Question

If x = e^ty^2 , t= V cos v , y= v sin v. Find dx/dv at v= 3.142/2

Answer 1

$$x=e^ty^2$$

$$x(v)=e^{v\cos(v)}v^2\sin^2(v)$$

$$dx/dv=e^{v\cos(v)}(\cos(v)-v\sin(v))$$

$$+e^{v\cos(v)}(2v\sin(v)+2v^2\sin(v)\cos(v))$$

$v=\pi/2$

$$dx/dv|_{v=\pi/2}=e^{0}(0-\pi/2)$$

$$+e^{0}(2(\pi/2)(1)+2(\pi/2)^2(1)(0)) =-\pi/2+\pi=\pi/2$$