Question

if x=3t²-1 ,y=t³-t then dy/dx is equal to​

Answer 1

Given :

x=3t²-1 and y=t³-t

To find :

dy/dx

Solution:

We have to find dy/dx

$\sf{x=3t^2-1}$

Now Differentiate it with respect to t

$\sf{\dfrac{dx}{dt}=\dfrac{d(3t^2)}{dt}-\dfrac{d(1)}{dt}}$

$\sf{\dfrac{dx}{dt}=6t}....(1)$

$\sf{y=t^3-t}$

$\sf{\dfrac{dy}{dt}=\dfrac{d(t^3)}{dt}-\dfrac{d(t)}{dt}}$

$\sf{\dfrac{dy}{dt}=3t^2-1}...(2)$

Now divide equation (1) by (2)

$\sf\dfrac{\frac{dx}{dt}}{\frac{dy}{dt}}=\dfrac{6t}{3t^2}$

$\sf{\dfrac{dx}{dy}=\dfrac{2}{t}}$

It is the required solution!

$\rule{200}2$

Theory :

Parametric Function

if x=f(t) and y =g(t)

Then ,

$\sf{\dfrac{dy}{dx}=\dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}}$

${\underline{\sf{Formula's}}}$

$1)\sf\:\frac{d(x {}^{n} )}{dx} = nx {}^{n - 1}$

$2)\sf\:\frac{d(constant)}{dx} = 0$

$3) \sf\dfrac{d( \tan \: x)}{dx} = \sec{}^{2}\: x$

$\sf4) \dfrac{d(e {}^{x}) }{dx} = {e}^{x}$

Answer 2

Answer:

here's the right ans hope it's useful for all as follows:::