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provide solution for RD Sharma maths class 12 chapter Differentiation exercise  10.2 question 72

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Answer:Proved

Hint: you must know the rules of solving derivatives.

Given: y=\sqrt{a^{2}-x^{2}}


Prove:y \frac{d y}{d x}+x=0


Solution:

y=\sqrt{a^{2}-x^{2}}

Squaring both sides,

y^{2}=a^{2}-x^{2}

Differentiate with respect to x,

\begin{aligned} &2 y \frac{d y}{d x}=0-2 x \\\\ &2 y \frac{d y}{d x}=-2 x \end{aligned}

\begin{aligned} &y \frac{d y}{d x}=-x \\\\ &y \frac{d y}{d x}+x=0 \end{aligned}


∴ Proved

Posted by

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