Derivative Rules

Constant Rule

d/dx (Constant) = 0

Power Rule

d/dx (axⁿ) = naxⁿ⁻¹

Sum-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) - g'(x)f(x)]/[g(x)²]

Derivative of Sin

d/dx sin(x) = cos(x)

Derivative of Cos

d/dx cos(x) = -sin(x)

Derivative of Tan

d/dx tan(x) = sec²(x)

Derivative of Sec

d/dx sec(x) = sec(x)tan(x)

Derivative of Cot

d/dx cot(x) = -csc²(x)

Derivative of Csc

d/dx csc(x) = -csc(x)cot(x)

Chain Rule

d/dx [f(g(x)] = f'(g(x))*g'(x)

Exponential Func. Rule

d/dx eⁿ = n'(eⁿ)

Natural Log Func. Rule

d/dx ln x = 1/x

Limit Definition

lim (h→0) = [f(x+h) - f(x)]/[h]

Alt. Limit Definition

lim (x→a) = [f(x) - f(a)]/[x-a]

Sin(A+B)

Sin(A)Cos(B)+Cos(A)Sin(B)

Cos(A+B)

Cos(A)Cos(B)-Sin(A)Sin(B)

Cos²(A)+Sin²(A)

1

Tan(a)

Sin(A)/Cos(A)

Cot(A)

Cos(A)/Sin(A)

Csc(A)

1/Sin(A)

Sec(A)

1/Cos(A)