#### Please solve RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 5 maths textbook solution

The answer of the given question will be 2.

Given:

$\text { If } f^{\prime}(x)=\sqrt{2 x^{2}-1} \text { and } y=f\left(x^{2}\right) \text { then find } \frac{d y}{d x} \text { at } x=1$

Hint:

$\frac{d y}{d x}=\frac{d}{d x}\left[f\left(x^{2}\right)\right]=f^{\prime}\left(x^{2}\right) \cdot \frac{d}{d x}\left(x^{2}\right)$

Solution:

\begin{aligned} &y=f\left(x^{2}\right) \\\\ &\Rightarrow \frac{d y}{d x}=f^{\prime}\left(x^{2}\right) \cdot \frac{d}{d x}\left(x^{2}\right) \\\\ &=2 x \cdot f^{\prime}\left(x^{2}\right) \end{aligned}

\begin{aligned} &\Rightarrow \frac{d y}{d x}=2 x \cdot \sqrt{2\left(x^{2}\right)^{2}-1} \\\\ &\Rightarrow \frac{d y}{d x}=2 x \cdot \sqrt{2 x^{4}-1} \\\\ &\Rightarrow \frac{d y}{d x}(\text { at } x=1)=2.1 \cdot \sqrt{2(1)^{4}-1} \end{aligned}

\begin{aligned} &=2 \sqrt{2-1} \\\\ &=2 \times 1 \\\\ &=2 \end{aligned}

So, the answer will be 2.