Find the derivative: f(x)=tan(x^(2) +5)

Question

Find the derivative:
f(x)=tan
`(x^(2) +5)`

Answer 1

`2x \sec^2 (x^2 + 5)`

Explanation:

`f(x) = \tan (x^2 + 5)`

`(d)/(dx) \tan u = \sec^2 u (d)/(dx) u`

`(d)/(dx) \tan (x^2 + 5) = \sec^2 (x^2 + 5) (d)/(dx) (x^2 + 5)`

`(d)/(dx) \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x`

`(d)/(dx) \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5)`