What is the derivative of y= 4/(7x^7) ?

The derivative of y= 4/(7x^7) is -4/(x^8)

What is the first derivative of y= 4/(7x^7) ?

The first derivative of y= 4/(7x^7) is -4/(x^8)

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derivative of

y = \frac{4}{7 x ^{7}}

- \frac{4}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{4}{7 x ^{7}})

Take the constant out:

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

= \frac{4}{7} \frac{d}{d x} (\frac{1}{x ^{7}})

Apply exponent rule:

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

= \frac{4}{7} \frac{d}{d x} (x^{- 7})

Apply the Power Rule:

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

= \frac{4}{7} (- 7 x^{- 7 - 1})

Simplify

\frac{4}{7} (- 7 x^{- 7 - 1}) : - \frac{4}{x ^{8}}

= - \frac{4}{x ^{8}}

What is the derivative of y= 4/(7x^7) ?
The derivative of y= 4/(7x^7) is -4/(x^8)
What is the first derivative of y= 4/(7x^7) ?
The first derivative of y= 4/(7x^7) is -4/(x^8)