What is the derivative of f(x)= 1/((2x^3)) ?

The derivative of f(x)= 1/((2x^3)) is -3/(2x^4)

What is the first derivative of f(x)= 1/((2x^3)) ?

The first derivative of f(x)= 1/((2x^3)) is -3/(2x^4)

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derivative of

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

- \frac{3}{2 x ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{3}{2 x ^{4}}

x \to 5 lim (\frac{2}{( x - 5 ) ^{3}})

\frac{d}{d x} (2 - 4 x)

\int \frac{1}{4 x ^{2} + 2} d x

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 10

\frac{d}{d x} (\frac{6 x}{1 + 3 x ^{2}})

What is the derivative of f(x)= 1/((2x^3)) ?
The derivative of f(x)= 1/((2x^3)) is -3/(2x^4)
What is the first derivative of f(x)= 1/((2x^3)) ?
The first derivative of f(x)= 1/((2x^3)) is -3/(2x^4)