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  • explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 70 maths

explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 70 maths

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Answer:Proved

Hint: you must know the rules of solving derivatives.

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


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


Solution:

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

Squaring both sides,      

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

Differentiate both sides,

\begin{aligned} &2 y \frac{d y}{d x}=\frac{d}{d x}\left(x^{2}+a^{2}\right) \\\\ &2 y \frac{d y}{d x}=2 x+0 \end{aligned}

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


∴ Proved

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