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

The derivative of 5/((2x^3)) is -(15)/(8x^4)

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

The first derivative of 5/((2x^3)) is -(15)/(8x^4)

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

- \frac{15}{8 x ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

= - \frac{3}{( 2 x ) ^{4}} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= 5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2)

Simplify

5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2) : - \frac{15}{8 x ^{4}}

= - \frac{15}{8 x ^{4}}

\frac{\partial}{\partial x} (x^{2} - y^{2})

\int (tan (\frac{x}{10}))^{5} d x

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

x^{2} + y^{2} = 25, (- 4, - 3)

\int 2 x sin (x^{2}) d x

What is the derivative of 5/((2x^3)) ?
The derivative of 5/((2x^3)) is -(15)/(8x^4)
What is the first derivative of 5/((2x^3)) ?
The first derivative of 5/((2x^3)) is -(15)/(8x^4)