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How do you use implicit differentiation to find dy/dx given #x^2+4y^2=7+3xy#?

Answer 1

Emily Ammerman

#dy/dx=(3y-2x)/(8y-3x)#

#x^2+4y^2=7+3xy# #rArr2x+8y(dy/dx)=0+3(y+x(dy/dx))# #rArr2x+8y(dy/dx)=3y+3x(dy/dx)#

#rArr8ydy/dx-3x(dy/dx)=3y-2x#

#rArrdy/dx(8y-3x)=3y-2x#

#rArrdy/dx=(3y-2x)/(8y-3x)#

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Answer 2

Ezra Adams

To use implicit differentiation to find ( \frac{dy}{dx} ) given ( x^2 + 4y^2 = 7 + 3xy ), follow these steps:

Differentiate both sides of the equation with respect to (x).
For terms involving (y), apply the chain rule by differentiating (y) with respect to (x), i.e., ( \frac{dy}{dx} ).
Solve the resulting equation for ( \frac{dy}{dx} ).

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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.