Question

what is the derivative to ((3x^2)(e^2x-1))/((2x^2)(-3x) +1)). If you can explain how you got the answer it would be super helpful. Thanks

Answer 1

First you have the use the quotient rule. At the same time you need to use the multiplication rule also.

Answer 2

Product Rule I meant.

Answer 3

\[y=\frac{3x^2(e^{2x}-1)}{2x^2(-3x+1)}\]?

Answer 4

So the quotient rule, how I remember it is Low-Di-High minus Hi-Di-Low
all over Low*Low.

Answer 5

if you want to you could find the derivative using log implicit differentiation,

Answer 6

or actually you could cancel those x^2's out first

Answer 7

that would make the quotient rule prettier

Answer 8

But I'm not totally sure what I'm seeing exactly

Answer 9

\(\bf \large {
\cfrac{d}{dx}\left[\cfrac{(3x^2)(e^{2x-1})}{(2x^2)(-3x)}+1\right]? \ or \
\cfrac{d}{dx}\left[\cfrac{(3x^2)(e^{2x-1})}{(2x^2)(-3x+1)}\right]?
}\)

Answer 10

you could use the whiteboard, or post a picture btw

Answer 11

\[\frac{ 3x ^{2}(e ^{2x-1})}{ (2x ^{2})(-3x+1)}\] Thanks

Answer 12

Cancel by x^2 before doing the derivative

Answer 13

\[
\frac{3 x^2 e^{2 x-1}}{2 x^2 (1-3
x)}=\frac{3 e^{2 x-1}}{2 (1-3 x)}
\]
Now use the quotient rule of the RHS

Answer 14

Use this to check your answer
\[
\frac {d}{dx} \frac{3 e^{2 x-1}}{2 (1-3
x)}=-\frac{3 e^{2 x-1} (6
x-5)}{2 (3 x-1)^2}
\]

Answer 15

Thank you!