Question

find derivative for y = (x^5)(e^(6x^2))...
i find this to be awkward

Answer 1

\[\large y=x^5e^{6x^2}\]
By the product rule, you have
\[\large y'=\color{red}{(x^5)'e^{6x^2}}+\color{blue}{x^5\left(e^{6x^2}\right)'}\]
For the first term, you'd just use power rule. For the second, you'd use chain rule:
\[\large(x^5)'e^{6x^2}=\color{red}{5x^4e^{6x^2}}\\
\large x^5\left(e^{6x^2}\right)'=x^5\cdot6(2x)\left(e^{6x^2}\right)=\color{blue}{12x^6e^{6x^2}}\]

Answer 2

it's a multiple choice question and that's not one of them...

Answer 3

The red and blue terms have a common factor of \(\large x^4e^{6x^2}\). Factor that out first.

Answer 4

You'll find that it's the same as the second answer.

Answer 5

oh

Answer 6

snoogins, tank you

Answer 7

You're welcome!