- #1

karush

Gold Member

MHB

- 3,269

- 5

If If $y=x \sin x,$ then $\dfrac{dy}{dx}=$

(A) $\sin x + \cos x$

(B) $\sin x + x \cos x$

(C) $\sin x + \cos x$

(D) $x(\sin x + \cos x)$

(E) $x(\sin x - \cos x)$

Solution

Apply the Product Rule $$(f\cdot g)'=f\:'\cdot g+f\cdot g'$$

then

$$y'=x'\sin x+(\sin x)' x$$

simplify

$$y'=\sin x+x\cos x \quad (B)$$

ok this is a relatively simple problem but was wondering if $y'$ should be used in combination with $\dfrac{dy}{dx}=$

also any other typos ,, suggestion,, etc