What is (\partial)/(\partial x)((a*b)/(c*x)) ?

The answer to (\partial)/(\partial x)((a*b)/(c*x)) is -(ab)/(cx^2)

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(\partial)/(\partial x)((ab)/(cx))

\frac{\partial}{\partial x} (\frac{a \cdot b}{c \cdot x})

- \frac{ab}{c x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{ab}{c x})

Treat

a, b, c

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= \frac{ab}{c} (- 1 \cdot x^{- 1 - 1})

Simplify

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

= - \frac{ab}{c x ^{2}}

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

\int sin (x) (cos (x))^{5} d x

f (x) = 5 ln (4 x)

f (x) = \frac{x - 5}{( x + 3 ) ^{4}}

\int sin (x) sec^{10} (x) d x

What is (\partial)/(\partial x)((a*b)/(c*x)) ?
The answer to (\partial)/(\partial x)((a*b)/(c*x)) is -(ab)/(cx^2)