What is the derivative of sec2(4x)?

1 Answer

The final answer is: dydx=8sec2(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=sec2(4x) is mathematical shorthand for:

y=(sec(4x))2, so the outermost function is y=u2.

Thus we have dydx=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:

dydx=8sec2(4x)tan(4x)