AP Calc Unit 2

Derivatives

derivative of a constant

0

derivative of a linear (mx+b)

m

natural exponential function (e^x)

e^x

constant multiple rule (c*f(x))

cf’(x)

power rule (xⁿ)

nx^n-1

sin(x)

cos(x)

cos(x)

-sin(x)

natural log functions (ln(x))

1/x for x>0

sum and difference rule (f(x)±g(x))

f’(x)±g’(x)

product rule (f(x)g(x))

f(x)g’(x)+g(x)f’(x)

quotient rule (f(x)/g(x))

(f’(x)g(x)-f(x)g’(x))/g(x)²

tan(x)

sec²(x)

cot(x)

-csc²(x)

csc(x)

-csc(x)cot(x)

sec(x)

sec(x)tan(x)

chain rule (f(g(x)))

f’(g(x))g’(x)

general power rule (h(x)ⁿ)

n(h(x))^n-1*h’(x)

derivative doesn’t exist if:

discontinuity, corner, vertical asymptote