What is the derivative of 4/(sqrt(x)+2/x+x/2) ?

The derivative of 4/(sqrt(x)+2/x+x/2) is 1/2+(-2x^2-2x^{3/2})/(x^{7/2)}

What is the first derivative of 4/(sqrt(x)+2/x+x/2) ?

The first derivative of 4/(sqrt(x)+2/x+x/2) is 1/2+(-2x^2-2x^{3/2})/(x^{7/2)}

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\frac{d}{d x} (\frac{4}{x} + \frac{2}{x} + \frac{x}{2})

\frac{1}{2} + \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{4}{x} + \frac{2}{x} + \frac{x}{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (\frac{2}{x}) + \frac{d}{d x} (\frac{x}{2})

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

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

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

= - \frac{2}{x ^{\frac{3}{2}}} - \frac{2}{x ^{2}} + \frac{1}{2}

Combine the fractions

- \frac{2}{x ^{\frac{3}{2}}} - \frac{2}{x ^{2}} : \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

= \frac{1}{2} + \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

\int \frac{( x - 1 ) ( x + 1 )}{x} d x

x \to π lim (15)

x \to 3 lim (5 x^{3} - 2 x^{2} + x - 7)

- 0.6 t^{3} + 7.2 t^{2} + 61

What is the derivative of 4/(sqrt(x)+2/x+x/2) ?
The derivative of 4/(sqrt(x)+2/x+x/2) is 1/2+(-2x^2-2x^{3/2})/(x^{7/2)}
What is the first derivative of 4/(sqrt(x)+2/x+x/2) ?
The first derivative of 4/(sqrt(x)+2/x+x/2) is 1/2+(-2x^2-2x^{3/2})/(x^{7/2)}