Alright, I need some calculus help. ?

Question

Here's the problem.

If e^sin y = x, then find dy/dx

Answer 1

The first answerer's result is actually dx/dy.

To find dy/dx, must first solve for y in terms of x:

e^sin y = x

ln(e^sin y) = ln(x)

sin(y) = ln(x)

y = arcsin[ln(x)]

Now use the differentiation chain rule:

dy/dx = [ 1 / sqrt( 1 - (ln(x))^2 ) ] * 1/x

= 1 / [ x * sqrt( 1 - (ln(x))^2 ) ].

{ The derivative of arcsin(u) should be in the reference pages of your text. }

Answer 2

chain rule it:

e^sin(y)*cos(y)

but I haven't done calc in a while, so this may not be correct... I'm pretty sure though