Question

How do you find the derivative of `f(x)= (5x^2 tan(x))/sec(x)`?

Answer 1

`f'(x)=5x^2cos(x)+10xsin(x)`

Explanation:

Rewrite `tan(x)` as `sin(x)/cos(x)` and `1/sec(x)` as `cosx`. As you can see, both the cos(x) cancel out leaving you with a simpler function to solve for.

`f(x)=5x^2sin(x)`

From here, use the product rule. Note that the derivative of `sinx` is `cosx`:

`f'(x)=5x^2cos(x)+sin(x)(10x)`

Simplify:

`f'(x)=5x^2cos(x)+10xsin(x)`