Question

The differentiable functions xxx and yyy are related by the following equation: \sin(y)=-xsin(y)=−5x sin, (, x, ), equals, minus, 5, x Also, \dfrac{dy}{dt}=10 dt dy ​ =10start fraction, d, y, divided by, d, t, end fraction, equals, 10. Find \dfrac{dx}{dt} dt dx ​ start fraction, d, x, divided by, d, t, end fraction when y=-\piy=−πy, equals, minus, pi.

Answer 1

Answer: Khan Academy says -1.4

Explanation:

Answer 2

`(dx)/(dt)=2`

Explanation:

We are given that

`siny=-5x`

`(dy)/(dt)=10`

We have to find the value of
`(dx)/(dt)` when
`y=-\pi`

Differentiate w.r.t time

`cosy(dy)/(dt)=-5(dx)/(dt)`

Using formula:
`(d(sinx))/(dx)=cosx`

Substitute the values then we get

`cos(-\pi)* 10=-5(dx)/(dt)`

We know that
`cos(-x)=cosx, cos(\pi)=-1`

Therefore, we get

`cos(\pi)* 10=-5(dx)/(dt)`

`(dx)/(dt)=(10cos\pi)/(-5)`

`(dx)/(dt)=(10(-1))/(-5)=2`

Hence,
`(dx)/(dt)=2`