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For the differentiation of $a\frac{ \cos x}{3}$ , I get $\frac{1}{3}\frac {\sin x}{3}$

But in answer they showed a as well in my textbook.Why is $a$ not differentiated?

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    Welcome to Maths SX! Probably $a$ is a constant. – Bernard Nov 25 '20 at 12:54
  • Check the rules of differentiation. You will see that $D(k\cdot f(x))=kDf(x)$, where $D$ is the differentiation operator (with respect to $x$, in this case). In other words, constants are not differentiated. – Matti P. Nov 25 '20 at 12:56
  • @MattiP. Why have you written constants are not differentiated whereas Mr.Gae S has done it. –  Nov 25 '20 at 13:34
  • Well, what I ultimately mean is that the derivative of a constant is zero, as demonstrated in Gae's post. The effect that this has, is that the constant can be moved in front of the differentiation. – Matti P. Nov 25 '20 at 13:37
  • Ok.I got it now. –  Nov 25 '20 at 13:39

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I presume that it has been differentiated: $$\frac{d}{dx}\left[a\frac{\cos x}3\right]=\frac{\cos x}{3}\frac{d}{dx}[a]+a\frac{d}{dx}\left[\frac{\cos x}{3}\right]=0\cdot \frac{\cos x}{3}+a\cdot\left(-\frac{\sin x}3\right)=-\frac{ a\sin x}{3}$$