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

The derivative of (2x-y/(x+2y)) is (-5x\frac{dy)/(dx)+5y}{(x+2y)^2}

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

The first derivative of (2x-y/(x+2y)) is (-5x\frac{dy)/(dx)+5y}{(x+2y)^2}

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

\frac{- 5 x \frac{d y}{d x} + 5 y}{( x + 2 y ) ^{2}}

Solution steps

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

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 y}{d x}

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

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

Expand

(2 - \frac{d y}{d x}) (x + 2 y) - (1 + 2 \frac{d y}{d x}) (2 x - y) : - 5 x \frac{d y}{d x} + 5 y

= \frac{- 5 x \frac{d y}{d x} + 5 y}{( x + 2 y ) ^{2}}

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

f (x) = x^{3} + 2 x, at x = 0

\frac{\partial}{\partial x} (8 x y + 2 x^{4} + 2 y^{4})

\frac{d}{d x} (sin^{n - 2} (x))

\frac{\partial}{\partial x} (\frac{- cos ( x )}{x})

What is the derivative of (2x-y/(x+2y)) ?
The derivative of (2x-y/(x+2y)) is (-5x\frac{dy)/(dx)+5y}{(x+2y)^2}
What is the first derivative of (2x-y/(x+2y)) ?
The first derivative of (2x-y/(x+2y)) is (-5x\frac{dy)/(dx)+5y}{(x+2y)^2}