Differentiation question using 'tan'

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

find f ' (x)?

thx for your help?

The derivative of tan x is (sec x)^2 dx.

In this problem the x variable is 2*x^2.

The first step is (sec( 2*x^2))^2 dx.

BUT we are not done. The derivative of the inside is 4x dx. and we replace this with the first answer making:

4x*(sec( 2*x^2))^2 dx

.

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

f ' (x) = sec^2(2x^2)*(4x) = 4x sec^2(2x^2)