# How do you find the derivative of sqrt(7x)?

Oct 26, 2016

Change $\sqrt{7 x}$ to ${\left(7 x\right)}^{\frac{1}{2}}$ and use the power rule, which gets you $\sqrt{7} \cdot \frac{1}{2} {\left(x\right)}^{- \frac{1}{2}}$.

#### Explanation:

First, you should change $\sqrt{7 x}$ to ${\left(7 x\right)}^{\frac{1}{2}}$ through the property of fractional exponents. Distribute the $\frac{1}{2}$ power to both the 7 and the x, which will get you $\sqrt{7} \cdot {\left(x\right)}^{\frac{1}{2}}$.

Temporarily ignore the $\sqrt{7}$, as by the constant multiple rule, you can simply multiply the $\sqrt{7}$ by the rest of the derivative after the other calculations.

Then, you can use the power rule to find the derivative of ${\left(x\right)}^{\frac{1}{2}}$. Drop the $\frac{1}{2}$ in front and decreasing the exponent by 1. So you get $\frac{1}{2} {\left(x\right)}^{- \frac{1}{2}}$.

Finally, multiply the $\sqrt{7}$ by the part you just obtained, which results in $\sqrt{7} \cdot \frac{1}{2} {\left(x\right)}^{- \frac{1}{2}}$.