Diffrentiate the following w. r. t. x. ^ -1 (x^ 3 2 ) - Vidyadip

Question

Diffrentiate the following w. r. t. x.
$\sin ^{-1}\left(x^{\frac{3}{2}}\right)$

✓

Answer

Let $y =\sin ^{-1}\left(x^{\frac{3}{2}}\right)$Differentiating w.r.t. x, we get
$\frac{d y}{d x}=\frac{d}{d x}\left[\sin ^{-1}\left(x^{\frac{3}{2}}\right)\right]$
$=\frac{1}{\sqrt{1-\left(x^{\frac{3}{2}}\right)^2}} \cdot \frac{d}{d x}\left(x^{\frac{3}{2}}\right)$
$=\frac{1}{\sqrt{1-x^3}} \times \frac{3}{2} x^{\frac{1}{2}}$
$=\frac{3 \sqrt{x}}{2 \sqrt{1-x^3}} .$

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 "Answer the following questions in short." 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

Rewrite the following statements without using if .. then.It f(2) = 0 then f(x) is divisible by (x – 2).

An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes the number of black balls drawn. What are the possible values of X?

Write the negations of the following : Ǝ x ∈ A, such that x + 9 ≤ 15.

Using rules of negation write the negations of the following with justification. ~q → p

Find the vector equation of the plane passing through the point having position vector $2 \hat{i}+3 \hat{j}+4 \hat{k}$ and perpendicular to the vector $2 \hat{i}+\hat{j}-2 \hat{k}$.

Differentiate the following w. r. t. x.$\tan ^{-1}\left(\frac{2 e^x}{1-e^{2 x}}\right)$

If X ~ B(n, p), E(X) = 12, V(X) = 4, then find n

Evaluate: $\int_0^1 \frac{ e ^x}{\sqrt{ e ^x-1}} d x$

Show that the function $f(x)=x^3+10 x+7$ for $x \in \mathrm{R}$ is strictly increasing.

Evaluate:
$\int \frac{\tan x}{\sec x+\tan x} \cdot d x$