Question

Find the derivative.
y=3e^(-3/t)

Answer 1

Let \(u = -3/t\).

Answer 2

\[
y = 3e^{u}
\]

Answer 3

\[
\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}
\]

Answer 4

Can you find these two derivatives?

Answer 5

there is no u substitutions when finding the derivative

Answer 6

What is \(dy/du\)?

Answer 7

integrals

Answer 8

I am not doing an integral.

Answer 9

\[
y = 3e^u
\]What is the derivative?

Answer 10

Im not sure with that u

Answer 11

Well, I want \(dy/du\) so you are differentiating with respect to \(u\). It is an easy one.

Answer 12

Ok, can you walk me through this?

Answer 13

Okay. Well \[
y=3e^{u}\implies \frac{dy}{du}=3e^u
\]Does this make sense?

Answer 14

so u=-3t^-1?

Answer 15

Yes, just go with me for a moment. \[
u = -\frac{3}{t}
\]

Answer 16

We need to find \(du/dt\) now.

Answer 17

du=3t^-2

Answer 18

Ok, so now we say: \[
\frac{dy}{dt} = \frac{dy}{du}\frac{du}{dt} = 3e^u\frac{3}{t^2}
\]Now, we can change \(u\) back into terms of \(t\): \[
\frac{dy}{dt}=3e^{-3/t}\frac{3}{t^2}
\]

Answer 19

Does this make sense?

Answer 20

@Bosse15 Trust wio, he's just doing the Chain Rule, it just looks a little different than what you're probably used to.

Answer 21

yes it does

Answer 22

Help?

Answer 23

\[\int\limits_{?}^{?}xe ^{^{^{-3x ^{2}}}}dx\]

Answer 24

Help with what?

Answer 25

This time let \(u = -3x^2\)

Answer 26

\[
du = d(-3x^2) =(-3x^2)'dx = -6xdx
\]

Answer 27

ok, then du=-6xdx

Answer 28

-1/6 e^-3x^2+C?

Answer 29

\[
\int e^{u}xdx
\]We can do this: \[
=\frac{-6}{-6}\int e^{u}xdx = -\frac{1}{6}\int e^{u}(-6x)dx
\]

Answer 30

Then it becomes: \[
-\frac{1}{6}\int e^u\;du
\]

Answer 31

Oh, your answer is correct.

Answer 32

Cool! lol thanks, could you stay on here just to make sure i can finish the rest of these up?

Answer 33

\[\int\limits_{}^{}\frac{ e ^{\frac{ 1 }{ x }} }{ x ^{2} }\]

Answer 34

dx\

Answer 35

try using wolfram alpha

Answer 36

never heard of that

Answer 37

www.wolframalpha.com It's really helpful for checking the answers to calculus problems.

Answer 38

\[\int\limits_{}^{}\frac{ e ^{2x} }{ e ^{2x}+1 }dx\]

Answer 39

@wio

Answer 40

Wait I'm overcomplicating this. This is really quite a simple u-subsitution problem.

e^2x+1=u