Table of Contents

Formulas and Rules for Derivative in Calculus

\( \)\( \)\( \)

Formulas

\( f(x) \)

\( \dfrac{d f(x)}{dx} \)

\( x^n \) \( n x^{n-1} \)
\( e^x \) \( e^x \)
\( b^x \) \( \ln b \cdot b^x \)
\( \ln x \) \( \dfrac{1}{x} \)
\( \log_b x \) \( \dfrac{1}{ x \ln b} \)
\( \sin x \) \( \cos x \)
\( \cos x \) \( - \sin x \)
\( \tan x \) \( \sec^2 x \)
\( \cot x \) \( - \csc^2 x \)
\( \sec x \) \( \sec x \tan x \)
\( \csc x \) \( - \csc x \cot x\)
\( \sin^{-1} x\) \( \dfrac{1}{\sqrt{1-x^2}} \)
\( \cos^{-1} x\) \( - \dfrac{1}{\sqrt{1-x^2}} \)
\( \tan^{-1} x\) \( \dfrac{1}{1+x^2} \)
\( \sinh x \) \( \cosh x \)
\( \cosh x \) \( \sinh x \)
\( \tanh x \) \( \text{sech}^2 x \)
\( \coth x \) \( - \text{csch}^2 x \)
\( \text{sech} \; x \) \( -\text{sech} \; x \tanh x \)
\( \text{csch} \; x \) \( - \text{csch} \; x \coth x\)
\( \sinh^{-1} x\) \( \dfrac{1}{\sqrt{x^2+1}} \)
\( \cosh^{-1} x\) \( \dfrac{1}{\sqrt{x^2-1}} \)
\( \tanh^{-1} x\) \( \dfrac{1}{1-x^2} \)
\( \coth^{-1} x\) \( \dfrac{1}{1-x^2} \)

Rules

Let \( u \) and \( v \) be two functions with derivatives \( u' \) and \( v' \)



More References and Links

Handbook of Mathematical Functions Engineering Mathematics with Examples and Solutions