What is (\partial)/(\partial x)((xy)/(x+7)) ?

The answer to (\partial)/(\partial x)((xy)/(x+7)) is (7y)/((x+7)^2)

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(\partial)/(\partial x)((xy)/(x+7))

\frac{\partial}{\partial x} (\frac{x y}{x + 7})

\frac{7 y}{( x + 7 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x y}{x + 7})

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (\frac{x}{x + 7})

Apply the Quotient Rule:

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

= y \frac{\frac{\partial}{\partial x} ( x ) ( x + 7 ) - \frac{\partial}{\partial x} ( x + 7 ) x}{( x + 7 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x + 7) = 1

= y \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}}

Simplify

y \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}} : \frac{7 y}{( x + 7 ) ^{2}}

= \frac{7 y}{( x + 7 ) ^{2}}

\int arcsec (x) d x

3^{x}

f (x) = sin (sin (x)), at x = 2 π, 0

f (x) = arccos (x)

\frac{d}{d x} (3 sin (x) + 2 cos (x))

What is (\partial)/(\partial x)((xy)/(x+7)) ?
The answer to (\partial)/(\partial x)((xy)/(x+7)) is (7y)/((x+7)^2)