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mathcalculus
Group Title
can someone explain to me Implicit Differentiation:
if y^3 = 25x^2, determine dx/dt when x = 5 and dy/dt = 1
 one year ago
 one year ago
mathcalculus Group Title
can someone explain to me Implicit Differentiation: if y^3 = 25x^2, determine dx/dt when x = 5 and dy/dt = 1
 one year ago
 one year ago

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mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
these 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
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
isn't y=2.92402?
 one year ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
(1/3)**
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@satellite73
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
Let'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 \[\Large 3 y^2 *\frac{ dy }{ dt }\]
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so I can't replace the dy/dt by 1 since it's given?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@agent0smith
 one year ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@agent0smith
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
Because you have to multiply by the derivative of y with respect to t.
 one year ago

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

tpmys Group TitleBest ResponseYou've already chosen the best response.1
normally 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'
 one year ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
ok... :/ it's a little confusing..
 one year ago

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

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
It'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.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
why can't we plug in the numbers right away if it's given?
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
You can... you're probably just better off not doing it until you really know what you're doing.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
right i understand that... @ranga
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
well i was taught to plug in.. that's why.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
that's the confusing part.
 one year ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
exactly what i have right now.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so dy/dt is 1...
 one year ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
y=8.55? y is suppose to be 2.92402.
 one year ago

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

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
When 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
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so y=2.92402 is correct?
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
y^3 = 625 y = cube root 625 = 8.55
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i did this in the calculator: sort(625)^(1/3)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
sqrt*
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
And you'll get 8.55... 2.94 cubed is close to 3^3 which is 27. Not 625.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i swear im getting 2.92402
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i plugged it in exactly like iwrote it.
 one year ago

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

agent0smith Group TitleBest ResponseYou've already chosen the best response.3
y^3 = 625 y = 625^(1/3)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i thought the sqrt could do cube root.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
if we did the exponent also.
 one year ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
thank you! i got it !
 one year ago
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