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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

Answers (1)

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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