What is the derivative of (100/(x^5)) ?

The derivative of (100/(x^5)) is -(500)/(x^6)

What is the first derivative of (100/(x^5)) ?

The first derivative of (100/(x^5)) is -(500)/(x^6)

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\frac{d}{d x} (\frac{100}{x ^{5}})

- \frac{500}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{100}{x ^{5}})

Take the constant out:

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

= 100 \frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= 100 \frac{d}{d x} (x^{- 5})

Apply the Power Rule:

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

= 100 (- 5 x^{- 5 - 1})

Simplify

100 (- 5 x^{- 5 - 1}) : - \frac{500}{x ^{6}}

= - \frac{500}{x ^{6}}

\int 3 e^{x} - 2 cos (x) d x

f (x) = x^{4} + 8 x^{2} - x, at x = 1

\int \frac{5}{x ^{2}} d x

\frac{d}{d x} (1 + \frac{1}{3 x})

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 5})

What is the derivative of (100/(x^5)) ?
The derivative of (100/(x^5)) is -(500)/(x^6)
What is the first derivative of (100/(x^5)) ?
The first derivative of (100/(x^5)) is -(500)/(x^6)