Question

Find the derivative of the function at the given number
G(x)= 1+2sqr(x) at 4
I used the definition of a function for this problem and
I'm stuck here: 1+2sqr(4+h)-1+2sqr(4) all over h. I have that fraction and now I am unsure of my next step. Any help will be extremely appreciated.

Answer 1

I meant definition of a derivative not function.

Answer 2

$$ \Large {G(x)= 1+2\sqrt{x}
\\~\\G~'(4) = \lim_{h\to 0} \frac{G(4+h)-G(4)}{h}
\\~\\=\lim_{h\to 0} \frac{1 + 2\sqrt{4+h} - (1 + 2\sqrt{4}~)}{h}
\\~\\=\lim_{h\to 0} \frac{1 + 2\sqrt{4+h} - 1 - 2\sqrt{4}}{h}
\\~\\=\lim_{h\to 0} \frac{ 2\sqrt{4+h} - 2\cdot 2 }{h}
\\~\\=\lim_{h\to 0} \frac{ 2 ( \sqrt{4+h} - 2) }{h}

}$$
now multiply by the conjugate