What is derivative of x(x+i)+y(y-i)+i=13 ?

The answer to derivative of x(x+i)+y(y-i)+i=13 is (dy)/(dx)=(1-4xy)/(1+4y^2)+i(-2x-2y)/(1+4y^2)

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derivative of x(x+i)+y(y-i)+i=13

derivative of

x (x + i) + y (y - i) + i = 13

\frac{d y}{d x} = \frac{1 - 4 x y}{1 + 4 y ^{2}} + i \frac{- 2 x - 2 y}{1 + 4 y ^{2}}

Solution steps

x (x + i) + y (y - i) + i = 13

Treat

y

y (x)

Differentiate both sides:

(2 x + 2 y \frac{d y}{d x}) + i (1 - \frac{d y}{d x}) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - 4 x y}{1 + 4 y ^{2}} + i \frac{- 2 x - 2 y}{1 + 4 y ^{2}}

\frac{d y}{d x} = \frac{1 - 4 x y}{1 + 4 y ^{2}} + i \frac{- 2 x - 2 y}{1 + 4 y ^{2}}

x^{2} = 2 + t

y^{2} = 4 a (x + a)

x = \frac{( 1 + t ) ^{3}}{t ^{2}}

y^{2} = 2 x

x^{2} y^{2} = 1

What is derivative of x(x+i)+y(y-i)+i=13 ?
The answer to derivative of x(x+i)+y(y-i)+i=13 is (dy)/(dx)=(1-4xy)/(1+4y^2)+i(-2x-2y)/(1+4y^2)