Question

Find the derivative of $(x^2 + 1)\, cos\, x$.

• A. $2x\, cos \,x - (x^2 + 1) sin \,x$
• B. $2x \,sin\, x - x^2 \,cos\, x$
• C. $x^{2}\left(cos\,x-sin\,x\right)$
• D. $2x(sin\, x + cos\, x)$

Answer 1

Answer: (A)

$2x\, cos \,x - (x^2 + 1) sin \,x$

Answer 2

Let $f(x) = (x^2 + 1) cos\, x$ $\therefore f'\left(x\right)=\left(x^{2}+1\right)'cos\,x+\left(cos\,x\right)'\left(x^{2}+1\right)$ $= \left(2x + 0\right)cos \,x + \left(-sin\, x\right)\left(x^{2} + 1\right)$ $=2x\,cos\,x-\left(x^{2}+1\right)sin\, x$