Question

x^2+3xy-y^2=11,find dy/dx at (1,2)​

Answer 1

SOLUTION

GIVEN

$\sf{ {x}^{2} + 3xy - {y}^{2} = 11 }$

TO DETERMINE

$\displaystyle \sf{ \frac{dy}{dx} \: \: at \: \: (1 ,2)}$

EVALUATION

Here it is given that

$\sf{ {x}^{2} + 3xy - {y}^{2} = 11 }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ 2x + 3x\frac{dy}{dx} + 3y - 2y\: \frac{dy}{dx} = 0 }$

Putting x = 1 , y = 2 we have

$\displaystyle \sf{ 2.1 + 3.1.\frac{dy}{dx} \bigg| _{(1,2) } + 3.2 - 2.2.\: \frac{dy}{dx} \bigg| _{(1,2) }= 0 }$

$\displaystyle \sf{ \implies \: 2 + 3\frac{dy}{dx} \bigg| _{(1,2) } + 6- 4\: \frac{dy}{dx} \bigg| _{(1,2) }= 0 }$

$\displaystyle \sf{ \implies \: 8 - \frac{dy}{dx} \bigg| _{(1,2) }= 0 }$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} \bigg| _{(1,2) }= 8 }$

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Answer 2

Answer:

Step-by-step explanation: