implicit differentiation1.if y^2=× 2.if ×^2+3×y+2y^2=3,find dy/dx at point (-1,2)

2022-02-09 Answered

implicit differentiation1.if y^2=×

2.if ×^2+3×y+2y^2=3,find dy/dx at point (-1,2)

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Answers (1)

Vasquez
Answered 2022-03-13 Author has 460 answers

x2+3xy+2y2=3

Differentiate both sides of the equation.

ddx(x2+3xy+2y2)=ddx3

Differentiate the left side of the equation.

3xy+4yy+2x+3y

Since 3 is constant with respect to x, the derivative of 3 with respect to x is 0.

Reform the equation by setting the left side equal to the right side.

3xy+4yy+2x+3y=0

Solve for y

y=2x+3y3x+4y

Replace y with dydx

dydx=2x+3y3x+4y

Put (1,2), where x=1, y=2

dydx=2(1)+3(2)3(1)+4(2)

dydx=45

 

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