Question

What is the derivative of `y=sec^3(x)`?

Answer 1

`sec x` is equal to `1/cosx`.

Thus, `sec^3 x` is an equivalent statement to `1/(cosx)^3`.

And, we know that this is equivalent to `(cos x)^(-3)`.

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

`dy/dx = -3*(cos x)^(-4) * d/dx[cos x]`

`= -3*(cos x)^(-4) * (-sinx)`

`= 3sinx(cos x)^(-4)`

`= (3sinx)/(cos^4 x)`