Implicit differentiaion using the number e (lon-capa)

[Nana-chan]

Implicit differentiaion using the number "e" (lon-capa)

Hello~ :3 this is my first time posting here, so I hope I didn't do anything wrong. I'm currently in Calculus 1, university level, and I have to enter all my answers using lon-capa (evil evil program). In lon-capa:

*= multiplication sign
exp= number e (exponents are instead put in parenthesis, as in my answer below)

Homework Statement

Find dy/dx if the curve is defined by

10 x^2 e^(7 y) + 8 y^4 e^(5 x) = 19.

The Attempt at a Solution

This is my lon-capa attempt:
(10*x^2*7*exp(7*y)+20*x*exp(7*y)+8*y^4*5*exp(5*x))/(-32*y^3*exp(5*x))

This is a more reasonable-looking version:
(10x^2*7e(7y)+20x*e(7y)+8y^4*5e(5x))/(-32y^3*e(5x))

I used both the product rule and implicit differentiation, but lon-capa keeps telling me my answer is wrong. I'm not sure if it's a mistake with the parenthesis or the answer itself, but I'd be grateful for any help/advice.

 

[SammyS]

Hello~ :3 this is my first time posting here, so I hope I didn't do anything wrong. I'm currently in Calculus 1, university level, and I have to enter all my answers using lon-capa (evil evil program). In lon-capa:

*= multiplication sign
exp= number e (exponents are instead put in parenthesis, as in my answer below)

Homework Statement

Find dx/dy if the curve is defined by

10 x^2 e^(7 y) + 8 y^4 e^(5 x) = 19.

The Attempt at a Solution

This is my lon-capa attempt:
(10*x^2*7*exp(7*y)+20*x*exp(7*y)+8*y^4*5*exp(5*x))/(-32*y^3*exp(5*x))

This is a more reasonable-looking version:
(10x^2*7e(7y)+20x*e(7y)+8y^4*5e(5x))/(-32y^3*e(5x))

I used both the product rule and implicit differentiation, but lon-capa keeps telling me my answer is wrong. I'm not sure if it's a mistake with the parenthesis or the answer itself, but I'd be grateful for any help/advice.

Hello Nana-chan. Welcome to PF !

Show how you did the problem, not just your final result.

What do you get when implicitly differentiated the following?

10 x² e^7y + 8 y⁴ e^5x = 19​

Did you take the derivative with respect to x or with respect to y?

Did they really ask for dx/dy ?

 

[Nana-chan]

Thanks, here's what I did:

10 x2 e7y + 8 y4 e5x = 19

I did the product rule on both sides:

10x^2*e(7y)*7 + 20x*e(7y) + 8y^4*e(5x)*5 + 32y^3*dy/dx*e(5x)= 0

Then I moved the value that contained dy/dx to the other side:

10x^2*e(7y)*7 + 20x*e(7y) + 8y^4*e(5x)*5 = 32y^3*dy/dx*e(5x) = (32y^3*e(5x))(dy/dx)

Then I divided both sides by (32y^3*e(5x)) in order to get dy/dx and got the answer that you saw above.

And no, I'm sorry, they didn't ask for dx/dy, they asked for dy/dx, I made a typo in my original post, which I will now proceed to edit.

 

[SammyS]

Thanks, here's what I did:

10 x² e^7y + 8 y⁴ e^5x = 19

I did the product rule on both sides:

10x^2*e(7y)*7*dy/dx + 20x*e(7y) + 8y^4*e(5x)*5 + 32y^3*dy/dx*e(5x)= 0

Then I moved the value that contained dy/dx to the other side:

10x^2*e(7y)*7 + 20x*e(7y) + 8y^4*e(5x)*5 = 32y^3*dy/dx*e(5x) = (32y^3*e(5x))(dy/dx)

Then I divided both sides by (32y^3*e(5x)) in order to get dy/dx and got the answer that you saw above.

And no, I'm sorry, they didn't ask for dx/dy, they asked for dy/dx, I made a typo in my original post, which I will now proceed to edit.

(To write superscripts or subscripts, use the "Go Advanced" option for the message window. Then use the X² or X₂ ikon above the message box.)

You are missing a dydx . See it in red above .

 

[Nana-chan]

Ohhh~ you see I wasn't sure if the derivative of 7y would be 7 alone or what you stated above. I entered it in on lon-capa and my answer is now correct! Thank you very much!