What is (\partial)/(\partial x)((100x)/((x+y)^2)) ?

The answer to (\partial)/(\partial x)((100x)/((x+y)^2)) is (100(-x+y))/((x+y)^3)

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(\partial)/(\partial x)((100x)/((x+y)^2))

\frac{\partial}{\partial x} (\frac{100 x}{( x + y ) ^{2}})

\frac{100 ( - x + y )}{( x + y ) ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{100 x}{( x + y ) ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 100 \frac{\partial}{\partial x} (\frac{x}{( x + y ) ^{2}})

Apply the Quotient Rule:

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

= 100 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x + y ) ^{2} - \frac{\partial}{\partial x} ( ( x + y ) ^{2} ) x}{( ( x + y ) ^{2} ) ^{2}}

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

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

= 100 \cdot \frac{1 \cdot ( x + y ) ^{2} - 2 ( x + y ) x}{( ( x + y ) ^{2} ) ^{2}}

Simplify

100 \cdot \frac{1 \cdot ( x + y ) ^{2} - 2 ( x + y ) x}{( ( x + y ) ^{2} ) ^{2}} : \frac{100 ( - x + y )}{( x + y ) ^{3}}

= \frac{100 ( - x + y )}{( x + y ) ^{3}}

\int 10 e^{- 2 x} d x

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

\frac{d}{d x} (3 + 4 x)

\int \frac{- 30}{( 2 x + 1 ) ^{2}} d x

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

What is (\partial)/(\partial x)((100x)/((x+y)^2)) ?
The answer to (\partial)/(\partial x)((100x)/((x+y)^2)) is (100(-x+y))/((x+y)^3)