Derivatives Rules and Trig Functions

Memorize the derivatives of the 12 trig functions.

Derivative of a Constant

0

Derivative of (Constant)(f(x))

(Constant)(f’(x))

Derivative of f(x)±g(x)

f’(x)±g’(x)

Derivative of f(x)g(x)

g’(x)f(x)+g(x)f’(x)

Derivative of f(x)/g(x) (Numerator/Denominator)

g(x)f'(x)-f(x)g'(x)       DN'-ND'
-------------------   OR  -------
      [g(x)]^2              D^2

Chain Rule. f(u)

(Outer)(inner) f’(x)*u’

Power Rule

nx^(n-1)

Derivative of e^x

e^x

Derivative of sin(x)

cos(x)

Derivative of cos(x)

Derivative of -sin(x)

Derivative of tan(x)

sec²(x)

Derivative of sec(x)

sec(x)tan(x)

Derivative of csc(x)

-csc(x)cot(x)

Derivative of cot(x)

-csc²(x)

Derivative of ln(x)

1/x

Derivative of a^x

a^x * ln(a)

Derivative of loga(x)

1/x(ln(a))

Derivative of arcsin(x)

1/root(1-x²)

Derivative of arctan(x)

1/(1+x²)

Derivative of arcsec(x)

1/(x(root(x²-1))

Derivative of arccos(x)

-1/root(1-x²)

Derivative of arccot(x)

-1/(1+x²)

Derivative of arccsc(x)

-1(x(root(x²-1))