If x=t^2, y=t^3 then find d^2 y d x^2 . - Vidyadip

Question

If $x=t^2, y=t^3$ then find $\frac{d^2 y}{d x^2}$.

✓

Answer

$x=t^2$
$\Rightarrow \frac{d x}{d t}=2 t$
$y=t^3$
$\Rightarrow \frac{d y}{d t}=3 t^2$
then$\frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{3 t^2}{2 t}=\frac{3}{2} t$
$ \therefore \frac{d^2 y}{d x^2} =\frac{d}{d x}\left(\frac{3}{2} t\right)=\frac{3}{2} \cdot \frac{d t}{d x}=\frac{3}{2} \times \frac{1}{2 t}$
$ =\frac{3}{4 t}$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E: ‘the card drawn is a king or queen’
F: ‘the card drawn is a queen or jack’

A random variable has the following probability distribution:

$X = X_i$	1	2	3	4
$P(X = X_i)$	k	2k	3k	4k

Write the value of $\text{P}(\text{X}\geq3).$

Evaluate the following determinant:
$\begin{vmatrix}1&-3&2\\4&-1&2\\3&5&2\end{vmatrix}$

Find the adjoint of the following matrices: $\text{C}=\begin{bmatrix} \cos\alpha & \sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$Verify that (adjoint A) A = |A|I = A (adjoint A) for the above matrices.

Evaluate the following integrals:
$\int3^{2\log_3\text{x}}\text{dx}$

Write the domain of the real function $\text{f(x)}=\frac{1}{\sqrt{|\text{x}|-\text{x}}}.$

Answer the following quations in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.

If A is symmetric matrix, write whether $A^T$ is symmetric or skew-symmetric.

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

Evaluate $\int\frac{\text{e}^{\tan^{-1\text{x}}}}{1+\text{x}^2}\text{ dx}$