Question

if y=xy+x^2+1 then when x=-1, dy/dx is?

Answer 1

-1/2 is the right answer

Answer 2

The function dy/dx when x is 1 is (y-1)/2

Given the function $y=xy+x^2+1$

To get the differential of the function, we need to differentiate the function implicitly to have;

$y'=xy'+y+2x+0\\y'-xy'=y+2x\\y'(1-x)=y+2x$

Divide both sides by 1 - x to have;

$\frac{y'(1-x)}{1-x} =\frac{y+2x}{1-x} \\y'=\frac{y+2x}{1-x}$

If x = -1

$y'=\frac{y+2(-1)}{1-(-1)}\\y'=\frac{y-1}{2}$

Hence the function dy/dx when x is 1 is (y-1)/2

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