Question

What is the derivative of `f(x)=secx^2cos^2x`?

Answer 1

`2 cdot sec^2 x^2 cdot (cos^2x cdot sin x^2 cdot x - cos x cdot sin x cdot cos x^2)`

Explanation:

I understood `y = (sec x^2) (cos^2 x)`. Is it?

`(df)/(dx) = d/(dx) (frac{cos^2 x}{cosx^2}) = frac{d/(dx) (cos^2x) cdot cos x^2 - cos^2x cdot d/(dx) (cos x^2)}{cos^2 x^2}`

`= frac{2 cos x cdot d/(dx) (cos x) cdot cos x^2 - cos^2x cdot (-sin x^2) d/(dx) (x^2)}{cos^2 x^2}`

`= frac{2 cos x cdot (-sin x) cdot cos x^2 - cos^2x cdot (-sin x^2) cdot 2x}{cos^2 x^2}`

`= 2 cdot sec^2 x^2 cdot ( - cos x cdot sin x cdot cos x^2 + cos^2x cdot sin x^2 cdot x)`