Q:

Differentiating $7x$

I have the question "Differentiate with respect to $x, 7x$."
I use the rule $nx^{n-1}$ with n being the power. 
So using this rule I got since the power is $1$, 
$1-1 = 0 $  and so  $7x^0$ should be $1$ because anything to the power $0$ is $1$.
But the solutions say that the answer should be $7$ why is this ? 

A:

To apply the power rule here, you must recognize that
$$\frac d{dx}7x=7\left(\frac d{dx}x\right)$$
And that
$$\frac d{dx}x=1\times x^0=1$$
So that our original derivative is
$$\frac d{dx}7x=7\times1=7$$

