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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

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

\int \frac{2 x}{x ^{2} - 1} d x

\int \frac{x ^{2}}{6 - x ^{3}} d x

\frac{d}{d x} (x^{4} - 9 x^{2} + 16)

\frac{2 s - 1}{s ^{2} ( s + 1 ) ^{3}}

\int \frac{ln ( 4 x )}{x} d x

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