Differentiating exponential functions

[joshmeyer]

For the most part, I understand how it works. This step I don't get at all.

How in the world does that numerator turn into the bottom numerator? I don't understand how the unlike terms are combining.

 

[Dr.Peterson]

For the most part, I understand how it works. This step I don't get at all.
View attachment 31928
How in the world does that numerator turn into the bottom numerator? I don't understand how the unlike terms are combining.

As they say, they factored the numerator.

Both terms, [imath]4x^{16}e^{4x}[/imath] and [imath]16x^{15}e^{4x}[/imath], are multiples of [imath]4x^{15}e^{4x}[/imath], so put that on the outside of a pair of parentheses, and put the extra factors on the inside.

 

[joshmeyer]

As they say, they factored the numerator.

Both terms, [imath]4x^{16}e^{4x}[/imath] and [imath]16x^{15}e^{4x}[/imath], are multiples of [imath]4x^{15}e^{4x}[/imath], so put that on the outside of a pair of parentheses, and put the extra factors on the inside.

and just like that, it clicked. The terms didn't combine at all, they were just factored. Thanks!