Find dy dx , when x = at2 and y = 2at - Vidyadip

Question

Find $\frac{\text{dy}}{\text{dx}},$ when
x = at² and y = 2at

✓

Answer

We have x = at² and y = 2 at
$\Rightarrow\frac{\text{dx}}{\text{dx}}=2\text{at}\text{ and }\frac{\text{dy}}{\text{dx}}=2\text{a}$
$\therefore\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{2\text{a}}{2\text{at}}=\frac{1}{\text{t}}$

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" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{f(x)}=\begin{cases}\frac{\text{x}^2-16}{\text{x}-4},&\text{if }\text{ x}\neq4\\\text{k},&\text{if }\text{ x}=4\end{cases}$ is continuous at x = 4, find k.

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-coplanar vectors, then find the value of $\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$

Write the slop of the normal to the curve $\text{y}=\frac{1}{\text{x}}$ at the point $\Big(3,\frac{1}{3}\Big).$

Find the components along the coordinate axis of the position vector of the following point:

S(4,-3)

Determine P(E|F) in Exercises.
Mother, father and son line up at random for a family picture.
E : Son on one end, F : Father in middle.

Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$

Let A and B be square matrices of the order "3 × 3", Is (AB)² = A²B²? Give reasons.

Find the value of x, if:
$\begin{vmatrix}2&4\\5&1\end{vmatrix}=\begin{vmatrix}2\text{x}&4\\6&\text{x}\end{vmatrix}$

Verify that the function x + y = tan^-1y (explicit or implicit) is a solution of differential equation y²y' + y² + 1 = 0.

In a pack of 52 cards, one by one, two cards are drawn randomly without replacement. Find the probability of both card will be red in colour.