If x= 1+ t^2 ,y= 3+2 t , find dy dx - Vidyadip

Question

If $\text{x}=\frac{1+\log\text{t}}{\text{t}^2},\text{y}=\frac{3+2\log\text{t}}{\text{t}},$ find $\frac{\text{dy}}{\text{dx}}$

✓

Answer

$\text{x}=\frac{1+\log\text{t}}{\text{t}^2},\text{y}=\frac{3+2\log\text{t}}{\text{t}}$
$\frac{\text{dy}}{\text{dt}}=\frac{\text{t}^2\big(\frac{1}{\text{t}}\big)-(1+\log\text{t})(2\text{t})}{\text{t}^4} \\ =\frac{\text{t}-2\text{t}-2\text{t}\log\text{t}}{\text{t}^4}=\frac{-2\log\text{t}-1}{\text{t}^3}$
$\frac{\text{dy}}{\text{dt}}=\frac{\text{t}\big(\frac{2}{\text{t}}\big)-(3+2\log\text{t})(1)}{\text{t}^2} \\ =\frac{2-3-2\log\text{t}}{\text{t}^2}=\frac{-2\log\text{t}-1}{\text{t}^2}$
$\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{\frac{-2\log\text{t}-1}{\text{t}^2}}{\frac{-2\log\text{t}-1}{\text{t}^3}}=\text{t}$

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 "3 Marks Question" from Differentiation→Differentiation — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Determine that value of the constant 'k' so that function $\text{f(x)}=\begin{cases}\frac{\text{kx}}{|\text{x}|},&\text{if }\text{ x}<0\\3,&\text{if }\text{ x}\geq0\end{cases}$ is continuous at x = 0.

Evaluate the following definite integrals:
$\int_{0}^\limits{2\pi}\text{e}^{\text{x}}\cos\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)\text{dx}$

Solve: $\cos\big(\sin^{-1}\text{x}\big)=\frac{1}{6}$

Using properties of determinants, prove the following:$ \begin{vmatrix} a & b & c \\ a - b & b - c & c - a \\ b + c & c + a & a + b \end{vmatrix} = a^{3} + b^{3} + c^{3} - 3abc$

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

If $\vec{a}=3 \hat{i}-\hat{j}$ and $\vec{b}=2 \hat{i}+\hat{j}-3 \hat{k}$, then express $\vec{b}$ in the form $\vec{b}=\vec{b}_1+\vec{b}_2$, where $\vec{b}_1 \| \vec{a}$ and $\vec{b}_2 \perp \vec{a}$.

Evaluate the following integrals:
$\int\sec^42\text{x}\text{ dx}$

If $\text{A}\begin{bmatrix}1&0&1\\0&1&2\\0&0&4\end{bmatrix},$ then show that |3A| = 27|A|.

Show that $\text{AB}\neq\text{BA}$ in the following cases:
$\text{A}=\begin{bmatrix}1&3&0\\1&1&0\\4&1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}0&1&0\\1&0&0\\0&5&1\end{bmatrix}$

A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.