# What is the derivative of y=xln(x)+7x?

$\frac{d}{\mathrm{dx}} \left(x \setminus \ln \left(x\right) + 7 x\right) = \frac{d}{\mathrm{dx}} x \setminus \ln \left(x\right) + \frac{d}{\mathrm{dx}} 7 x$
The easy part is calculating that $\frac{d}{\mathrm{dx}} 7 x = 7 \frac{d}{\mathrm{dx}} x$: for the power rule $\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$, applied with $n = 1$, one has that $\frac{d}{\mathrm{dx}} x = 1$, and so $\frac{d}{\mathrm{dx}} 7 x = 7$.
As for $x \setminus \ln \left(x\right)$, we apply the product rule, which says that $\left(f g\right) ' = f ' g + f g '$. In your case, $f \left(x\right) = x$ and $g \left(x\right) = \setminus \ln \left(x\right)$. We have that $f ' \left(x\right) = 1$ and $g ' \left(x\right) = \frac{1}{x}$. So, $\frac{d}{\mathrm{dx}} x \setminus \ln \left(x\right) = 1 \setminus \cdot \setminus \ln \left(x\right) + x \setminus \cdot \frac{1}{x}$
$\frac{d}{\mathrm{dx}} \left(x \setminus \ln \left(x\right) + 7 x\right) = \setminus \ln \left(x\right) + 1 + 7 = \setminus \ln \left(x\right) + 8$