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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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