Question

What is dy/dx (derivative) if `y=(3 + x^2)^15`?

Answer 1

`(dy)/(dx)=30x(3+x^2)^14`

Solution

You'll need the power rule: `d/(dx)(x^n) = n x^(n-1)`
and the chain rule.
(This combination is sometimes called the generalized power rule.)

`d/(dx)[(g(x))^n]=n(g(x))^(n-1)*g'(x)`

or `d/(dx)(u^n) = n u^(n-1) (du)/(dx)`

`d/(dx)((3+x^2)^15)=15(3+x^2)^14*2x=30x(3+x^2)^14`