find equation of tangent to curve y = 1/root x at (1, 1)

[wind]

Find the equation of the tangent to the curve at the given point:

y = 1/root x at (1,1)

[f(a + h) - f(a)] / h

f(1 + h) - (1)

(1/root 1 + h) / h

(1/root 1 + h)((root 1 + h)/(root 1 + h)) / h

(root 1 + h / 1 + h )(1 / h)

(root 1 + h / h(1 + h)

But at this point, I can't plug in zero for h. Can someone pleas help me? Thank you!

 

[pka]

\(\displaystyle \L\begin{array}{rcl}
F(x) = \frac{1}{{\sqrt x }} \\
\frac{{F(x + h) - F(x)}}{h} & = & \frac{{\frac{1}{{\sqrt {x + h} }} - \frac{1}{{\sqrt x }}}}{h} \\
& = & \frac{{\sqrt x - \sqrt {\left( {x + h} \right)} }}{{h\sqrt {\left( x \right)\left( {x + h} \right)} }} \\
& = & \frac{{\sqrt x - \sqrt {\left( {x + h} \right)} }}{{h\sqrt {\left( x \right)\left( {x + h} \right)} }}\frac{{\sqrt x + \sqrt {\left( {x + h} \right)} }}{{\sqrt x + \sqrt {\left( {x + h} \right)} }} \\
& = & \frac{{ - h}}{{h\sqrt {\left( x \right)\left( {x + h} \right)} \left( {\sqrt x + \sqrt {\left( {x + h} \right)} } \right)}} \\
\end{array}\)