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

1 Answer
Oct 26, 2016

Answer:

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)#.