What is the derivative of (9x^{5/2}-2/x) ?

The derivative of (9x^{5/2}-2/x) is (27x^{5/2}+4)/(2x^2)

What is the first derivative of (9x^{5/2}-2/x) ?

The first derivative of (9x^{5/2}-2/x) is (27x^{5/2}+4)/(2x^2)

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\frac{d}{d x} (\frac{9 x ^{\frac{5}{2}} - 2}{x})

\frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 x ^{\frac{5}{2}} - 2}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 9 x ^{\frac{5}{2}} - 2 ) x - \frac{d x}{d x} ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}}

\frac{d}{d x} (9 x^{\frac{5}{2}} - 2) = \frac{45 x ^{\frac{3}{2}}}{2}

\frac{d x}{d x} = 1

= \frac{\frac{45 x ^{\frac{3}{2}}}{2} x - 1 \cdot ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}}

Simplify

\frac{\frac{45 x ^{\frac{3}{2}}}{2} x - 1 \cdot ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}} : \frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}

= \frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}

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What is the derivative of (9x^{5/2}-2/x) ?
The derivative of (9x^{5/2}-2/x) is (27x^{5/2}+4)/(2x^2)
What is the first derivative of (9x^{5/2}-2/x) ?
The first derivative of (9x^{5/2}-2/x) is (27x^{5/2}+4)/(2x^2)