Question

if f(x)=x cos x, find f"(x), or $\frac{d^{2}y}{d{x}^2}$

• A. - xsinx + cosx
• B. - xcosx - 2sinx
• C. xsinx - cosx
• D. none of these

Answer 1

The correct option is B

- xcosx - 2sinx

Using the Product Rule, we have f'(x)=x$\frac{d}{dx}$(cos x)+cos x$\frac{d}{dx}$(x)=-xsinx+cosx
To find f"(x) we differentiate f'(x):
f"(x)=$\frac{d}{dx}$(-x sin x+cos x)=-x$\frac{d}{dx}$(sin x)+sin x $\frac{d}{dx}$(-x)+$\frac{d}{dx}$(cos x)
=-x cos x-sin x-sin x = -x cos x-2 sin x