What is the derivative of sqrt(2x) ?

1 Answer
Jan 29, 2016

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 2s will cancel.

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