Help with Differentiation question ?

Question

Hi,

I would like to find out the answer to this question.

I want to

know the derivative f '(x) when

f(x) = tan( 5 x^2 )

Thanks for any help received. It is very much appreciated.

Answer 1

is it f(x)=tan(5 x^2)

well if it's the question

to get the derivative this in a form tan(u) where in u will get the derivative of tan which is sec^2 then just copy the u which is 5x^2 multiplied by the derivative of u which is 10x.

and you'll get

10xsec^2(5x^2)=F'(x)

Answer 2

recall...

the derivative of tan u  = sec² u du

so...

y = tan (5x²)

u = 5x², du = 10x

y' = sec² (5x²) (10x)

or

y' = 10x sec² (5x²)