If y = ^ -1 [ 5x + 12 1 - x^ 2 13 ], find dy dx . - Vidyadip

Question

If $y = \sin^{-1} \Bigg[\frac{\text{5x + 12}\sqrt{1 - \text{x}^{2}}}{13}\Bigg],\text{ find }\frac{\text{dy}}{\text{dx}}.$

✓

Answer

Let $\frac{5}{13}$= $\cos \alpha$ and x = $\sin\theta$
$\therefore\sin\alpha=\frac{12}{13},\ \cos\theta=\sqrt{1-\text{x}^{2}}$
$\therefore\text{y}=\sin^{-1}(\sin\theta\cos\alpha+\cos\theta\sin\alpha)=\sin^{-1}[\sin(\theta+\alpha)]$
$=\theta+\alpha=\sin^{-1}\text{x}+\text{constant}$
$\therefore\text{dy}/\text{dx}=\frac{1}{\sqrt{1-\text{x}^{2}}}$.

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 "5 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Solve the following initial value problems:
$(1+\text{y}^2)\text{dx}+(\text{x}-\text{e}^{\tan^{-1}\text{y}})\text{dy}=0,\text{ y}(0)=0$

Prove that:
$\begin{vmatrix}\text{a}^2&\text{bc}&\text{ac}+\text{c}^2\\\text{a}^2+\text{ab}&\text{b}^2&\text{ac}\\\text{ab}&\text{b}^2+\text{ac}&\text{c}^2\end{vmatrix}=4\text{a}^2\text{b}^2\text{c}^2$

A bag contains 4 white, 7 black and 5 red balls. Three balls are drawn one after the other without replacement. Find the probability that the balls drawn are white, black and red respectively.

Discuss the continuity of the function $\text{f(x)}=\begin{cases}2\text{x}-1,&\text{if }\text{ x}<2\\\frac{3\text{x}}{2},&\text{if }\text{ x}\geq2\end{cases}$

Differentiate $\sin^{-1}\Big(2\text{x}\sqrt{1-\text{x}^2}\Big)$ with respect to $\tan^{-1}\Big(\frac{\text{x}}{\sqrt{1-\text{x}^2}}\Big),$ if $-\frac{1}{\sqrt{2}}<\text{x}<\frac{1}{\sqrt{2}}$

Evaluate the following intregals:
$\int\frac{\text{x}+2}{\sqrt{\text{x}^2-1}}\text{dx}$

Evaluate the following integrals:
$\int\text{x}^3\tan^{-1}\text{x dx}$

12 cards, numbered 1 to 12, are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.

Differentiate w.r.t. x the function in Exercise:
$(\sin\text{x}-\cos\text{x)}^{(\sin\text{x}-\cos\text{x})},\ \frac{\pi}{4}<\text{x}<\frac{3\pi}{4}$

From a lot of 15 bulbs which include 5 defective, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence, find the mean of the distribution.