Derivative Rules

Constant Rule

d/dx[c]= 0

Constant Multiple Rule

d/dx[cf(x)] = cf’(x)

Sum Rule

d/dx[f(x)+g(x)] = f’(x)+g’(x)

Difference Rule

d/dx[f(x)-g(x)] = f’(x)-g’(x)

Product Rule

d/dx[f(x)g(x)] = f’(x)g(x) + f(x)g’(x)

Quotient Rule

d/dx[f(x)/g(x)] = (g(x)f’(x) - f(x)g’(x)) / [g(x)]²

Chain Rule

d/dx[f(g(x))] = f’(g(x))g’(x)

Power Rule

nx^n-1

Sine

cos(x)

Cosine

-sin(x)

Tangent

sec²(x)

Cosecant

-csc(x)cot(x)

Secant

sec(x)tan(x)

Cotangent

-csc²(x)

Arcsine

1/√1-x²

Arccosine

-1/√1-x²

Arctangent

1/1+x²

Arccosecant

-1/|x|√x²-1

Arcsecant

1/|x|√x²-1

Arccotangent

-1/1+x²

Exponential (base e)

d/dx |e^x| = e^x

Exponential (base a)

d/dx |a^x| = a^xln(a)

Natural Logarithm

d/dx'[ln(x)] = 1/x

Logarithm (base a)

d/dx[loga(x)] = 1/x ⋅ ln(a)