How do you differentiate: $y = (x^{4}) (e^{x})$ $y=(x^4)(e^x)$ ?

Question

7395 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-21T20:14:37

Use the product rule, together with the fact that $\frac{d}{d x} (e^{x}) = e^{x}$ $d/dx(e^x) = e^x$

I use the product rule in the order: $(fg)' = f'g+fg'$

$y=x^4e^x$

$y' = 4x^3e^x+x^4e^x$

(Yes, I know its hard to tell where I took the derivative of $e^x$ I did it in the second term.)

Here it is again with derivatives in $color(red)"red"$

$y=x^4e^x$

$y' = color(red)(4x^3)e^x+x^4color(red)(e^x)$

Of course we can factor if it seems like a good idea:

$y'=x^3e^x(4+x)$

How do you differentiate: y=(x^4)(e^x)y=(x4)(ex)y=(x^4)(e^x)?