What is the derivative of (3a/(4x^5)) ?

The derivative of (3a/(4x^5)) is -(15a)/(4x^6)

What is the first derivative of (3a/(4x^5)) ?

The first derivative of (3a/(4x^5)) is -(15a)/(4x^6)

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\frac{d}{d x} (\frac{3 a}{4 x ^{5}})

- \frac{15 a}{4 x ^{6}}

Solution steps

\frac{d}{d x} (\frac{3 a}{4 x ^{5}})

Take the constant out:

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

= \frac{3 a}{4} \frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= \frac{3 a}{4} \frac{d}{d x} (x^{- 5})

Apply the Power Rule:

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

= \frac{3 a}{4} (- 5 x^{- 5 - 1})

Simplify

\frac{3 a}{4} (- 5 x^{- 5 - 1}) : - \frac{15 a}{4 x ^{6}}

= - \frac{15 a}{4 x ^{6}}

What is the derivative of (3a/(4x^5)) ?
The derivative of (3a/(4x^5)) is -(15a)/(4x^6)
What is the first derivative of (3a/(4x^5)) ?
The first derivative of (3a/(4x^5)) is -(15a)/(4x^6)