Solution assignment 26 Product and Quotient rule

Differentiate:

$y=e^{3x}$

We can write this function as:

$y=e^{2x}e^x$

and can apply the product rule twice. However, then we need to differentiate the function $e^{2x}$ .

We have:

$e^{2x}=e^x\cdot{e^x}$

and thus, by applying the product rule, we get:

$[e^{2x}]'=e^x\cdot{e^x}+e^x\cdot{e^x}=2e^x$

Applying the product rule again, we get:

$y'=2e^{2x}e^x+e^{2x}e^x=3e^{3x}$

If you are familiar with the chain rule you can get this result much easier and faster.