What is the derivative of 2cos(x^3-2/x) ?

The derivative of 2cos(x^3-2/x) is -6x^2sin(x^3)+2/(x^2)

What is the first derivative of 2cos(x^3-2/x) ?

The first derivative of 2cos(x^3-2/x) is -6x^2sin(x^3)+2/(x^2)

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

- 6 x^{2} sin (x^{3}) + \frac{2}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= - 6 x^{2} sin (x^{3}) + \frac{2}{x ^{2}}

What is the derivative of 2cos(x^3-2/x) ?
The derivative of 2cos(x^3-2/x) is -6x^2sin(x^3)+2/(x^2)
What is the first derivative of 2cos(x^3-2/x) ?
The first derivative of 2cos(x^3-2/x) is -6x^2sin(x^3)+2/(x^2)