3 unit maths q (identity derivatives) (1 Viewer)

[VenomP]

Hey all.

I'm a bit stuck with this maths question at the moment...

From the derivative of sin x and cos x deduce the derivative of sec x.

The answer is apparantly sin x sec^2 x.

I'm really at a loss as to how to approach this. Any help is appreciated.

 

[independantz]

y=secx=(cosx)^-1

dy/dx=-1(cosx)^-2(-sinx), by the chain rule.
=sinx.(cosx)^-2
=sinx.sec^2x

 

[VenomP]

Many thanks :]

There's just one more I can't get:

cosecx

And the answer is -cos x cosec^2 x

 

[namburger]

The derivative of 1/u = -u'/u^2
1/sin = - (cos x)/(sin x)^2
= -cos x cosec^2 x