Question

$$f ( x ) = \sqrt { x + 2 } , f ^ { \prime } ( 2 ) = \cdots$$

Answer

h=(Le*f*x)/(2*e*n*f'*sqrt(x+2))

Solution


Cancel \(t\) on both sides.
\[Lefx=\sqrt{x+2}henf'\times 2\]
Regroup terms.
\[Lefx=2ehnf'\sqrt{x+2}\]
Divide both sides by \(2\).
\[\frac{Lefx}{2}=ehnf'\sqrt{x+2}\]
Divide both sides by \(e\).
\[\frac{\frac{Lefx}{2}}{e}=hnf'\sqrt{x+2}\]
Simplify  \(\frac{\frac{Lefx}{2}}{e}\)  to  \(\frac{Lefx}{2e}\).
\[\frac{Lefx}{2e}=hnf'\sqrt{x+2}\]
Divide both sides by \(n\).
\[\frac{\frac{Lefx}{2e}}{n}=hf'\sqrt{x+2}\]
Simplify  \(\frac{\frac{Lefx}{2e}}{n}\)  to  \(\frac{Lefx}{2en}\).
\[\frac{Lefx}{2en}=hf'\sqrt{x+2}\]
Divide both sides by \(f'\).
\[\frac{\frac{Lefx}{2en}}{f'}=h\sqrt{x+2}\]
Simplify  \(\frac{\frac{Lefx}{2en}}{f'}\)  to  \(\frac{Lefx}{2enf'}\).
\[\frac{Lefx}{2enf'}=h\sqrt{x+2}\]
Divide both sides by \(\sqrt{x+2}\).
\[\frac{\frac{Lefx}{2enf'}}{\sqrt{x+2}}=h\]
Simplify  \(\frac{\frac{Lefx}{2enf'}}{\sqrt{x+2}}\)  to  \(\frac{Lefx}{2enf'\sqrt{x+2}}\).
\[\frac{Lefx}{2enf'\sqrt{x+2}}=h\]
Switch sides.
\[h=\frac{Lefx}{2enf'\sqrt{x+2}}\]