Question

Differentiate Cos^-2(x)

Answer 1

Use the Chain Rule for inner function \(g(x)=\cos x\) and outer function \(f(x)=\frac{1}{x^2}\). \[f(g(x)) = \left(\cos x\right)^{-2}\]

Answer 2

i thought u use the inverse rule

Answer 3

I'm not familiar with any inverse rule?

Answer 4

Presumably you are differentiating with respect to x? I hate to be picky, but you should get use to specifying that. Later on (higher math courses and/or more involved problems) it won't be so obvious.

y =( cosx)^-2

dy/dx = -2[(cosx)^-3] (cosx)'
dy/dx = -2[cosx)^-3] (-sinx)
dy/dx = 2 [(cosx)^-3] sinx
dy/dx = 2 sinx (secx)^3