Using the product rule, find the derivative of the following function:

Question

(x^1/2 cscx sinx).

Answer 1

First off, csc * sin = 1
So, y = √x

However, if you insist on doing it the hard way

y = √x cscx sinx
y' = 1/2√x cscx sinx + √x(cscx sinx)'
= 1/2√x * 1 + √x(-cscx ctnx * sinx + cscx cosx)
= 1/2√x + √x(-ctnx + ctnx)
= 1/2√x

same answer