Derivative Rules

Derivative of sin x

cos x

derivative of cos x

-sin x

derivative of tan x

sec²x

derivative of cot x

-csc²x

derivative of sec x

sec x tan x

derivative of csc x

-csc x cot x

derivative of e^x

e^x

derivative of ln x

1/x

Product Rule

f(x)g’(x) + g(x)f’(x)

Quotient Rule f(x)/g(x)

(g(x)f’(x) - f(x)g’(x)) / (g(x))²

Power Rule (derivative of xⁿ)

nx^n-1

• x³=3x²

Constant Rule (derivative of a constant)

0

• 5=0

• pi=0

Constant Multiple Rule (cf(x))

cf’(x)

• 5x⁴=20x³

Sun and Difference Rules (derivative of f(x) ± g(x))

f’(x) ± g’(x)

• x⁴+3x²-1 = 4x³+6x

Checking for continuity

set piecewise function equal to eachother

checking for differentiablity

Set derivatives of piecewise function equal to eachother