What is the derivative of-x^5-(x^3/6+3/x-1/(x^2)) ?

The derivative of-x^5-(x^3/6+3/x-1/(x^2)) is -5x^4-(x^2)/2-3/(x^2)+2/(x^3)

What is the first derivative of-x^5-(x^3/6+3/x-1/(x^2)) ?

The first derivative of-x^5-(x^3/6+3/x-1/(x^2)) is -5x^4-(x^2)/2-3/(x^2)+2/(x^3)

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\frac{d}{d x} (- x^{5} - \frac{x ^{3}}{6} + \frac{3}{x} - \frac{1}{x ^{2}})

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

Solution steps

\frac{d}{d x} (- x^{5} - \frac{x ^{3}}{6} + \frac{3}{x} - \frac{1}{x ^{2}})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (x^{5}) - \frac{d}{d x} (\frac{x ^{3}}{6}) + \frac{d}{d x} (\frac{3}{x}) - \frac{d}{d x} (\frac{1}{x ^{2}})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (\frac{x ^{3}}{6}) = \frac{x ^{2}}{2}

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

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

= - 5 x^{4} - \frac{x ^{2}}{2} - \frac{3}{x ^{2}} - (- \frac{2}{x ^{3}})

Simplify

= - 5 x^{4} - \frac{x ^{2}}{2} - \frac{3}{x ^{2}} + \frac{2}{x ^{3}}

y = \frac{7}{( 6 x ) ^{6}}

4 x, 64 - x^{2}, [0, 6.928]

x \to 69.9 lim (\frac{ln ( \frac{x - 70}{230} )}{- 0.19})

y = x^{2} - 12, y = 11 x

\frac{d}{d x} (\frac{x ^{2}}{x - 11})

What is the derivative of-x^5-(x^3/6+3/x-1/(x^2)) ?
The derivative of-x^5-(x^3/6+3/x-1/(x^2)) is -5x^4-(x^2)/2-3/(x^2)+2/(x^3)
What is the first derivative of-x^5-(x^3/6+3/x-1/(x^2)) ?
The first derivative of-x^5-(x^3/6+3/x-1/(x^2)) is -5x^4-(x^2)/2-3/(x^2)+2/(x^3)