Question

What is the derivative of `tan^3 (3x-1)`?

Answer 1

`9tan^2(3x-1)sec^2(3x-1)`

Explanation:

differentiate using the`color(blue)(" chain rule")`

`d/dx[f(g(x))] = f'(g(x)).g'(x)`

and `d/dx(tanx) = sec^2x`

`d/dx(tan^3(3x-1)) = 3tan^2(3x-1) d/dx(tan(3x-1) d/dx(3x-1))`

`= 3tan^2(3x-1).sec^2(3x-1).3 = 9tan^2(3x-1)sec^2(3x-1)`