What is the derivative of (6x^2+7)(x^2-1/x) ?

The derivative of (6x^2+7)(x^2-1/x) is 24x^3+14x+7/(x^2)-6

What is the first derivative of (6x^2+7)(x^2-1/x) ?

The first derivative of (6x^2+7)(x^2-1/x) is 24x^3+14x+7/(x^2)-6

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derivative of

(6 x^{2} + 7) (x^{2} - \frac{1}{x})

24 x^{3} + 14 x + \frac{7}{x ^{2}} - 6

Solution steps

\frac{d}{d x} ((6 x^{2} + 7) (x^{2} - \frac{1}{x}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 6 x^{2} + 7, g = x^{2} - \frac{1}{x}

= \frac{d}{d x} (6 x^{2} + 7) (x^{2} - \frac{1}{x}) + \frac{d}{d x} (x^{2} - \frac{1}{x}) (6 x^{2} + 7)

\frac{d}{d x} (6 x^{2} + 7) = 12 x

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

= 12 x (x^{2} - \frac{1}{x}) + (2 x + \frac{1}{x ^{2}}) (6 x^{2} + 7)

Simplify

12 x (x^{2} - \frac{1}{x}) + (2 x + \frac{1}{x ^{2}}) (6 x^{2} + 7) : 24 x^{3} + 14 x + \frac{7}{x ^{2}} - 6

= 24 x^{3} + 14 x + \frac{7}{x ^{2}} - 6

What is the derivative of (6x^2+7)(x^2-1/x) ?
The derivative of (6x^2+7)(x^2-1/x) is 24x^3+14x+7/(x^2)-6
What is the first derivative of (6x^2+7)(x^2-1/x) ?
The first derivative of (6x^2+7)(x^2-1/x) is 24x^3+14x+7/(x^2)-6