Find the 1st derivative using "the long way" method. Show all the algebra.(adsbygoogle = window.adsbygoogle || []).push({});

[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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find the 1st derivative

**Physics Forums | Science Articles, Homework Help, Discussion**