Answer:
[tex]\frac{dx}{dt}=2[/tex]
Step-by-step explanation:
We are given that
[tex]siny=-5x[/tex]
[tex]\frac{dy}{dt}=10[/tex]
We have to find the value of [tex]\frac{dx}{dt}[/tex] when [tex]y=-\pi[/tex]
Differentiate w.r.t time
[tex]cosy\frac{dy}{dt}=-5\frac{dx}{dt}[/tex]
Using formula:[tex]\frac{d(sinx)}{dx}=cosx[/tex]
Substitute the values then we get
[tex]cos(-\pi)\times 10=-5\frac{dx}{dt}[/tex]
We know that [tex]cos(-x)=cosx, cos(\pi)=-1[/tex]
Therefore, we get
[tex]cos(\pi)\times 10=-5\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt}=\frac{10cos\pi}{-5}[/tex]
[tex]\frac{dx}{dt}=\frac{10(-1)}{-5}=2[/tex]
Hence, [tex]\frac{dx}{dt}=2[/tex]
