Question

What is the derivative of `y=ln(x^4sin^2x)`?

Answer 1

`dy/dx=4/x+2cotx.`

Explanation:

We first simplify `y` using the Rules of Log.

`y=ln(x^4*sin^2x)=lnx^4+lnsin^2x=4lnx+2lnsinx`

`:. dy/dx=(4lnx)'+(2lnsinx)'`

`=4*1/x+2*1/sinx*(sinx)'`.................[Chain Rule]
`=4/x+2/sinx*cosx`

`:. dy/dx=4/x+2cotx.`