What is the derivative of y=sec^3(x)y=sec3(x)?

1 Answer
Aug 6, 2014

sec xsecx is equal to 1/cosx1cosx.

Thus, sec^3 xsec3x is an equivalent statement to 1/(cosx)^31(cosx)3.

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

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

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

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

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

= (3sinx)/(cos^4 x) =3sinxcos4x