What is (\partial)/(\partial x)(1/(1-5/x)) ?

The answer to (\partial)/(\partial x)(1/(1-5/x)) is -5/((x-5)^2)

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(\partial)/(\partial x)(1/(1-5/x))

\frac{\partial}{\partial x} (\frac{1}{1 - \frac{5}{x}})

- \frac{5}{( x - 5 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{1 - \frac{5}{x}})

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((1 - \frac{5}{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - \frac{5}{x} ) ^{2}} \frac{\partial}{\partial x} (1 - \frac{5}{x})

= - \frac{1}{( 1 - \frac{5}{x} ) ^{2}} \frac{\partial}{\partial x} (1 - \frac{5}{x})

\frac{\partial}{\partial x} (1 - \frac{5}{x}) = \frac{5}{x ^{2}}

= - \frac{1}{( 1 - \frac{5}{x} ) ^{2}} \cdot \frac{5}{x ^{2}}

Simplify

- \frac{1}{( 1 - \frac{5}{x} ) ^{2}} \cdot \frac{5}{x ^{2}} : - \frac{5}{( x - 5 ) ^{2}}

= - \frac{5}{( x - 5 ) ^{2}}

\int (e^{t} + 2 t + ln (t)) d t

y^{^{'}} = 5 y (1 - \frac{y}{7})

\frac{d}{d s} (1)

\frac{d}{d x} ((- 2 x - 3)^{5} (3 x + 1)^{3})

n = 2 \sum \infty ln (n)

What is (\partial)/(\partial x)(1/(1-5/x)) ?
The answer to (\partial)/(\partial x)(1/(1-5/x)) is -5/((x-5)^2)