# Thread: Slope of tangent line

1. ## Slope of tangent line

I have to find the derivative of this problem but I can't figure the algebra out. I can't use the power rule either. I have to use the (f(x+h)-f(x))/h rule.

1/x^(1/2)

2. Originally Posted by TenaciousE
I have to find the derivative of this problem but I can't figure the algebra out. I can't use the power rule either. I have to use the (f(x+h)-f(x))/h rule.

1/x^(1/2)
$\displaystyle\lim_{h\to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}$

3. @dwsmith I have that much figured out. I'm having trouble simplifying it to find the equation for the slope of the tangent line

4. $\displaystyle \frac{1}{h}\left(\sqrt{x+h}-\sqrt{x}\right)$

$\displaystyle \frac{1}{h}\left(\sqrt{x+h}-\sqrt{x}\times \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\ri ght)$

Have a go from here...

5. Originally Posted by TenaciousE
@dwsmith I have that much figured out. I'm having trouble simplifying it to find the equation for the slope of the tangent line
$\displaystyle\lim_{h\to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}=\lim_{x\to 0}\frac{\frac{\sqrt{x}-\sqrt{x+h}}{\sqrt{x}\sqrt{x+h}}}{h}=\lim_{x\to 0}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x}\sqrt{x+h}}$

Multiple by the conjugate.

6. Got it figured out now. Thanks!