Question

What is the derivative of `sec^2(4x)`?

Answer 1

The final answer is: `(dy)/(dx)=8sec^2(4x)tan(4x)`

Explanation:

This is a composite function consisting of three separate functions, so we use the chain rule, starting with the "outside" function and working to the "inside" function. We must first recall that

`y=sec^2(4x)` is mathematical shorthand for:

`y=(sec(4x))^2`, so the outermost function is `y=u^2`.

Thus we have `(dy)/(dx)=2sec(4x)*sec(4x)tan(4x)*4`, where the second function was `secu` and the final function was `4x`.

We can now simplify this, giving us:

`(dy)/(dx)=8sec^2(4x)tan(4x)`