Calculus: Derivative Rules

d/dx [c], where c is a constant

0

d/dx [x]

1

d/dx [cx], where c is a constant

c

d/dx [x^n]

n*x^(n-1)

d/dx [cx^n], where c is a constant

cnx^(n-1)

d/dx [f(x)*g(x)] (product rule for f and g)

f'(x)g(x) + g'(x)f(x)

d/dx [g(x)*h(x)] (product rule for g and h)

g'(x)h(x)+h'(x)g(x)

d/dx [f(x)/g(x)] (quotient rule for f over g)

[f'(x)g(x)-g'(x)f(x)] / [(g(x))^2]

d/dx [g(x)/h(x)] (quotient rule for g over h)

[g'(x)h(x)-h'(x)g(x)] / [(h(x))^2]

d/dx sin x

cos x

d/dx cos x

-sin x

d/dx tan x

sec^2 x

d/dx cot x

-csc^2 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 log_a (x)

1/(xln a)

d/dx arcsin (x)

1/(sqrt(1-x^2))

d/dx arccos (x)

-1/(sqrt(1-x^2))

d/dx arctan (x)

1/(1+x^2)

d/dx arccot (x)

-1/(1+x^2)

d/dx arcsec (x)

1/(x * sqrt(x^2-1))

d/dx arccsc (x)

-1/(x * sqrt(x^2-1))