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Would I use the chain rule in the following derivative problem: $$(sinx/x)$$ So far I have simplified it to: sin(x)(-1x^(-2))+x^(-1)(cosx)

Would I have to further take the derivative of cosx

Basically I do not quite understand when to use the chain rule.

Hello
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  • The Chain Rule is used for composition of functions. Say you wanted to differentiate $f(x)=(x-1)^2.$ Note that this is a composition of functions $f(x)=g(x)\circ h(x)$, where $g(x)=x-1$ and $h(x)=x^2$. Then the chain rule states that the derivative of $f(x)$ is $2(x-1)(x-1)'=2(x-1)=2x-2$. – Sujaan Kunalan Sep 28 '14 at 16:59

2 Answers2

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$$\frac{d(\sin x/x)}{dx}=\frac1x\cdot\frac{d(\sin x)}{dx}+\sin x\cdot\frac{d(x^{-1})}{dx}$$

$$=\frac{\cos x}x+\sin x\cdot(-1)x^{-1-1}$$

and we are done

lab bhattacharjee
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Quotient rule works here too:\begin{align} \frac d{dx} \frac{\sin x}x&=\frac{\frac d{dx}(\sin x)\cdot x-\sin x \frac d{dx}(x)}{x^2} \\ &= \frac{x\cos x-\sin x}{x^2} \end{align}

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