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How do you use implicit differentiation to find #(dy)/(dx)# given #2x^3=2y^2+5#?

Answer 1

Aurora Alvarado

Differentiate both sides f the equation with respect to #x#:

#d/dx(2x^3) = d/dx(2y^2+5)#

#6x^2 = 4ydy/dx#

#dy/dx = (3x^2)/(2y)#

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Answer 2

Axel Alvarez

To find (\frac{dy}{dx}) using implicit differentiation for the equation (2x^3 = 2y^2 + 5), follow these steps:

Differentiate both sides of the equation with respect to (x).
Apply the chain rule when differentiating terms involving (y).
Solve for (\frac{dy}{dx}) after differentiation.

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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.