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