim x-->a f(x)

### point slope form

(y - y_1) = m (x - x_1)

sin/cos

dy/dx = y'/x'

### Horizontal asymptote

y = (numerator's leading coefficient) / (denominator's leading coefficient) = 1/1 = 1
If there isn't a variable in the numerator, the ha is at 0

### Vertical asymptote

set denominator = 0 and solve

Example:

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