Question

How do you take the derivative of `tan^10 5x`?

Answer 1

Consider the regular derivative of `tanu`.

`d/(dx)[tanu] = sec^2u*((du)/(dx))`

Since `u(x) = 5x` and we have a power function:

`d/(dx)[(tanu)^n] = n(tanu)^(n-1)*sec^2u*((du)/(dx))`

`d/(dx)[(tan(5x))^(10)] = 10(tan(5x))^9*sec^2(5x)*5`

`= 50tan^9(5x)sec^2(5x)`