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How do you use implicit differentiation to find dy/dx given #x^2+y^2+3x-4y=9#?

Answer 1

Cameron Alexander

#dy/dx= -(2x+3)/(2y-4)#

#x^2+y^2+3x-4y=9#

Using implicit differentiation: #2x+2ydy/dx+3-4dy/dx=0#

#(2y-4)dy/dx=-2x-3#

#dy/dx= -(2x+3)/(2y-4)#

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Answer 2

Ezekiel Alexander

To find ( \frac{dy}{dx} ) using implicit differentiation with the equation ( x^2 + y^2 + 3x - 4y = 9 ), follow these steps:

Differentiate both sides of the equation with respect to ( x ).
Apply the chain rule whenever you differentiate terms that involve ( y ).
After differentiation, solve the resulting equation for ( \frac{dy}{dx} ).

The process involves several steps of calculus, including the chain rule and implicit differentiation techniques. Once you've differentiated both sides, isolate ( \frac{dy}{dx} ) to find the derivative.

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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.