Question

How do you differentiate `f(x)=(t^3)(tan6t)`?

Answer 1

If it's the correct question, `0` since differentiating constants give you `0`. If the question is `f(t)=(t^3)(tan 6t)`, then by using the chain rule, you should get `f'(t)=(3t^2)(tan 6t)[1 +(2t sec^2 6t)]`.

Explanation:

`f(t)=(t^3)(tan 6t)`
`f'(t)=(3t^2)(tan 6t) +(t^3)(6 tan 6t sec^2 6t)`
`f'(t)=(3t^2)(tan 6t) +(3t^2 tan 6t)(2t sec^2 6t)`
`f'(t)=(3t^2)(tan 6t)[1 +(2t sec^2 6t)]`