Derivative Rules and Derivatives of Trig Functions

Formulas for finding derivatives of forms of functions and common trig functions. Necessary memorization for UT Math 408C, Differential and Integral Calculus

g(x)/h(x)

(g’(x)h(x) - g(x)h’(x)) / (h(x))²

xⁿ

nx^n-1

g(h(x))

g’(h(x))h’(x)

g(x)h(x)

g’(x)h(x) + h’(x)g(x)

sin(x)

cos(x)

cos(x)

-sin(x)

tan(x)

sec²(x)

cot(x)

-csc²(x)

sec(x)

sec(x)tan(x)

csc(x)

-csc(x)cot(x)

arcsin(x)

1/√(1-x²)

arccos(x)

-1/√(1-x²)