Derivative of f(x)= x+sqrt(x) - Domain & Derivative

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Homework Statement



Find the derivative of the function using the definition of derivative. state the domain of the function and the derivative.

f(x)= x +sqrt(x)

The Attempt at a Solution



lim f(x)= [x+h+sqrt(x+h) -x -sqrt(x)]/h
h-->0

limf(x)=[h + sqrt(x+h) - sqrt(x)]/h
h->0

not sure how to proceed?
 
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Separate out the h/h term and rationalize the numerator in what is left.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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