5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions
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17)<math>\int{}{}1+tan^{2}x*dx = \frac{d}{dx}(tan(x))</math> | 17)<math>\int{}{}1+tan^{2}x*dx = \frac{d}{dx}(tan(x))</math> | ||
<math>\frac{d}{dx}(tan(x))=\frac{d}{dx}\left(\frac{sin(x)}{cos(x)}\right)=\frac{cos^{2}x-(-sin(x))}{cos^{2}(x)}</math> | <math>\frac{d}{dx}(tan(x))=\frac{d}{dx}\left(\frac{sin(x)}{cos(x)}\right)=\frac{cos^{2}x-(-(sin(x))(sin(x))}{cos^{2}(x)}</math> | ||
<math>=\frac{cos^{2}x+sin^2(x))}{cos^{2}(x)}=\frac{cos^{2}x}{cos^{2}(x)}+\frac{sin^{2}x}{cos^{2}(x)}</math> | |||
<math>=1+tan^2(x)</math> | |||
Revision as of 00:30, 29 August 2022
17)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}(tan(x))=\frac{d}{dx}\left(\frac{sin(x)}{cos(x)}\right)=\frac{cos^{2}x-(-(sin(x))(sin(x))}{cos^{2}(x)}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =\frac{cos^{2}x+sin^2(x))}{cos^{2}(x)}=\frac{cos^{2}x}{cos^{2}(x)}+\frac{sin^{2}x}{cos^{2}(x)}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =1+tan^2(x)}