M408k Exam 2 Formulas and Derivative Identities

Power Rule

d/dx Xⁿ = nX^n-1

Product Rule

f(x)g’(x) + g(x)f’(x)

Quotient Rule

(f(x)g’(x) - g(x)f’(x)) / g²

d/dx (Sin x)

Cos x

d/dx (Cos x)

-Sin x

d/dx (Tan x)

Sec² x

d/dx (Csc x)

-Cos x Cot x

d/dx (Sec x)

Sec x Tan x

d/dx (Cot x)

-Csc² x

Chain Rule

f’(g(x)) ⋅ g’(x)

d/dx (y=b^x)

y’ = b^x ln b

y= b^{a^(x)}

b⋅a(x) ln(a) ⋅ a’(x)

d/dx (log_b(x))

1/x ln b

d/dx (log_b |x|)

1/x ln b, x ≠ 0

d/dx (ln(x))

1/x

d/dx (ln |x|)

1/x, x ≠ 0

d/dx Sin^-1(x)

1/(√1+x²)

d/dx Cos^-1(x)

-1/(√1+x²)

d/dx Tan^-1(x)

1/(1+x²)

Linear Approximation Equation

L(x) = f’(a)(x-a)

Differential of f Equation

dy = f’(x)dx