Question

Find a general formula for f (n)(x) if f(x) = 4xe−x

Answer 1

what does \(f_n(x)\) mean in this context? you looking for the power series?

Answer 2

I'm looking for the nth derivative of the equation

Answer 3

so \[f^n(x)\]

Answer 4

\(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles
\[\begin{align*}
f(x)&=4xe^{-x}\\
&=-4e^{-x}(0-x)\\
f'(x)&=4e^{-x}-4xe^{-x}\\
&=4e^{-x}(1-x)\\
f''(x)&=-4e^{-x}(1-x)-4e^{-x}\\
&=-4e^{-x}(1-x+1)\\
&=-4e^{-x}(2-x)\\
f'''(x)&=4e^{-x}(2-x)+4e^{-x}\\
&=4e^{-x}(2-x+1)\\
&=4e^{-x}(3-x)\\
&\vdots\\
\end{align*}\]
See a pattern?