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  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 14

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise  10.2 question 14

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Answer: \frac{-2 x a^{2}}{\sqrt{a^{2}-x^{2}}\left(a^{2}+x^{2}\right)^{\frac{3}{2}}}

Hint: You must know the rules of solving derivative of polynomial function

Given: \sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}}

Solution:

Let  y=\sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}}

y=\left(\frac{a^{2}-x^{2}}{a^{2}+x^{2}}\right)^{\frac{1}{2}}

Differentiating with respect to x

\frac{d y}{d x}=\frac{d}{d x}\left(\frac{a^{2}-x^{2}}{a^{2}+x^{2}}\right)^{\frac{1}{2}}

\frac{d y}{d x}=\frac{1}{2}\left(\frac{a^{2}-x^{2}}{a^{2}+x^{2}}\right)^{\frac{1}{2}-1} \times \frac{d}{d x}\left(\frac{a^{2}-x^{2}}{a^{2}+x^{2}}\right)

 

\frac{d y}{d x}=\frac{1}{2}\left(\frac{a^{2}-x^{2}}{a^{2}+x^{2}}\right)^{-\frac{1}{2}} \times\left\{\frac{\left(a^{2}+x^{2}\right) \frac{d}{d x}\left(a^{2}-x^{2}\right)-\left(a^{2}-x^{2}\right) \frac{d}{d x}\left(a^{2}+x^{2}\right)}{\left(a^{2}+x^{2}\right)^{2}}\right\}..........\frac{d}{d x}\left(\frac{u}{v}\right)=\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^{2}}

\frac{d y}{d x}=\frac{1}{2}\left(\frac{a^{2}+x^{2}}{a^{2}-x^{2}}\right)^{\frac{1}{2}}\left\{\frac{-2 x\left(a^{2}+x^{2}\right)-2 x\left(a^{2}-x^{2}\right)}{\left(a^{2}+x^{2}\right)^{2}}\right\}

\frac{d y}{d x}=\frac{1}{2}\left(\frac{a^{2}+x^{2}}{a^{2}-x^{2}}\right)^{\frac{1}{2}}\left\{\frac{-2 x a^{2}-2 x^{3}-2 x a^{2}+2 x^{3}}{\left(a^{2}+x^{2}\right)^{2}}\right\}

\frac{d y}{d x}=\frac{1}{2}\left(\frac{a^{2}+x^{2}}{a^{2}-x^{2}}\right)^{\frac{1}{2}}\left\{\frac{-4 x a^{2}}{\left(a^{2}+x^{2}\right)^{2}}\right\}

\frac{d y}{d x}=\frac{-2 x a^{2}}{\sqrt{a^{2}-x^{2}}\left(a^{2}+x^{2}\right)^{\frac{3}{2}}}

 

 

 

Posted by

infoexpert26

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