What is the derivative of 2sqrt(x)+1/(3x^3) ?

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

What is the first derivative of 2sqrt(x)+1/(3x^3) ?

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

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\frac{d}{d x} (2 x + \frac{1}{3 x ^{3}})

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

Solution steps

\frac{d}{d x} (2 x + \frac{1}{3 x ^{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{1}{3 x ^{3}})

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

\frac{d}{d x} (\frac{1}{3 x ^{3}}) = - \frac{1}{x ^{4}}

= \frac{1}{x} - \frac{1}{x ^{4}}

Simplify

\frac{1}{x} - \frac{1}{x ^{4}} : \frac{x ^{\frac{7}{2}} - 1}{x ^{\frac{7}{2}} x}

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

x + \frac{x ^{3}}{3} - tan (x)

x \to \infty lim (\frac{( e ^{x} + e ^{- x} )}{2})

\frac{d}{d x} (x^{2} arctan (2 x))

\frac{d}{d x} (4 sin (x) - 4 x cos (x))

n = 3 \sum \infty \frac{1}{n ^{2} + 3 n}

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