## anonymous one year ago Using the difference quotient, find f'(x) from 2sqrtx

1. anonymous

I know the answer is $\frac{ 1 }{ \sqrt{x} }$

2. anonymous

But I get only as far as $\frac{ 2x + 2h + 2x}{ 2\sqrt{x} + 2\sqrt{x}}$

3. anonymous

ok so difference quotient: $$\dfrac{f(x+h)-f(x)}{h}$$ I would find what $$f(x+h)$$ is and state what $$f(x)$$ is separately, then just plug it into the formula. $f(x) = 2\sqrt{x}$$f(x+h) = 2\sqrt{x+h}$\begin{align} f'(x)= \dfrac{2\sqrt{x+h}-2\sqrt{x}}{h} \\ &=\frac{2\sqrt{x+h} -2\sqrt{x}}{h} \cdot \frac{2\sqrt{x+h}+2\sqrt{x}}{2\sqrt{x+h}+2\sqrt{x}} \\ &=\frac{4(x+h)-4x}{h(2\sqrt{x+h}+2\sqrt{x})} \\&=\frac{4h}{h(2\sqrt{x+h}+2\sqrt{x})} \\ &=\color{red}{\frac{4}{2\sqrt{x+h}+2\sqrt{x}}} \end{align}

4. anonymous

THANK YOU

5. anonymous

did you follow?

6. anonymous

Yes I messed up I saw my mistake you da bestest!

7. anonymous

Remember that: $$(a-b)(a+b) = a^2-b^2$$

8. anonymous

thanks i follow....:)

9. anonymous

Awesome

10. anonymous

i love u