Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SEE EXPERT ANSWER

To see the expert answer you'll need to create a free account at Brainly

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
isn't y=2.92402?
i did this on the calculator: sqrt (625)^(1/2)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

(1/3)**
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 \[\Large 3 y^2 *\frac{ dy }{ dt }\]
so I can't replace the dy/dt by 1 since it's given?
Well yes but i was seeing if you understood the differentiation... don't worry about plugging in numbers till later.
and 3y^2 is already the derivative, why do we need to use the chain rule?
Because you have to multiply by the derivative of y with respect to t.
3y^2 is NOT the derivative of y^3, UNLESS you're just differentiating with respect to y.
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'
It's the same with dy/dx... the derivative of y with respect to x is not just 1... it's 1*dy/dx
ok... :/ it's a little confusing..
agent0smith explained it nicely: \[\frac{ d }{ dy }(y ^{3}) =3y ^{2}\] But \[\frac{ d }{ dt }y ^{3} = \frac{ d }{ dy }y ^{3}\frac{ dy }{ dt } = 3y ^{2}\frac{ dy }{ dt }\]
It's the same thing with the chain rule \[\huge \frac{ d }{ dx } f(x)^n = n*f(x)^{n-1} * f \prime (x)\] you have to always multiply by the derivative at the end.
why can't we plug in the numbers right away if it's given?
You can... you're probably just better off not doing it until you really know what you're doing.
right i understand that... @ranga
well i was taught to plug in.. that's why.
that's the confusing part.
Fair enough... but you can't plug in until you have this step: 3y^2*dy/dt = 50x*dx/dt
exactly what i have right now.
so dy/dt is 1...
in the steps above, why is this: 3(8.55)^3*1 = 50*5*dx/dt?
y=8.55? y is suppose to be 2.92402.
and it's raised to the 3rd, and why not 2?
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
so y=2.92402 is correct?
y^3 = 625 y = cube root 625 = 8.55
how?
i did this in the calculator: sort(625)^(1/3)
sqrt*
And you'll get 8.55... 2.94 cubed is close to 3^3 which is 27. Not 625.
i swear im getting 2.92402
i plugged it in exactly like iwrote it.
sort(625)^(1/3) why are you taking the square root of a cubed root...
y^3 = 625 y = 625^(1/3)
OHHH
i thought the sqrt could do cube root.
if we did the exponent also.
That would mean ((625^(1/3))^(1/2) = 625^(1/6)
thank you! i got it !

Not the answer you are looking for?

Search for more explanations.

Ask your own question