What is the derivative of f(x)=(sqrt(10))/(x^7) ?

The derivative of f(x)=(sqrt(10))/(x^7) is -(7sqrt(10))/(x^8)

What is the first derivative of f(x)=(sqrt(10))/(x^7) ?

The first derivative of f(x)=(sqrt(10))/(x^7) is -(7sqrt(10))/(x^8)

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derivative of

f (x) = \frac{10}{x ^{7}}

- \frac{7 10}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{10}{x ^{7}})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{1}{x ^{7}})

Apply exponent rule:

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

= 10 \frac{d}{d x} (x^{- 7})

Apply the Power Rule:

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

= 10 (- 7 x^{- 7 - 1})

Simplify

10 (- 7 x^{- 7 - 1}) : - \frac{7 10}{x ^{8}}

= - \frac{7 10}{x ^{8}}

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What is the derivative of f(x)=(sqrt(10))/(x^7) ?
The derivative of f(x)=(sqrt(10))/(x^7) is -(7sqrt(10))/(x^8)
What is the first derivative of f(x)=(sqrt(10))/(x^7) ?
The first derivative of f(x)=(sqrt(10))/(x^7) is -(7sqrt(10))/(x^8)