What is (\partial)/(\partial x)((a^3b^4)/(c^2x^4)) ?

The answer to (\partial)/(\partial x)((a^3b^4)/(c^2x^4)) is -(4a^3b^4)/(c^2x^5)

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(\partial)/(\partial x)((a^3b^4)/(c^2x^4))

\frac{\partial}{\partial x} (\frac{a ^{3} b ^{4}}{c ^{2} x ^{4}})

- \frac{4 a ^{3} b ^{4}}{c ^{2} x ^{5}}

Solution steps

\frac{\partial}{\partial x} (\frac{a ^{3} b ^{4}}{c ^{2} x ^{4}})

Treat

a, b, c

as constants

Take the constant out:

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

= \frac{a ^{3} b ^{4}}{c ^{2}} \frac{\partial}{\partial x} (\frac{1}{x ^{4}})

Apply exponent rule:

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

= \frac{a ^{3} b ^{4}}{c ^{2}} \frac{\partial}{\partial x} (x^{- 4})

Apply the Power Rule:

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

= \frac{a ^{3} b ^{4}}{c ^{2}} (- 4 x^{- 4 - 1})

Simplify

\frac{a ^{3} b ^{4}}{c ^{2}} (- 4 x^{- 4 - 1}) : - \frac{4 a ^{3} b ^{4}}{c ^{2} x ^{5}}

= - \frac{4 a ^{3} b ^{4}}{c ^{2} x ^{5}}

What is (\partial)/(\partial x)((a^3b^4)/(c^2x^4)) ?
The answer to (\partial)/(\partial x)((a^3b^4)/(c^2x^4)) is -(4a^3b^4)/(c^2x^5)