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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Simplify

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

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

y = 2 x^{3} - x^{2} + 9, (2, 21)

\int \frac{1}{x - 4} d x

\frac{\partial}{\partial y} (x^{2} e^{5 x y})

y = - x^{2} - 2 x + 3, y = x^{2} - 1

- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

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