## anonymous one year ago 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.

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1. anonymous

I meant definition of a derivative not function.

2. perl

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