Question

How do you find the derivative of `y=e^(2x^3)`?

Answer 1

`(dy)/(dx)=6x^2e^(2x^3)`

Explanation:

Use the chain rule: `(dy)/(dx)=(dy)/(du)*(du)/(dx)`

`y=e^(2x^3),` let `u=2x^3`

`(dy)/(du)=e^u=e^(2x^3), (du)/(dx)=6x^2`

So `(dy)/(dx)=e^(2x^3)*6x^2=6x^2e^(2x^3)`