Thread: Differentiate the given function y=√2x

1. Differentiate the given function y=√2x

i'm having trouble doing the following problem - Differentiate the given function y=√2x.

can anyone help with this?

2. Re: Differentiate the given function y=√2x

assuming you mean ...

$\displaystyle y = \sqrt{2x} = (2x)^{1/2}$

... now use the chain rule.

3. Re: Differentiate the given function y=√2x

my book gives me the answer dy/dx =√2/2√x

if i used the chain rule then i got something like 1/2 * 2x^-1/2 = 1x^-1/2 = 1/√x... right?

4. Re: Differentiate the given function y=√2x

Originally Posted by arcticreaver
my book gives me the answer dy/dx =√2/2√x
if i used the chain rule then i got something like 1/2 * 2x^-1/2 = 1x^-1/2 = 1/√x... right?
If $\displaystyle y=\sqrt{f(x)}$ then $\displaystyle y^{\prime}=\frac{f^{\prime}(x)}{2\sqrt{f(x)}}$.

5. Re: Differentiate the given function y=√2x

$\displaystyle y = \sqrt{2x} = (2x)^{1/2}$

$\displaystyle \frac{dy}{dx} = \frac{1}{2} (2x)^{-1/2} \cdot 2 = \frac{1}{\sqrt{2x}}$