66.5: Table of Derivatives
- Page ID
- 91935
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\begin{aligned}
& \frac{d}{d x} a=0 \\
& \frac{d}{d x} x=1 \\
& \frac{d}{d x} x^{n}=n x^{n-1} \\
& \frac{d}{d x} \sqrt{x}=\frac{1}{2 \sqrt{x}} \\
& \frac{d}{d x} \sin x=\cos x \\
& \frac{d}{d x} \cos x=-\sin x \\
& \frac{d}{d x} \tan x=\sec { }^{2} x \\
& \frac{d}{d x} \sec x=\tan x \sec x \\
& \frac{d}{d x} \csc x=-\cot x \csc x \\
& \frac{d}{d x} \cot x=-\csc ^{2} x
\end{aligned}
\]
\[
\begin{aligned}
& \frac{d}{d x} e^{x}=e^{x} \\
& \frac{d}{d x} \ln x=\frac{1}{x} \\
& \frac{d}{d x} a^{x}=a^{x} \ln a \\
& \frac{d}{d x} \log _{a} x=\frac{1}{x \ln a} \\
& \frac{d}{d x} \sin ^{-1} x=\frac{1}{\sqrt{1-x^{2}}} \\
& \frac{d}{d x} \cos ^{-1} x=\frac{-1}{\sqrt{1-x^{2}}} \\
& \frac{d}{d x} \tan ^{-1} x=\frac{1}{1+x^{2}} \\
& \frac{d}{d x} \sec ^{-1} x=\frac{1}{|x| \sqrt{x^{2}-1}} \\
& \frac{d}{d x} \csc ^{-1} x=\frac{-1}{|x| \sqrt{x^{2}-1}} \\
& \frac{d}{d x} \cot ^{-1} x=\frac{-1}{1+x^{2}} \\
& \frac{d}{d x} \sinh x=\cosh x \\
& \frac{d}{d x} \cosh x=\sinh x \\
& \frac{d}{d x} \tanh x=\operatorname{sech}^{2} x
\end{aligned}
\]