What is the derivative of 9sqrt(x)-1/x ?

The derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}

What is the first derivative of 9sqrt(x)-1/x ?

The first derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}

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\frac{d}{d x} (9 x - \frac{1}{x})

\frac{9 x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

Solution steps

\frac{d}{d x} (9 x - \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 x) - \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (9 x) = \frac{9}{2 x}

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

= \frac{9}{2 x} - (- \frac{1}{x ^{2}})

Simplify

\frac{9}{2 x} - (- \frac{1}{x ^{2}}) : \frac{9 x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

= \frac{9 x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

What is the derivative of 9sqrt(x)-1/x ?
The derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}
What is the first derivative of 9sqrt(x)-1/x ?
The first derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}