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

$\text{x}=3\sin\text{t}-\sin3\text{t},\text{y}=3\cos\text{t}-\cos3\text{t}$
$\frac{\text{dx}}{\text{dt}}=3\cos\text{t}-3\cos3\text{t}$
$\frac{\text{dy}}{\text{dt}}=-3\sin\text{t}+3\sin3\text{t}$
$\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{3\sin\text{t}+3\sin3\text{t}}{3\cos\text{t}-3\cos3\text{t}}$
When $\text{t}=\frac{\pi}{3}$
$\frac{\text{dy}}{\text{dx}}=\frac{-3\sin\big(\frac{\pi}{3}\big)+3\sin(\pi)}{3\cos\big(\frac{\pi}{3}\big)-3\cos(\pi)}=\frac{3\times\frac{\sqrt{3}}{2}+0}{3\times\frac{1}{2}-3(-1)}=-\frac{1}{\sqrt{3}}$

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 "4 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

The cost of 4kg onion, 3kg wheat and 2kg rice is Rs. 60. The cost of 2kg onion, 4kg wheat and 6kg rice is Rs. 90. The cost of 6kg onion 2kg wheat and 3kg rice is Rs. 70. Find the cost of each item per kg by matrix method.

A fair coin is tossed four times. Let X denote the number of heads occuring. Find the probability distribution, mean and variance of X.

Evaluate the following integrals:
$\int\frac{1}{\text{x}^4+3\text{x}^2+1}\ \text{dx}$

Evaluate the following integrals:
$\int\text{e}^{\text{x}}\sin^2\text{x }\text{dx}$

Using integration, find the area of the following region:
$\Big\{(\text{x},\text{y}):\frac{\text{x}^2}{9}+\frac{\text{y}^2}{4}\leq1\leq\frac{\text{x}}{3}+\frac{\text{y}}{2}\Big\}$

How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

Evaluate the definite integral in Exercise:
$\int\limits^{\frac{\pi}{2}}_{0}\frac{\cos^{2}\text{dx}}{\cos^{2}\text{x}+4\sin^{2}\text{x}}$

Solve the following system of equations by matrix method:

x - y + 2z = 7

3x + 4y - 5z = -5

2x - y + 3z = 12

Find the Cartesian equation of the plane passing through the points A(0, 0, 0) and B(3, –1, 2) and parallel to the line $\frac{\text{x-4}}{1}=\frac{\text{y+3}}{-4}=\frac{\text{z+1}}{7}$ .

Evaluate the following integrals:
$\int\frac{\text{x}^2-3\text{x}+1}{\text{x}^4+\text{x}^2+1}\ \text{dx}$