What is the derivative of 2/(5x^3) ?

The derivative of 2/(5x^3) is -6/(5x^4)

What is the first derivative of 2/(5x^3) ?

The first derivative of 2/(5x^3) is -6/(5x^4)

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derivative of

\frac{2}{5 x ^{3}}

- \frac{6}{5 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{2}{5 x ^{3}})

Take the constant out:

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

= \frac{2}{5} \frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= \frac{2}{5} \frac{d}{d x} (x^{- 3})

Apply the Power Rule:

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

= \frac{2}{5} (- 3 x^{- 3 - 1})

Simplify

\frac{2}{5} (- 3 x^{- 3 - 1}) : - \frac{6}{5 x ^{4}}

= - \frac{6}{5 x ^{4}}

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

x \to 0 lim (8000 x)

\frac{1}{x}, at 1

x \to 0 lim (10)

f (x) = cos (π x)

What is the derivative of 2/(5x^3) ?
The derivative of 2/(5x^3) is -6/(5x^4)
What is the first derivative of 2/(5x^3) ?
The first derivative of 2/(5x^3) is -6/(5x^4)