How do you implicitly differentiate $15 = \frac{x^{2}}{y} + y^{2}$ $15=x^2/y+y^2$ ?

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Answer 1 · 2018-03-18T15:36:27

$\frac{d y}{d x} = \frac{2 x}{15 - 3 y^{2}}$ $dy/dx=[2x]/[15-3y^2]$

$15 = \frac{x^{2}}{y} + y^{2}$ $15=x^2/y +y^2$ , Multiply both sides by $y$ $y$

$15 y = x^{2} + y^{3}$ $15y=x^2+y^3$ and so differentiating implicitly with respect to $x$ $x$

$15 \frac{d y}{d x} = 2 x + 3 y^{2} \frac{d y}{d x}$ $15dy/dx=2x+3y^2dy/dx$

$15 \frac{d y}{d x} - 3 y^{2} \frac{d y}{d x} = 2 x$ $15dy/dx-3y^2dy/dx=2x$

$\frac{d y}{d x} [15 - 3 y^{2}] = 2 x$ $dy/dx[15-3y^2]=2x$

$\frac{d y}{d x} = \frac{2 x}{15 - 3 y^{2}}$ $dy/dx=[2x]/[15-3y^2]$ .

How do you implicitly differentiate 15=x^2/y+y^215=x2y+y215=x^2/y+y^2?