Common Derivatives

Product Rule

f’(x)g(x) + f(x)g’(x)

Quotient Rule (

f’(x)g(x) - f(x)g’(x) / (g(x))²

Chain Rule

f’(g(x))g’(x)

d/dx( c)

0

d/dx(x)

1

d/dx(cx)

C

d/dx(x^n)

nx^(n -1)

d/dx(cx^n)

ncx^(n-1)

d/dx[sin(x)]

Cos(x)

d/dx[cos(x)]

-sin(x)

d/dx[tan(x)]

Sec²(x)

d/dx[csc(x)]

-csc(x)cot(x)

d/dx[sec(x)]

Sec(x)tan(x)

d/dx[cot(x)]

-csc²(x)

d/dx[sin^-1(x)] (arcsin(x))

1/sqrt(1 - x²)

d/dx[cos^-1(x)] (acos)

-1/sqrt(1-x²)

d/dx[tan^-1(x)] (arctan)

1/1+x²

d/dx[csc^-1(x)]

-1/|x|sqrt(x²-1)

d/dx[sec^-1(x)]

1/|x|sqrt(x²-1)

d/dx[cot^-1(x)]

-1/1+x²

d/dx[a^x]

a^xln(a)

d/dx[e^x]

e^x

d/dx[ln(x)]

1/x

d/dx[loga(x)]

1/xln(a)

d/dx[sinh(x)]

Cosh(x)

d/dx[cosh(x)]

sinh(x)

d/dx[tanh(x)]

Sech²(x)

d/dx[csch(x)]

-csch(x)coth(x)

d/dx[sech]

-sech(x)tanh(x)

d/dx[coth(x)]

-csch²(x)