Derivative rules

on 28.10.18


Rule Function Derivative
Multiplication by constant \( cf \) \(cf’ \)
Power rule \( x^n \) \(nx^{x-1} \)
Sum rule \( f + g \) \(f’ + g’ \)
Difference rule \( f - g \) \(f’ - g’ \)
Product rule \( f \times g \) \(f’g + fg’ \)
Quotient rule \( f/g \) \(\ (f’g - fg’)/g^2 \)
Reciprocal rule \( 1/f \) \( −f’/f^2 \)
Chain rule \( f \circ g \) \( (f’ \circ g) \times g’ \)
Exponential \( e^x \) \( e^x \)
  \( a^x \) \( a^x \ln(a) \)
Logarithms \( \ln(x) \) \( 1/x \)
  \( \log_a(x) \) \( 1/(x \ln(a)) \)
Trigonometry \( \sin(x) \) \( \cos(x) \)
  \( \cos(x) \) \( -\sin(x) \)
  \( \tan(x) \) \( \sec^2(x) \)
Inverse trigonometry \( \sin^{-1}(x) \) \( 1/\sqrt{1-x^2} \)
  \( \cos^{-1}(x) \) \( -1/\sqrt{1-x^2} \)
  \( \tan^{-1}(x) \) \( 1/(1+x^2) \)