If x=t^2,y=t^3 Then d^2y dx^2 = 1. 3 2 2. 3 4t 3. 3 2t 4. 3t 2 - Vidyadip

Question

If $\text{x}=\text{t}^2,\text{y}=\text{t}^3$ Then $\frac{\text{d}^2\text{y}}{\text{dx}^2}=$

$\frac{3}{2}$
$\frac{3}{4\text{t}}$
$\frac{3}{2\text{t}}$
$\frac{3\text{t}}{2}$

✓

Answer

$\frac{3\text{t}}{2}$

Solution:

$\text{x}=\text{t}^2\Rightarrow\frac{\text{dx}}{\text{dt}}=2\text{t}$

$\text{y}=\text{t}^3\Rightarrow\frac{\text{dy}}{\text{dt}}=3\text{t}^2$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{3\text{t}^2}{2\text{t}}$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{3\text{t}}{2}$

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 "M.C.Q (1 Marks)" 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

${d \over {dx}}\{ \cos (\sin {x^2})\} = $

$\int\sin^{-1}\text{xdx}$ is equal to:

$\cos^{-1}\text{x}+\text{c}$
$\text{x}\sin^{-1}\text{x}+\sqrt{1-\text{x}^2}+\text{c}$
$\frac{1}{\sqrt{1-\text{x}^2}}+\text{c}$
$\text{x}\sin^{-1}\text{x}-\sqrt{1-\text{x}^2}+\text{c}$

Given a system of inequation: $2\text{y}-\text{x}\leq4$ $-2\text{x}+\text{y}\geq-4$Find the value of s, which is the greatest possible sum of the x and y co - ordinates of the point which satisfies the following inequalities as graphed in the xy plane.

8
12
2
4

$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $

If $V=\frac{4}{3} \pi r^3$, at what rate in cubic units is $V$ increasing when $r=10$ and $\frac{d r}{d t}=0.01$ ?

For non-singular square matrix A, B and C of the same order (AB^-1 C) =

A^-1 BC^-1
C^-1 B^-1 A^-1
CBA^-1
C^-1 BA^-1

Let $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$. If $\vec{c}$ is a vector such that $\vec{a} \cdot \vec{c}=11, \vec{b} \cdot(\vec{a} \times \vec{c})=27$ and $\vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|$, then $|\vec{a} \times \vec{c}|^2$ is equal to

For every point P(x, y, z) on the xy-plane,

If $\text{A}=\begin{bmatrix}2&0&-3\\4&3&1\\-5&7&2\end{bmatrix}$ is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is:

$\begin{bmatrix}2&2&-4\\2&3&4\\-4&4&2\end{bmatrix}$
$\begin{bmatrix}2&4&-5\\0&3&7\\-3&1&2\end{bmatrix}$
$\begin{bmatrix}4&4&-8\\4&6&8\\-8&8&4\end{bmatrix}$
$\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

The matrix $\begin{bmatrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & \text{b} \end{bmatrix}$ is a singular matrix, if the value of b is:

-3
3
0
Now-existent