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Expert-verifiedFound in: Page 232

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

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Section Derivatives of Trigonometric and Hyperbolic Functions states the derivative of Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions, and Inverse Hyperbolic Functions.

The given section topic is Derivatives of Trigonometric and Hyperbolic Functions.

Derivatives of the Trigonometric Functions are follows

$\frac{d}{dx}\left(\mathrm{sin}x\right)=\mathrm{cos}x\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(\mathrm{cos}x\right)=-\mathrm{sin}x\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(\mathrm{tan}x\right)=se{c}^{2}x\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(secx\right)=secx\mathrm{tan}x\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(cscx\right)=-cscxcotx\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(cotx\right)=-cs{c}^{2}x$

Derivatives of Inverse Trigonometric Functions are following.

$\frac{d}{dx}{\mathrm{sin}}^{-1}x=\frac{1}{\sqrt{1-{x}^{2}}}\phantom{\rule{0ex}{0ex}}\frac{d}{dx}{\mathrm{tan}}^{-1}x=\frac{1}{1+{x}^{2}}\phantom{\rule{0ex}{0ex}}\frac{d}{dx}se{c}^{-1}x=\frac{1}{\left|x\right|\sqrt{{x}^{2}-1}}$

Derivatives of Hyperbolic Functions are following.

$\frac{d}{dx}\left(\mathrm{sin}hx\right)=\mathrm{cos}hx\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(\mathrm{cos}hx\right)=\mathrm{sin}hx\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\left(\mathrm{tan}hx\right)=sec{h}^{2}x$

Derivatives of Inverse Hyperbolic Functions are following.

$\frac{d}{dx}\mathrm{sin}{h}^{-1}x=\frac{1}{\sqrt{{x}^{2}+1}}\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\mathrm{cos}{h}^{-1}x=\frac{1}{\sqrt{{x}^{2}-1}}\phantom{\rule{0ex}{0ex}}\frac{d}{dx}\mathrm{tan}{h}^{-1}x=\frac{1}{1-{x}^{2}}$

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