What is the derivative of-(y^2/((x-y)^2)) ?

The derivative of-(y^2/((x-y)^2)) is -(2y(x\frac{dy)/(dx)-y)}{(x-y)^3}

What is the first derivative of-(y^2/((x-y)^2)) ?

The first derivative of-(y^2/((x-y)^2)) is -(2y(x\frac{dy)/(dx)-y)}{(x-y)^3}

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\frac{d}{d x} (- \frac{y ^{2}}{( x - y ) ^{2}})

- \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{y ^{2}}{( x - y ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{y ^{2}}{( x - y ) ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d x} ( y ^{2} ) ( x - y ) ^{2} - \frac{d}{d x} ( ( x - y ) ^{2} ) y ^{2}}{( ( x - y ) ^{2} ) ^{2}}

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

\frac{d}{d x} ((x - y)^{2}) = 2 (x - y) (1 - \frac{d y}{d x})

= - \frac{2 y \frac{d y}{d x} ( x - y ) ^{2} - 2 ( x - y ) ( 1 - \frac{d y}{d x} ) y ^{2}}{( ( x - y ) ^{2} ) ^{2}}

Cancel

\frac{2 y \frac{d y}{d x} ( x - y ) ^{2} - 2 ( x - y ) ( 1 - \frac{d y}{d x} ) y ^{2}}{( ( x - y ) ^{2} ) ^{2}} : \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

= - \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

2^{x^{2}}

\int \frac{1}{( x ^{2} + 2 ) ^{\frac{3}{2}}} d x

\int \frac{1}{x ^{2} + 8 x + 25} d x

x y^{^{'}} + (1 - x) y = 2 x e^{x}

x \to 4 - lim (\frac{5}{x - 4})

What is the derivative of-(y^2/((x-y)^2)) ?
The derivative of-(y^2/((x-y)^2)) is -(2y(x\frac{dy)/(dx)-y)}{(x-y)^3}
What is the first derivative of-(y^2/((x-y)^2)) ?
The first derivative of-(y^2/((x-y)^2)) is -(2y(x\frac{dy)/(dx)-y)}{(x-y)^3}