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

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

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(\partial)/(\partial x)(a/(a-x))

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= a \frac{\partial}{\partial x} ((a - x)^{- 1})

Apply the chain rule:

- \frac{1}{( a - x ) ^{2}} \frac{\partial}{\partial x} (a - x)

= - \frac{1}{( a - x ) ^{2}} \frac{\partial}{\partial x} (a - x)

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

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

Simplify

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

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

y = \frac{( x + 3 ) ( x ^{2} - 3 x + 9 )}{x ^{3}}

ln (x + 6)

y^{^{'}} = 9 y^{2} + x y^{2}

\frac{d}{d x} (\frac{2 x}{x - 1})

y = e^{4} x^{2} + 18

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