A community for students.
Here's the question you clicked on:
 0 viewing
mathcalculus
 2 years ago
can someone explain to me Implicit Differentiation:
if y^3 = 25x^2, determine dx/dt when x = 5 and dy/dt = 1
mathcalculus
 2 years ago
can someone explain to me Implicit Differentiation: if y^3 = 25x^2, determine dx/dt when x = 5 and dy/dt = 1

This Question is Closed

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0these are the steps but i don't understand them :/ 3y^2*dy/dt = 50x*dx/dt When x = 5, y^3 = 25*5^2 y^3 = 625 y = cube root 625 = 8.55 3(8.55)^3*1 = 50*5*dx/dt 1875 = 250dx/dt 7.5 = dx/dt

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i did this on the calculator: sqrt (625)^(1/2)

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3Let's start with this part... \[\Large \frac{ d }{ dt } y^3\]use the chain rule to differentiate it... so bring down the exponent, reduce the exponent by one, then multiply by the derivative of y w. respect to t \[\Large 3 y^2 *\frac{ dy }{ dt }\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so I can't replace the dy/dt by 1 since it's given?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3Well yes but i was seeing if you understood the differentiation... don't worry about plugging in numbers till later.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and 3y^2 is already the derivative, why do we need to use the chain rule?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3Because you have to multiply by the derivative of y with respect to t.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.33y^2 is NOT the derivative of y^3, UNLESS you're just differentiating with respect to y.

tpmys
 2 years ago
Best ResponseYou've already chosen the best response.1normally we have y dependent on x here y, and x both are dependent on some t, so we dont know what the function is so instead of y^3 >>> 3y^2 we have the chain rule y^3 >>> 3y^2 * y'

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3It's the same with dy/dx... the derivative of y with respect to x is not just 1... it's 1*dy/dx

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ok... :/ it's a little confusing..

ranga
 2 years ago
Best ResponseYou've already chosen the best response.0agent0smith explained it nicely: \[\frac{ d }{ dy }(y ^{3}) =3y ^{2}\] But \[\frac{ d }{ dt }y ^{3} = \frac{ d }{ dy }y ^{3}\frac{ dy }{ dt } = 3y ^{2}\frac{ dy }{ dt }\]

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3It's the same thing with the chain rule \[\huge \frac{ d }{ dx } f(x)^n = n*f(x)^{n1} * f \prime (x)\] you have to always multiply by the derivative at the end.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0why can't we plug in the numbers right away if it's given?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3You can... you're probably just better off not doing it until you really know what you're doing.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0right i understand that... @ranga

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0well i was taught to plug in.. that's why.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0that's the confusing part.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3Fair enough... but you can't plug in until you have this step: 3y^2*dy/dt = 50x*dx/dt

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0exactly what i have right now.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0in the steps above, why is this: 3(8.55)^3*1 = 50*5*dx/dt?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0y=8.55? y is suppose to be 2.92402.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and it's raised to the 3rd, and why not 2?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3When x = 5, y^3 = 25*5^2 y^3 = 625 y = cube root 625 = 8.55 i think the next line after that is a mistake and it should by to the power of 2

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so y=2.92402 is correct?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3y^3 = 625 y = cube root 625 = 8.55

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i did this in the calculator: sort(625)^(1/3)

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3And you'll get 8.55... 2.94 cubed is close to 3^3 which is 27. Not 625.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i swear im getting 2.92402

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i plugged it in exactly like iwrote it.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3sort(625)^(1/3) why are you taking the square root of a cubed root...

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3y^3 = 625 y = 625^(1/3)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i thought the sqrt could do cube root.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0if we did the exponent also.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.3That would mean ((625^(1/3))^(1/2) = 625^(1/6)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thank you! i got it !
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.