Advertisement Remove all ads

If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and  hence, find dy/dx if x=a cost, y=a sint - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and  hence, find dy/dx if x=a cost, y=a sint

Advertisement Remove all ads

Solution

Given x=f(t),y=g(t) are differentiable function of parameter 't'

x=acost and y=asint

find dy/dx=?

x=acost

differentiate x w.r.t 't'

`dx/dt=d/dt(acost)`

`dx/dt=asint................(1)`

`y=asint`

`dy/dt=d/dt (asint)`

`dy/dt=-acost.............(2)`

dividing equation 2 by 1

`(dy/dt)/(dx/dt)=(-acost)/(asint)=-cost/sint......(3)`

`now " "x=acost`

`therefore cost=x/a`

`y=asint`

`therefore sintt=y/a`

from equation 3

`dy/dx=-(x/a)/(y/a)=-x/y`

 

 

Concept: Derivatives of Functions in Parametric Forms
  Is there an error in this question or solution?

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×