Differentiation Formulas

(d/dx)(k) = ?

0

(d/dx)[f(x) ± g(x)] = ?

f’(x) ± g’(x)

(d/dx)[k times f(x)] = ?

k times f’(x)

(d/dx)[f(x)g(x)] = ?

f(x)g’(x) + g(x)f’(x)

(d/dx)[f(x)/g(x)] = ?

[g(x)f’(x) - f(x)g’(x)]/[g(x)]²

(d/dx)[f(g(x))] = ?

f’(g(x)) times g’(x)

(d/dx)(x^n) = ?

nx^n-1

(d/dx){sin x) = ?

cos x

(d/dx)(cos x) = ?

-sin x

(d/dx)(tan x) = ?

sec² x

(d/dx)(cot x) = ?

-csc² x

(d/dx)(sec x) = ?

(sec x)(tan x)

(d/dx)(csc x) = ?

(-csc x)(cot x)

(d/dx)(e^x) = ?

e^x

(d/dx)(a^x) = ?

(a^x)(ln a)

(d/dx)(ln |x|) = ?

1/x

(d/dx)(sin^-1 x) = ?

1/sq rt (1 - x²)

(d/dx)(cos^-1 x) = ?

-1/sq rt (1 - x²)

(d/dx)(tan^-1 x) = ?

1/(x² + 1)

(d/dx)(cot^-1 x) = ?

-1/(x² + 1)

(d/dx)(sec^-1 x) = ?

1/|x| times sq rt (x² - 1)

(d/dx)(csc^-1 x) = ?

-1/|x| times sq rt (x² - 1)

(d/dx)(sq rt x) = ?

½ sq rt x

(d/dx)(1/x) = ?

-1/x²

(d/dx)(log base a of x) = ?

1/x * ln a