What is the derivative of 3/(4x^8) ?

The derivative of 3/(4x^8) is -6/(x^9)

What is the first derivative of 3/(4x^8) ?

The first derivative of 3/(4x^8) is -6/(x^9)

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\frac{d}{d x} (\frac{3}{4 x ^{8}})

- \frac{6}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{3}{4 x ^{8}})

Take the constant out:

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

= \frac{3}{4} \frac{d}{d x} (\frac{1}{x ^{8}})

Apply exponent rule:

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

= \frac{3}{4} \frac{d}{d x} (x^{- 8})

Apply the Power Rule:

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

= \frac{3}{4} (- 8 x^{- 8 - 1})

Simplify

\frac{3}{4} (- 8 x^{- 8 - 1}) : - \frac{6}{x ^{9}}

= - \frac{6}{x ^{9}}

What is the derivative of 3/(4x^8) ?
The derivative of 3/(4x^8) is -6/(x^9)
What is the first derivative of 3/(4x^8) ?
The first derivative of 3/(4x^8) is -6/(x^9)