What is the derivative of y=sec3(x)?

1 Answer
Aug 6, 2014

secx is equal to 1cosx.

Thus, sec3x is an equivalent statement to 1(cosx)3.

And, we know that this is equivalent to (cosx)3.

So, all we need to do is use the power rule, keeping in mind to use the chain rule on cosx:

dydx=3(cosx)4ddx[cosx]

=3(cosx)4(sinx)

=3sinx(cosx)4

=3sinxcos4x