Question

Find the derivative of the given function:

Answer 1

\[y=\frac{ (2x)^{2} }{ e ^{2x} }\]

Answer 2

Use quotient rule.

Answer 3

quotient property or quotient rule?

Answer 4

Err, Idr. The quotient rule for derivatives:
\[\frac{dy}{dx}[\frac{f(x)}{g(x)}] = \frac{g(x)*f'(x) - f(x)*g'(x)}{(g(x))^2}\]

Answer 5

ehh, i'll let u know. thanks

Answer 6

The bottom times the derivative of the top minus the top times the derivative of bottom. All over the bottom squared.
It's catchy.

Answer 7

its going to be hard with e^2x

Answer 8

I am currently on logarithms

Answer 9

I remember this formula; in the beggining of the year

Answer 10

I have a feeling it doesn't apply. :|

Answer 11

\[\frac{d}{dx} [e^{u}] = e^{u}*\frac{du}{dx}\]

Answer 12

Chain rule on exponential function with 'e' is simple.

Answer 13

@iPwnBunnies Help me with a hint?

Answer 14

I've never performed this before

Answer 15

Let's find the first term in the quotient rule: g(x)*f'(x)

Answer 16

(e^2x)(4x)

Answer 17

Try again. The numerator simplifies to 4x^2.

Answer 18

the derivative of 2x^2 simpliesfied to 4x

Answer 19

(2x)^2 = 4x^2

Answer 20

okay. i got that

Answer 21

What's the first term now? lol

Answer 22

(e^2x)(4x^2)

Answer 23

No. That's what the numerator in the original function simplifies to.

Answer 24

wait.

Answer 25

8x^3e+8xe^2x

Answer 26

did you expect me to find the derivative of e^2x

Answer 27

Whoa, let's go back to our simplifed original function.
\[y = \frac{4x^{2}}{e^{2x}}\]

Answer 28

lol

Answer 29

kinda lost

Answer 30

Ahh crap. Didn't realize this was gonna take this long. I'll show you the derivative of e^2x.

Answer 31

e=10?

Answer 32

In e^(2x), let u = 2x, and du = 2 dx
\[\frac{d}{dx}[e^{u}] = e^{u}*\frac{du}{dx}\]

Answer 33

As you can see, you keep the e^(2x), then multiply it by the derivative of its power.
The derivative of e^(2x) = e^(2x) * 2 = 2e^(2x)

Answer 34

what about dx?

Answer 35

It's in the du/dx

Answer 36

du = 2 dx, du/dx = 2

Answer 37

okay... i see

Answer 38

Now, if you follow the quotient rule for derivatives, you should be good. Sorry man. G2g.

Answer 39

thanks a lot