What is (\partial)/(\partial x)(x/(x-b)) ?

The answer to (\partial)/(\partial x)(x/(x-b)) is -b/((x-b)^2)

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(\partial)/(\partial x)(x/(x-b))

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

- \frac{b}{( x - b ) ^{2}}

Solution steps

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

Treat

b

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x - b ) - \frac{\partial}{\partial x} ( x - b ) x}{( x - b ) ^{2}}

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

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

= \frac{1 \cdot ( x - b ) - 1 \cdot x}{( x - b ) ^{2}}

Simplify

\frac{1 \cdot ( x - b ) - 1 \cdot x}{( x - b ) ^{2}} : - \frac{b}{( x - b ) ^{2}}

= - \frac{b}{( x - b ) ^{2}}

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\int_{5}^{\infty} \frac{1}{x ^{2}} d x

\frac{d}{d x} (tan^{2} (x - 3))

\int_{1}^{2} \frac{4 x ^{2} - 1}{x} d x

What is (\partial)/(\partial x)(x/(x-b)) ?
The answer to (\partial)/(\partial x)(x/(x-b)) is -b/((x-b)^2)