| Constant function |
\(\dfrac{d}{dx} k=0\) |
\(k\in\mathbb{R};k\) is constant |
| Power rule |
\(\dfrac{d}{dx}x^n=nx^{n-1}\) |
\(n\in\mathbb{R};n\neq 0\) |
| Exponential functions |
\(\dfrac{d}{dx}b^x=b^x\ln b\) |
\(b\in\mathbb{R};b\gt 0;b\neq 1\) |
| \(\dfrac{d}{dx}e^x=e^x\) |
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| Logarithmic functions |
\(\dfrac{d}{dx}\log_b x=\dfrac{1}{x\ln b}\) |
\(b\in\mathbb{R};b\gt 0;b\neq 1;x\gt 0\) |
| \(\dfrac{d}{dx}\ln x=\dfrac{1}{x}\) |
\(x\gt 0\) |
| Trigonometric functions |
\(\dfrac{d}{dx}\sin x=\phantom{-}\cos x\) |
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| \(\dfrac{d}{dx}\cos x=-\sin x\) |
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| \(\dfrac{d}{dx}\tan x=\phantom{-}\sec^2 x\) |
\(x\neq\frac{\pi}{2}+\pi n;n\in\mathbb{Z}\) |
| \(\dfrac{d}{dx}\cot x=-\csc^2 x\) |
\(x\neq \pi n;n\in\mathbb{Z}\) |
| \(\dfrac{d}{dx}\sec x=\phantom{-}\sec x\tan x\) |
\(x\neq\frac{\pi}{2}+\pi n;n\in\mathbb{Z}\) |
| \(\dfrac{d}{dx}\csc x=-\csc x\cot x\) |
\(x\neq \pi n;n\in\mathbb{Z}\) |