What is (\partial)/(\partial x)((3x)/((x+y)^3)) ?

The answer to (\partial)/(\partial x)((3x)/((x+y)^3)) is (3(-2x+y))/((x+y)^4)

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(\partial)/(\partial x)((3x)/((x+y)^3))

\frac{\partial}{\partial x} (\frac{3 x}{( x + y ) ^{3}})

\frac{3 ( - 2 x + y )}{( x + y ) ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x}{( x + y ) ^{3}})

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

3 \cdot \frac{1 \cdot ( x + y ) ^{3} - 3 ( x + y ) ^{2} x}{( ( x + y ) ^{3} ) ^{2}} : \frac{3 ( - 2 x + y )}{( x + y ) ^{4}}

= \frac{3 ( - 2 x + y )}{( x + y ) ^{4}}

f (x) = - 2 sin (x), at x = \frac{3 π}{4}

\int \frac{x ^{5}}{u} d x

x \to 0 lim (sin (0))

\frac{\partial}{\partial x} (200 (y - x^{2}))

x \to - 2 lim (\frac{x - 1}{x ^{2} - 4})

What is (\partial)/(\partial x)((3x)/((x+y)^3)) ?
The answer to (\partial)/(\partial x)((3x)/((x+y)^3)) is (3(-2x+y))/((x+y)^4)