What is the tangent of x/y =sin((pixy)/2),(1,1) ?

The tangent of x/y =sin((pixy)/2),(1,1) is y=x

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tangent of x/y =sin((pixy)/2),(1,1)

tangent of

\frac{x}{y} = sin (\frac{π x y}{2}), (1, 1)

y = x

Solution steps

Find the slope of

\frac{x}{y} = sin (\frac{π x y}{2}) : \frac{d y}{d x} = - \frac{π y ^{3} cos ( \frac{π x y}{2} ) - 2 y}{x ( 2 + π y ^{2} cos ( \frac{π x y}{2} ) )}

Compute the slope of

\frac{x}{y} = sin (\frac{π x y}{2})

(1, 1) : m = 1

Find the line with slope m=

1

and passing through

(1, 1) : y = x

y = x

\frac{\partial}{\partial x} (y^{2} + 2 x y - x^{2})

x \to 16 lim (x + 2 x)

y = x \cdot x

y = 4 x - 3 x^{2} (2 - 4)

3 x y^{3} d x - (x + 2) d y = 0

What is the tangent of x/y =sin((pixy)/2),(1,1) ?
The tangent of x/y =sin((pixy)/2),(1,1) is y=x