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

The derivative of 2/(sqrt(x^3)) is -3/(x^{5/2)}

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

The first derivative of 2/(sqrt(x^3)) is -3/(x^{5/2)}

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (x^{2} ln (x))

1 - t^{2}

\frac{d}{d x} (ln (6 x^{3}))

\int \frac{( 5 t - 2 )}{t + 1} d t

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

What is the derivative of 2/(sqrt(x^3)) ?
The derivative of 2/(sqrt(x^3)) is -3/(x^{5/2)}
What is the first derivative of 2/(sqrt(x^3)) ?
The first derivative of 2/(sqrt(x^3)) is -3/(x^{5/2)}