What is the derivative of-y/(x+4y) ?

The derivative of-y/(x+4y) is -x/((x+4y)^2)

What is the first derivative of-y/(x+4y) ?

The first derivative of-y/(x+4y) is -x/((x+4y)^2)

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derivative of

- \frac{y}{x + 4 y}

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

Solution steps

\frac{d}{d y} (- \frac{y}{x + 4 y})

Treat

x

as a constant

Take the constant out:

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

= - \frac{d}{d y} (\frac{y}{x + 4 y})

Apply the Quotient Rule:

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

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

\frac{d y}{d y} = 1

\frac{d}{d y} (x + 4 y) = 4

= - \frac{1 \cdot ( x + 4 y ) - 4 y}{( x + 4 y ) ^{2}}

Simplify

= - \frac{x}{( x + 4 y ) ^{2}}

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

x^{2} - 19, 18 x

\frac{\partial}{\partial x} (1 + x \cdot ln (x y - 5))

y^{^{'}} + x^{2} y = x^{2}

3 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

What is the derivative of-y/(x+4y) ?
The derivative of-y/(x+4y) is -x/((x+4y)^2)
What is the first derivative of-y/(x+4y) ?
The first derivative of-y/(x+4y) is -x/((x+4y)^2)