Differentiate.
-$\frac { \sin x } { x }$
A) cos x
B) $\frac { \cos x } { x }$
C) $\frac { 1 } { x }$ cos x - $\frac { 1 } { x ^ { 2 } }$ sin x
D) none of these

Question

Quizplus · Accepted Answer

To differentiate $\frac{\sin x}{x}$, we use the quotient rule: $\frac{d}{dx}\left(\frac{f}{g}\right) = \frac{f'g - fg'}{g^2}$. Here, $f = \sin x$ and $g = x$, so $f' = \cos x$ and $g' = 1$. Substituting these into the quotient rule gives $\frac{\cos x \cdot x - \sin x \cdot 1}{x^2}$, which simplifies to $\frac{x \cos x - \sin x}{x^2}$ or $\frac{1}{x}\cos x - \frac{1}{x^2}\sin x$.

Differentiate sin⁡xx\frac { \sin x } { x }xsinx​ A) Cos X B)

Differentiate $\frac { \sin x } { x }$ A) Cos X
B)