Question

Differentiate with respect to x : y =x^2cosx.

cos^2x−sinx
x(xsinx-cosx)
sinxcosx
x(2cosx-xsinx)

Answer 1

Answer on Question #47039 – Math – Differential Calculus | Equations

Differentiate with respect to $x : y = x^2 \cos x$.

$$\cos^2 x - \sin x$$ $$x (x \sin x - \cos x)$$ $$\sin x \cos x$$ $$x (2 \cos x - x \sin x)$$

Solution.

$$y = x^2 \cos x.$$

Use product rule

$$y' = (x^2)' \cos x + (\cos x)' x^2 = 2x \cos x - x^2 \sin x = x(2 \cos x - x \sin x).$$

www.AssignmentExpert.com