Question

can someone help me step by step?
Find the derivative

3x^(2)+e^(2y)=4y+tan(x)

Answer 1

solve for dx right?

Answer 2

dy/dx

Answer 3

Have you learned implicit differentiation?

Answer 4

I'm not good at it.

Answer 5

It'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 ?

Answer 6

I 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?

Answer 7

Yes you isolate dy/dx and then solve for dy/dx. Good, you got it!

Answer 8

for 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?

Answer 9

Excellent!!

Answer 10

yay, gosh finally.. imma try it for my next problem and see if i get it right.

Answer 11

Sure! I'll be on line for another hour or so, hence if you need anything, let me know.

Answer 12

thanks!

Answer 13

Welcome! Good Luck!

Answer 14

opps. 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??

Answer 15

Woops! 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

Answer 16

ohhhh okay let me try that again.

Answer 17

Exactly as @zepdrix said!

Answer 18

@monroe17 remember you only multiply by dy/dx when you take the derivative of y, not every time you write y.

Answer 19

oh i don't ?

Answer 20

I got..
10y(dy/dx)=3x^2+6x*y+e^(x)

Answer 21

Example:

x² + 2xy - 4 = 6y

2x + 2y + 2x(dy/dx) = 6(dy/dx)


Do you see what I did there?

Answer 22

how do i know which term goes to which side for this problem.

Answer 23

\[5y ^{2} = 3x ^{2}y + e ^{x}\]
\[10 y \frac{ dy }{ dx} = 3x ^{2 }\frac{ dy }{ dx } + 6xy + e ^{x}\]
\[\frac{ dy }{ dx } = \frac{ 6xy + e ^{x} }{ 10y - 3x }\]

Answer 24

You know the product rule for derivatives, right?

Answer 25

@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?

Answer 26

^thank you! lol

Answer 27

the product rule is f(x)g'(x)+g(x)f'(x) right?

Answer 28

Correct! 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?

Answer 29

If f = 3x² and g = y, then
f ' = 6x and g' = dy/dx

Do you see?

Answer 30

so.. 10y(dy/dx)=3x^2(dy/dx)+y(6x)+e^(x)
10y(dy/dx)=3x^(2)+6xy+e^(x)

Answer 31

why does 3x^2 go to the left side? I though you make all x to one side and y's the other?

Answer 32

(fg)' = fg' + gf'

(3x²y)' = 3x²(dy/dx) + 6xy

Do you see your mistake when you differentiated 3x²y on the right side?

Answer 33

@calculusfunctions sometimes you have to show some works and then explain it...sorry...

Answer 34

oh yeah my bad. I mixed them up.

Answer 35

@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!

Answer 36

@calculusfunctions ok...next time i won't do it again...sorry

Answer 37

@monroe17 do you understand now?

Answer 38

^ 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?

Answer 39

Because it is 3x²(dy/dx) and you're isolating dy/dx.

Answer 40

... im confused

Answer 41

OK Do you want me to show you step by step?

Answer 42

let me look at it real quick.

Answer 43

Since @eda2012 already posted the correct solution, go ahead and observe it and then tell me which of her steps confuses you, if any. Alright?

Answer 44

okay, give me a little time

Answer 45

Sure! 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.

Answer 46

I'm sorry that took forever, I had a lab report to complete. But, I re-looked over the problem and it seems to make a little more sense. Thank you so much for your help!