Answer to Question #313386 in Calculus for justt

Question

Find the derivative of a function using Limit definition of derivative.

y = 4 √x

Answer 1

$f'(x)=lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=4lim_{h \rightarrow 0}\frac{\sqrt{(x+h)}-\sqrt{(x)}}{h}=4\frac{\sqrt{(x+h)}-\sqrt{(x)}}{h}\frac{\sqrt{(x+h)}+\sqrt{(x)}}{{\sqrt{(x+h)}+\sqrt{(x)}}} =4lim_{h \rightarrow 0}\frac{1x+h-x}{h\sqrt{x+h}+\sqrt{x}}=4lim_{h \rightarrow 0}\frac{1}{\sqrt{x+h}+\sqrt{x}}=4lim_{h \rightarrow 0}\frac{1}{\sqrt{x+0}+\sqrt{x}}=\frac{2}{\sqrt{x}}$