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

The derivative of (-2x-y)/(x+2y) is -(3y)/((x+2y)^2)

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

The first derivative of (-2x-y)/(x+2y) is -(3y)/((x+2y)^2)

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derivative of

\frac{- 2 x - y}{x + 2 y}

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d ^{4}}{d x ^{4}} (sin (x^{2}))

\int (x - \frac{1}{x})^{2} \cdot x d x

\int \frac{sinh ( x )}{cosh ( x )} d x

\frac{d}{d x} (e^{c o s h (8 x)})

\frac{d}{d y} (4 y)

What is the derivative of (-2x-y)/(x+2y) ?
The derivative of (-2x-y)/(x+2y) is -(3y)/((x+2y)^2)
What is the first derivative of (-2x-y)/(x+2y) ?
The first derivative of (-2x-y)/(x+2y) is -(3y)/((x+2y)^2)