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

The derivative of (x^2/(sqrt(x-2y))) is (3x^2+2x^2\frac{dy)/(dx)-8xy}{2(x-2y)sqrt(x-2y)}

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

The first derivative of (x^2/(sqrt(x-2y))) is (3x^2+2x^2\frac{dy)/(dx)-8xy}{2(x-2y)sqrt(x-2y)}

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

\frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x x - 2 y - \frac{1 - 2 \frac{d y}{d x}}{2 x - 2 y} x ^{2}}{( x - 2 y ) ^{2}} : \frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

= \frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

\frac{6 x ^{2} + 8 x + 4}{x}

\int (a + b x)^{2} d x

f (t) = 2 t^{3}

\frac{d y}{d x} = - (2 x + ln (y)) \cdot \frac{y}{x}

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

What is the derivative of (x^2/(sqrt(x-2y))) ?
The derivative of (x^2/(sqrt(x-2y))) is (3x^2+2x^2\frac{dy)/(dx)-8xy}{2(x-2y)sqrt(x-2y)}
What is the first derivative of (x^2/(sqrt(x-2y))) ?
The first derivative of (x^2/(sqrt(x-2y))) is (3x^2+2x^2\frac{dy)/(dx)-8xy}{2(x-2y)sqrt(x-2y)}