Question

calculate y=(e^(4x))/x for y" and y"'

Answer 1

Ok, so what's the first derivative, y' ?

Answer 2

4e^x/1

Answer 3

Use the quotient rule, write y = u/v
where u = e^4x, v = x
Then
\[ y' = \frac{vu' - uv'}{v^2} \]

Answer 4

ok yeah I knew that. crap. I did that the first time, but it didnt come out right.
I had 4e^x *x - e^4x *1 / x^2

Answer 5

or 4ex-4ex/2x

Answer 6

Careful. It is
\[ y' = \frac{x.4e^{4x} - e^{4x}}{x^2} \]
\[ = \frac{4e^{4x}}{x} - \frac{e^{4x}}{x^2} \]

Now differentiate that again to find y''

Answer 7

so I differentiate before I use the quotient rule?

Answer 8

The quotient rule is a means of differentiating the quotient of two functions. Your question doesn't make sense.

Answer 9

well a lot about calculus doesnt make sense to me and my teacher stinks

Answer 10

I recommend you go back in your class notes or text book and review it. You're going to need to use it quite a lot with this question.

Answer 11

e^4x is just e^4x right?

Answer 12

The derivative of \( f(x) = e^{ax} \) for any constant \( a \) is
\[ \frac{df}{dx} = a e^{ax} \]

Answer 13

because the derivative of e^x is e^x

Answer 14

Yes.

Answer 15

so e^4x is just e^4x, right?