How do you find #(dy)/(dx)# given #3y^3+2=2x#?

Answer 1

#dy/dt=2/(9y^2)# or #dy/dt=2/(9(((2/3)x-(2/3))^(1/3))^2)#

Use implicit differentiation

#9y^2(dy/dx)=2#
Solve for #dy/dt#
#dy/dt=2/(9y^2)#

If you want, we can solve and plug in for y using the given equation and simplifying:

#3y^3+2=2x#
#3y^3=2x-2#
#y^3=(2/3)x-(2/3)#
#y=((2/3)x-(2/3))^(1/3)#

Now plug this in for y and simplify.

#dy/dt=2/(9(((2/3)x-(2/3))^(1/3))^2)#
#dy/dt=2/(9(((2/3)x-(2/3))^(2/3)))#
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Answer 2

To find (dy)/(dx) given the equation 3y^3 + 2 = 2x:

  1. Differentiate both sides of the equation with respect to x.
  2. Use implicit differentiation.
  3. Solve for (dy)/(dx).

The result is: (dy)/(dx) = (2/3)/(y^2)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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