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`        differentiate the following function with respect to x(1) sin^-1(x/sqrt(x^2+a^2)(2)sin^-1(2x^2 – 1),0(3) sin^-1(1-2x^2)0`
5 years ago

Rinkoo Gupta
80 Points
```							Y=sin-1v(1-x2)

Dy/dx=1/v1-(1-x2) .{-2x/v(1-x2)}

=-1/v(1-x2)

Y=sin-1x/v(x2+a2)

Dy/dx=[1/v1-{x/v(x2+a2)}2].[{v(x2+a2).1-x.2x/v(x2+a2)}/(x2+a2)]

```
5 years ago
Arun Kumar
IIT Delhi
256 Points
```							Hi$\\assume u=\frac{x}{x^2+a^2} \\\frac{d}{du}(sin^{-1}(u))=\frac{1}{\sqrt{1-u^2}} \\\frac{d}{dx}(sin^{-1}(u))=\frac{1}{\sqrt{1-u^2}}\frac{du}{dx} \\\frac{du}{dx}=\frac{\frac{d}{dx}\left(x\right)\left(x^2+a^2\right)-\frac{d}{dx}\left(x^2+a^2\right)x}{\left(x^2+a^2\right)^2} \\=\frac{a^2-x^2}{\left(a^2+x^2\right)^2} \\substitute to get the answer \\final answer should be=\frac{\left|a\right|}{a^2+x^2}$figure out the part why you're getting |a| and not just a.Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
```
5 years ago
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• 51 Video Lectures
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• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions