Download App

Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation2 Marks
Question
Find the derivative of the function $y=f(x)$ using the derivative of the inverse function $x=f^{-1}(y)$ in the following$y=\sqrt{1+\sqrt{x}}$
✓

Answer

$
y=\sqrt{1+\sqrt{x}}
$
We first find the inverse of the function $y=f(x)$, i.e. $x$ in term of $y$.
$
\begin{aligned}
& y^2=1+\sqrt{x} \text { i.e. } \sqrt{x}=y^2-1, \therefore x=f^{-1}(y)=\left(y^2-1\right)^2 \\
& \begin{aligned}
\frac{d y}{d x}=\frac{1}{\frac{d x}{d y}}=\frac{1}{\frac{d}{d y}\left[\left(y^2-1\right)^2\right]} & =\frac{1}{2\left(y^2-1\right) \frac{d}{d y}\left(y^2-1\right)} \\
= & \frac{1}{2\left(y^2-1\right)(2 y)}=\frac{1}{4 \sqrt{1+\sqrt{x}}\left[(\sqrt{1+\sqrt{x}})^2-1\right]} \\
= & \frac{1}{4 \sqrt{1+\sqrt{x}}(1+\sqrt{x}-1)}=\frac{1}{4 \sqrt{x} \sqrt{1+\sqrt{x}}}
\end{aligned}
\end{aligned}
$

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

Find the distance of the point (13, 13, -13) from the plane 3x + 4y – 12z = 0.
→
If $\text{A}=\begin{bmatrix}3 & -4 \\1 & -1 \end{bmatrix},$ show that $A - A^T$​​​​​​​ is a skew symmetric matrix.
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\text{xy}=0$
→
Find the principal solutions of $\cos \theta=\frac{1}{2}$.
→
Evaluate:
$\int \frac{4 x+3}{2 x+1} \cdot d x$
→
Find the values of $\lambda$ for which the angle between the vectors $\vec{a}=2 \lambda^2 \hat{i}+4 \lambda \hat{j}+\hat{k}$ and $\vec{b}=7 \hat{i}-2 \hat{j}+\lambda \hat{k}$
→
A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
exactly two bulbs are defective.
→
Integrate the following functions w.r.t. x:
$\frac{x \cdot \sec ^2\left(x^2\right)}{\sqrt{\tan ^3\left(x^2\right)}}$
→
Write the value of $\big[2\hat{\text{i }} 3\hat{\text{j }}4\hat{\text{k}}\big].$
→
Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\text{B})$
→