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Derivative of One Function w.r.t Another

if tan-1(x2-y...

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if tan-1(x2-y2/x2+y2) = a, show that dy/dx= x(1- tan a)/y(1+ tan a)

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{cos}^{- 1} (\frac{x^{2} - y^{2}}{x^{2} + y^{2}}) = {tan}^{- 1} (a)

, then show that

\frac{d y}{d x} = \frac{y}{x} .

$t a n^{- 1} (x^{2} + y^{2}) = a$

Evaluate $\frac{d y}{d x}$

{tan}^{- 1} (x^{2} + y^{2}) = α,

\frac{d y}{d x}

u = {tan}^{- 1} (\frac{x^{2} + y^{2}}{x + y})

x \frac{d u}{d x} + y \frac{d u}{d y} =

y = (t a n^{- 1} x)^{2}

{(x^{2} + 1)}^{2} y_{2} + 2 x (x^{2} + 1) y_{1} = 2

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Derivative of One Function w.r.t Another

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