Question

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

Answer 1

Change `sqrt(7x)` to `(7x)^(1/2)` and use the power rule, which gets you `sqrt(7)*1/2(x)^(-1/2)`.

Explanation:

First, you should change `sqrt(7x)` to `(7x)^(1/2)` through the property of fractional exponents. Distribute the `1/2` power to both the 7 and the x, which will get you `sqrt(7)*(x)^(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 `(x)^(1/2)`. Drop the `1/2` in front and decreasing the exponent by 1. So you get `1/2(x)^(-1/2)`.

Finally, multiply the `sqrt(7)` by the part you just obtained, which results in `sqrt(7)*1/2(x)^(-1/2)`.