What is the derivative of (25/(x^3)) ?

The derivative of (25/(x^3)) is -(75)/(x^4)

What is the first derivative of (25/(x^3)) ?

The first derivative of (25/(x^3)) is -(75)/(x^4)

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\frac{d}{d x} (\frac{25}{x ^{3}})

- \frac{75}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{25}{x ^{3}})

Take the constant out:

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

= 25 \frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= 25 \frac{d}{d x} (x^{- 3})

Apply the Power Rule:

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

= 25 (- 3 x^{- 3 - 1})

Simplify

25 (- 3 x^{- 3 - 1}) : - \frac{75}{x ^{4}}

= - \frac{75}{x ^{4}}

\int sin^{x} (d) x d x

\int \frac{t}{1 - t ^{2}} d t

sin (x) d x + y d y = 0, y (0) = - 2

\int \frac{1}{( x ^{2} + 10 x + 24 )} d x

\frac{d}{d x} (ln (arctan (x)))

What is the derivative of (25/(x^3)) ?
The derivative of (25/(x^3)) is -(75)/(x^4)
What is the first derivative of (25/(x^3)) ?
The first derivative of (25/(x^3)) is -(75)/(x^4)