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Differential Calculus> differentiate the following function with...

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differentiate the following function with respect to x
tan^-1(x – a/x+a)

taniska , 11 Years ago

Grade 12

2 Answers

Rinkoo Gupta

Last Activity: 11 Years ago

y=tan^-1{(x-a)/(x+a)}

dy/dx=1/[1+{(x-a)/(x+a)}²].[{(x+a).1-(x-a).1}/(x+a)²]

=(x+a)²/(x+a)²+(x-a)².[2a/(x+a)²]

=2a/2(x+a)²

⁼a/(x+a)²

^{Thanks & Regards}

^{Rinkoo Gupta}

^{AskIITians faculty}

Arun Kumar

Last Activity: 11 Years ago

Hi

$\\$apply chain rule$ \\\mathrm{Let\:}\frac{x-a}{x+a}\mathrm{=}u \\\frac{d}{du}\left(\arctan \left(u\right)\right)\frac{d}{dx}\left(\frac{x-a}{x+a}\right) \\=\frac{1}{u^2+1} \\\frac{d}{dx}\left(\frac{x-a}{x+a}\right) \\=\frac{2a}{\left(a+x\right)^2} \\$substituting$ \\=\frac{1}{\left(\frac{x-a}{x+a}\right)^2+1}\frac{2a}{\left(a+x\right)^2}$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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