If f'(x)= 2x^2-1 and y=f(x^2), then find dy dx at x=1. - Vidyadip

Question

If $\text{f}'\text{(x)}=\sqrt{2\text{x}^2-1}$ and $\text{y}=\text{f}(\text{x}^2),$ then find $\frac{\text{dy}}{\text{dx}}\text{at x}=1.$

✓

Answer

Here,
$\text{f}'\text{(x)}=\sqrt{2\text{x}^2-1}$
and $\text{y}=\text{f}\big(\text{x}^2\big)$
Differentiating it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\text{f}\big(\text{x}^2\big)$
$=\text{f}'\big(\text{x}^2\big)\frac{\text{d}}{\text{dx}}\big(\text{x}^2\big)$
$=\text{d}'\big(\text{x}^2\big)\times2\text{x}$
$\frac{\text{dy}}{\text{dx}}=2\text{xf}'\big(\text{x}^2\big)$
Put x = 1
$\frac{\text{dy}}{\text{dx}}=2(1)\text{f}'(1)$
$=2\times\text{f}'(1)$
$\frac{\text{dy}}{\text{dx}}=2\times1$
$\big[\text{Since},\text{f}'(1)=\sqrt{2(1)^2-1}=\sqrt{2-1}=1\big]$
$\frac{\text{dy}}{\text{dx}}=2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Integrate the following functions w.r.t. x:

$\frac{e^x}{x} \cdot\left[x(\log x)^2+2 \log x\right]$

Write the cofactor of $a_{12}$ in the following matrix $\begin{bmatrix}2&-3&5\\6&0&4\\1&5&-7\end{bmatrix}$

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
2 red balls.

Find the principal solutions of $\sin x=-\frac{1}{2}$

Solve graphically :x ≥ 0 and y ≤ 0

Find the feasible solution of the following inequation:
$3x + 2y \leq 18, 2x + y \leq 10, x \geq 0, y \geq 0$

Write a value of $\int\text{a}^{\text{x}}\text{e}^{\text{x}}\text{ dx}$

The probability distribution of a discrete random variable $X$ is :

$X =x$	1	2	3	4	5
$P ( X =x)$	$k$	$2k$	$3k$	$4k$	$5k$

Find $( X \leq 4$ )

Write the direction cosines of the vector $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ .

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
One red and one blue ball.