Derivative of y = x+sqrt(x) using definition of derivative.

**sdh2106** · September 1st 2010, 02:13 PM

Can someone help me find the derivative of f(x)=x+sqrt(x) using f'(x)=lim--> 0 [f(x+h)-f(h)/h]?

Thanks!

**pickslides** · September 1st 2010, 02:24 PM

$\displaystyle\lim_{x\to 0} \frac{f(x+h)-f(x)}{h}= \lim_{x\to 0} \frac{((x+h)+\sqrt{x+h})-(x+\sqrt{x})}{h}$

What next?

**sdh2106** · September 1st 2010, 02:29 PM

i got it from here (after some algebra and conjugate multiplication). i was reading the definition of the derivative wrong... its should have been -f(x) not -f(h). Thanks for the help!

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