Question

What is the derivative of ln(x^3 • sin x ^2)?

Answer 1

`dy/dx=3/x+2xcos(x^2)1/(sin(x^2))`

Explanation:

We want to find the derivative of

`y=ln(x^3sin(x^2))`

Using the properties of logarithms

`y=ln(x^3)+ln(sin(x^2))`

`color(white)(y)=3ln(x)+ln(sin(x^2))`

By the chain rule

`dy/dx=3/x+(d/dx(sin(x^2)))1/(sin(x^2))`

`color(white)(dy/dx)=3/x+2xcos(x^2)1/(sin(x^2))`

`color(white)(dy/dx)=3/x+2xcot(x^2)`