AP Calc AB/BC Unit 2 Derivative Rules

Power rule

d/dx = (xⁿ) = n * x^{n - 1}

constant rule

d/dx (constant) = 0

addition/subtraction of functions rule

(d/dx) * (f(x) ± g(x)) = (d/dx) * f(x) ± (d/dx) * g(x)

multiplication rule

(d/dx) * (f * g) = g * f’ + f * g’

division rule

(d/dx) * (f/g) = (g * f’ - f * g’) / g²

(d/dx) * sinx =

cosx

(d/dx) * cosx =

-sinx

(d/dx) * e^x =

e^x

(d/dx) * ln(x) OR logx / loge =

1/x

d/dx(log x / log a) =

1/xlog a

d/dx(tanx) = sec²x

d/dx(secx) = secx tanx

d/dx(cotx)

-csc²x

d/dx(cscx)

-cscx cotx

d/dx(1/x)

-1/x²

d/dx(√x)

1 / (2√x)

chain rule: d/dx f(g(x))

f’(g(x)) * g’(x)

d/dx sin^-1(x)

1 / √(1 - x²)

d/dx sec^-1(x)

1 / [|x| √(x² - 1)]

d/dx tan^-1(x)

1 / (1 + x²)

d/dx cos^-1(x)

-1 / √(1 - x²)

d/dx csc^-1(x)

-1 / [|x| √(x² - 1)]

d/dx cot^-1(x)

-1 / (1 + x²)

(f^-1)’(x)

1 / f’(f^-1(x))