What is the derivative of 5{g}(x(2x^3)+2/(x^2)) ?

The derivative of 5{g}(x(2x^3)+2/(x^2)) is 10(3x^2{g}(x)+derivative of {g}(x)x^3)-4/(x^3)

What is the first derivative of 5{g}(x(2x^3)+2/(x^2)) ?

The first derivative of 5{g}(x(2x^3)+2/(x^2)) is 10(3x^2{g}(x)+derivative of {g}(x)x^3)-4/(x^3)

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\frac{d}{d x} (5 g (x) (2 x^{3}) + \frac{2}{x ^{2}})

10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3}) - \frac{4}{x ^{3}}

Solution steps

\frac{d}{d x} (5 g (x) (2 x^{3}) + \frac{2}{x ^{2}})

Simplify

5 g (x) (2 x^{3}) + \frac{2}{x ^{2}} : 10 x^{3} g (x) + \frac{2}{x ^{2}}

= \frac{d}{d x} (10 x^{3} g (x) + \frac{2}{x ^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (10 x^{3} g (x)) + \frac{d}{d x} (\frac{2}{x ^{2}})

\frac{d}{d x} (10 x^{3} g (x)) = 10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3})

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

= 10 (3 x^{2} g (x) + \frac{d}{d x} (g (x)) x^{3}) - \frac{4}{x ^{3}}

What is the derivative of 5{g}(x(2x^3)+2/(x^2)) ?
The derivative of 5{g}(x(2x^3)+2/(x^2)) is 10(3x^2{g}(x)+derivative of {g}(x)x^3)-4/(x^3)
What is the first derivative of 5{g}(x(2x^3)+2/(x^2)) ?
The first derivative of 5{g}(x(2x^3)+2/(x^2)) is 10(3x^2{g}(x)+derivative of {g}(x)x^3)-4/(x^3)