How do you determine the derivative of x cos x?
Answer:
Find the first derivative and then differentiate again.
\(\frac{d y}{d x}=1(\cos x)+x(-\sin x)\)
Differentiate again.
\(\frac{d^{2} y}{d x^{2}}=-\sin x-(1(\sin x)+x(\cos x))\)
\(\frac{d^{2} y}{d x^{2}}=-\sin x-\sin x-x \cos x\)
\(\frac{d^{2} y}{d x^{2}}=-2 \sin x-x \cos x\)
Hopefully this helps!