Derivative Rules

Derivative of sin(x)

cos(x)

Derivative of cos(x)

-sin(x)

Derivative of csc(x)

-csc(x) ⋅ cot(x)

Derivative of tan(x)

sec²(x)

Derivative of h(x) = f(x) ÷ g(x)

(g(x) ⋅ f’(x) - f(x) ⋅ g’(x)) ÷ g(x)²

Derivative of a^x

a^x ⋅ ln(a)

Derivative of ln(x)

1/x

Derivative of sec(x)

sec(x) ⋅ tan(x)

Derivative of cot(x)

-csc²(x)

Derivative of f(x) = c

f’(x) = 0

Derivative of f(x) = c ⋅ f(x)

f’(x) = c ⋅ f’(x)

Derivative of f(x) = f(x) ± g(x)

f’(x) = f’(x) ± g’(x)

Derivative of xⁿ

n⋅x^n-1

Derivative of e^x

e^x

Derivative of h(x) = f(x) ⋅ g(x)

f(x) ⋅ g’(x) + f’(x) ⋅ g(x)

Limit Definition (using h)

What traits can you look for in Limit Definition (using h)

• h approaches 0

• answer says f’(x)

• denominator is h

• contains f(x+h) and f(x)

• no numbers in the parenthesis

Limit Definition (using x and a)

What traits can you look for in Limit Definition (using x and a)

• x approaches a

• answer says f’(a) [a specific point / value, not x]

• denominator is x - a

• contains f(x) and f(a) [a specific point / value, x]

• numbers in the parenthesis

Limit Definition (using h and a)

What traits can you look for in Limit Definition (using h and a)

• h approaches 0

• answer says f’(a) [a specific point / value, not x]

• denominator is h

• contains f(a+h) and f(a) [a specific point / value, not x]

• numbers in the parenthesis