What is the derivative of 8sqrt(x)-3/(sqrt(x)) ?

The derivative of 8sqrt(x)-3/(sqrt(x)) is 4/(sqrt(x))+3/(2x^{3/2)}

What is the first derivative of 8sqrt(x)-3/(sqrt(x)) ?

The first derivative of 8sqrt(x)-3/(sqrt(x)) is 4/(sqrt(x))+3/(2x^{3/2)}

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\frac{d}{d x} (8 x - \frac{3}{x})

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

Solution steps

\frac{d}{d x} (8 x - \frac{3}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (8 x) - \frac{d}{d x} (\frac{3}{x})

\frac{d}{d x} (8 x) = \frac{4}{x}

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

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

Simplify

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

What is the derivative of 8sqrt(x)-3/(sqrt(x)) ?
The derivative of 8sqrt(x)-3/(sqrt(x)) is 4/(sqrt(x))+3/(2x^{3/2)}
What is the first derivative of 8sqrt(x)-3/(sqrt(x)) ?
The first derivative of 8sqrt(x)-3/(sqrt(x)) is 4/(sqrt(x))+3/(2x^{3/2)}