Table of Derivatives

Here, for reference, is a table of the basic derivatives that you have met so far.

f (x) f'(x) Powers

x 1

x^a ax^{a - 1} a any constant

Trigonometric Functions (x in radians)

sin(x) cos(x)

cos(x) -sin(x)

tan(x) sec²(x)

$$\cosec$$ -cos(x)/sin²(x)

sec(x) sin(x)/cos²(x)

$$\cosec^{2}_{}$$ cot(x) Inverse Trig Functions

$$\sqrt{1-x^2}$$ arcsin(x)

$$\sqrt{1-x^2}$$ arccos(x)

arctan(x) 1/(1 + x²) Exp & Log

$$\ensuremath{\mathrm{e}}^{ax}$$ ae^ax a any constant

ln(x) 1/x x > 0

sinh(x) cosh(x)

cosh(x) sinh(x)