How do you differentiate y = x^(-sin(x) )y=xsin(x)?

1 Answer
Jul 8, 2016

Using the fact that

d/dx[u^v]=u^v * [(u'v+uv'ln(u))/(u)]

We let

u = x and v = -sin(x)

So

y' = x^(-sin(x)) * [(-sin(x) - xcos(x) ln(x))/(x)]

Explanation:

The formula we've used is

d/dx[u^v]=u^v * [(u'v+uv'ln(u))/(u)]