What is the derivative of #sqrt(2x) #?

1 Answer
Jan 29, 2016

Answer:

#1/sqrt(2x)#

Explanation:

The function can be rewritten as

#(2x)^(1/2)#

To differentiate this, use the power rule and chain rule.

#d/dx[(2x)^(1/2)]=1/2(2x)^(-1/2)d/dx[2x]#

Differentiating with the power rule gives the #1/2(2x)^(-1/2)# part, and through the chain rule you must multiply this by the derivative of the internal function, which is #2x#.

This gives:

#d/dx[(2x)^(1/2)]=1/2(2x)^(-1/2)(2)#

The #2#s will cancel.

#d/dx[(2x)^(1/2)]=(2x)^(-1/2)=1/(2x)^(1/2)=1/sqrt(2x)#