AP CALC AB

derivative of sin(x)

cos(x)

derivative of tan(x)

sec²(x)

derivative of cos(x)

-sin(x)

derivative of cot(x)

-csc²(x)

derivative of sec(x)

sec(x)tan(x)

derivative of csc(x)

-csc(x)cot(x)

derivative of ln(x)

1/x

derivative of e^x

e^x

derivative of log_ax

1/(xln(a))

derivative of a^x

a^xln(a)

derivative of arcsin(x)

x’ / √(1-x²)

derivative of arccos(x)

-x’ / √(1-x²)

derivative of arctan(x)

x’ / (1+x²)

The limit as h approaches 0 of (f(x+h)-f(x))/h

That limit is the definition of a derivative. h represents an infinitely small change in x. The whole limit equals f′(x), which is the derivative of the function f(x). The limit is talking about any function f(x) for which the limit exists

the limit as x approaches c of (f(x)-f(c))/(x-c)

This limit defines the derivative of the function at a point c, where c is a specific value in the domain of the function. It represents the slope of the tangent line to the graph of the function at that point.

f(x) increasing

f’(x)>0

f(x) decreasing

f’(x)<0

f(x) local max

f’(x) changes from + to -

f(x) local min

f’(x) changes from - to +

f(x) concave up

f’’(x)>0

f(x) concave down

f’’(x) <0