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

1 Answer
Aug 6, 2014

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)