Differentiate e^ sin^ -1 x w.r.t. x. - Vidyadip

Question

Differentiate $e^{sin^{-1}x}$ w.r.t. x.

✓

Answer

Let $y = e^{sin^{-1}x}$
Now, by using the chain rule, we get,
$\frac{d y}{d x}=\frac{d}{d x}\left(e^{\sin ^{-1} x}\right)$
$\Rightarrow \frac{d y}{d x}=e^{\sin ^{-1} x} \cdot \frac{d}{d x}\left(\sin ^{-1} x\right)$
= $e^{\sin ^{-1} x} \cdot \frac{1}{\sqrt{1-x^{2}}}$
= $\frac{e^{\sin ^{-1} x}}{\sqrt{1-x^{2}}}$
Thus $\frac{d y}{d x}=\frac{e^{\sin ^{-1} x}}{\sqrt{1-x^{2}}}$

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 "2 Marks Questions" from Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Verify that the function $y = \sqrt {{a^2} - {x^2}} , $ $x\in \left( { - a,a} \right)$ (explicit or implicit) is a solution of differential equation $x + y\frac{{dy}}{{dx}} = 0\left( {y \ne 0} \right)$

Find adjoint of each of the matrix.
$\begin{bmatrix}1&2\\3&4\end{bmatrix}$

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that
all are white?

Find the total number of binary operations on {a, b}.

Find the domain of$\sec^{-1}(3\text{x}-1)$

If $\begin{vmatrix}3\text{x}&7\\-2&4\end{vmatrix}=\begin{vmatrix}8&7\\6&4\end{vmatrix},$ find the value of x.

Write the value of $\sin^{-1}\Big(\sin\frac{3\pi}{5}\Big)$

Show the feasible region of the constraints $4 x+5 y \geq$ $20, x \geq 0, y \geq 0$.

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

Find differentiation of $\log (1+\theta)$ w.r.t. $\sin ^{-1} \theta$.