Find f'(x)

[Marcia]

f(x) = x^2tan(x^3 + 2x)

f'(x) = 2xtan(x^3 + 2x)
f'(x) = 2xsec^(x^3 + 2x)
f'(x) = 2xsec^2(2x^2 + 2)

Am I close?

 

[Unco]

You have a product.

You are multiplying x^2 by tan(x^3+2x).

The product rule is
(uv)' = u'v + uv'

So let u = x^2

and let v = tan(x^3+2x)

Can you take it from here?

 

[Marcia]

Not sure

so i have

(uv)' = u'v + uv'

2x(tan(x^3 +2x) + x^2(sec^2(x^3 + 2x))

what now? do i have to differentiate the (x^3 + 2x)

 

[tridelta246]

Re: Not sure

so i have

(uv)' = u'v + uv'

2x(tan(x^3 +2x) + x^2(sec^2(x^3 + 2x))

what now? do i have to differentiate the (x^3 + 2x)

YES. The final answer will be:
2x(tan(x^3 +2x) + x^2(sec^2(x^3 + 2x))*{Derivative of (x^3 + 2x)}

..