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monroe17
 2 years ago
can someone help me step by step?
Find the derivative
3x^(2)+e^(2y)=4y+tan(x)
monroe17
 2 years ago
can someone help me step by step? Find the derivative 3x^(2)+e^(2y)=4y+tan(x)

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calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Have you learned implicit differentiation?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2It's easy! Let me explain it to you in simple terms without getting wordy. If x and y are on the same side of the equal sign, then we say the function is written implicitly, and call it an implicit function. To find the derivative of an implicit function, take the derivative as you normally would but every time you differentiate y, multiply by dy/dx. Then solve for dy/dx. Example: x² + y³ = 5 2x + 3y²(dy/dx) = 0 3y²(dy/dx) = 2x dy/dx = 2x/3y² Understand @monroe17 ?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1I got it :) and when you have both x and y on each side you move the y terms to the left? and x on the right then divide?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Yes you isolate dy/dx and then solve for dy/dx. Good, you got it!

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1for instance with my problem i would subtract 6x from both sides and it ends up on the right side of the equal sign. Then 4 is substracted to the right side.. getting sec^2(x)6x/2e^(2y)4?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1yay, gosh finally.. imma try it for my next problem and see if i get it right.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Sure! I'll be on line for another hour or so, hence if you need anything, let me know.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Welcome! Good Luck!

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1opps. I came to a problem.. ;/ my next question is 5y^2=3x^(2)y+e^(x) i did.. 10y(dy/dx)=6x(dy/dx)+e^(x) dy/dx(10y*y)=6x+e^(x) dy/dx=6x+e^(x)/10y*y and that's wrong.. what was my mistake??

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Woops! When you took the derivative of the right side, it looks like you didn't apply the product rule on the 3x^2y term! :O

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1ohhhh okay let me try that again.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Exactly as @zepdrix said!

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2@monroe17 remember you only multiply by dy/dx when you take the derivative of y, not every time you write y.

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1I got.. 10y(dy/dx)=3x^2+6x*y+e^(x)

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Example: x² + 2xy  4 = 6y 2x + 2y + 2x(dy/dx) = 6(dy/dx) Do you see what I did there?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1how do i know which term goes to which side for this problem.

Eda2012
 2 years ago
Best ResponseYou've already chosen the best response.0\[5y ^{2} = 3x ^{2}y + e ^{x}\] \[10 y \frac{ dy }{ dx} = 3x ^{2 }\frac{ dy }{ dx } + 6xy + e ^{x}\] \[\frac{ dy }{ dx } = \frac{ 6xy + e ^{x} }{ 10y  3x }\]

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2You know the product rule for derivatives, right?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2@Eda2012 I am trying to teach her. I do not appreciate you just posting the solution. How is she supposed to learn to solve problems independently if you just give her the answers?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1the product rule is f(x)g'(x)+g(x)f'(x) right?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Correct! Thus if you have a term of 3x²y for example, then your f = 3x² and g = y. And you multiply by dy/dx iff you differentiate y. Understand?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2If f = 3x² and g = y, then f ' = 6x and g' = dy/dx Do you see?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1so.. 10y(dy/dx)=3x^2(dy/dx)+y(6x)+e^(x) 10y(dy/dx)=3x^(2)+6xy+e^(x)

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1why does 3x^2 go to the left side? I though you make all x to one side and y's the other?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2(fg)' = fg' + gf' (3x²y)' = 3x²(dy/dx) + 6xy Do you see your mistake when you differentiated 3x²y on the right side?

Eda2012
 2 years ago
Best ResponseYou've already chosen the best response.0@calculusfunctions sometimes you have to show some works and then explain it...sorry...

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1oh yeah my bad. I mixed them up.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2@Eda2012 so you show examples and explain the lessons not just give out the answers. I am a teacher so you really don't need to tell me how to do my job!

Eda2012
 2 years ago
Best ResponseYou've already chosen the best response.0@calculusfunctions ok...next time i won't do it again...sorry

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2@monroe17 do you understand now?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1^ calculus it's okay, I ignored it :) why does 3x^2 go to the left side? I though you make all x to one side and y's the other?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Because it is 3x²(dy/dx) and you're isolating dy/dx.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2OK Do you want me to show you step by step?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1let me look at it real quick.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Since @eda2012 already posted the correct solution, go ahead and observe it and then tell me which of her steps confuses you, if any. Alright?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1okay, give me a little time

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.2Sure! Someone else is asking for my help so I'll go and get them started. You call me when you're ready. Take your time.

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1I'm sorry that took forever, I had a lab report to complete. But, I relooked over the problem and it seems to make a little more sense. Thank you so much for your help!
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