- #1

tony873004

Science Advisor

Gold Member

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[tex]f(x)=x^2+\frac{4}{x}[/tex]

[tex]

\begin{array}{l}

f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) - f(x)}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{\left( {x + h} \right)^2 + 4\left( {x + h} \right)^{ - 1} - \left( {x^2 + 4x^{ - 1} } \right)}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{x^2 + 2xh + h^2 + 4\left( {x + h} \right)^{ - 1} - x^2 - 4x^{ - 1} }}{h} \\

\end{array}

[/tex]

Here's where I get stuck. I don't know what to do with

[tex]

{\left( {x + h} \right)^{ - 1} }

[/tex]

I forget the algebra for this step. Am I even going in the right direction to bring this term up from the denominator?