What is the derivative of (x+2/x (7-2x^3)) ?

The derivative of (x+2/x (7-2x^3)) is -8x^3-8x-(14)/(x^2)+7

What is the first derivative of (x+2/x (7-2x^3)) ?

The first derivative of (x+2/x (7-2x^3)) is -8x^3-8x-(14)/(x^2)+7

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\frac{d}{d x} ((x + \frac{2}{x}) (7 - 2 x^{3}))

- 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

Solution steps

\frac{d}{d x} ((x + \frac{2}{x}) (7 - 2 x^{3}))

Apply the Product Rule:

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

f = x + \frac{2}{x}, g = 7 - 2 x^{3}

= \frac{d}{d x} (x + \frac{2}{x}) (7 - 2 x^{3}) + \frac{d}{d x} (7 - 2 x^{3}) (x + \frac{2}{x})

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

\frac{d}{d x} (7 - 2 x^{3}) = - 6 x^{2}

= (1 - \frac{2}{x ^{2}}) (7 - 2 x^{3}) + (- 6 x^{2}) (x + \frac{2}{x})

Simplify

(1 - \frac{2}{x ^{2}}) (7 - 2 x^{3}) + (- 6 x^{2}) (x + \frac{2}{x}) : - 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

= - 8 x^{3} - 8 x - \frac{14}{x ^{2}} + 7

\frac{1}{y} \frac{d y}{d x} = e^{x} + ln (y)

(8 - r^{2}) d r = r^{3} sin (θ) d θ, r (0) = 2

\int 4 x^{3} - 6 x^{2} + 3 d x

\int 19 tan^{5} (x) sec^{4} (x) d x

f (x) = 2 e^{- 3 x + 9}

What is the derivative of (x+2/x (7-2x^3)) ?
The derivative of (x+2/x (7-2x^3)) is -8x^3-8x-(14)/(x^2)+7
What is the first derivative of (x+2/x (7-2x^3)) ?
The first derivative of (x+2/x (7-2x^3)) is -8x^3-8x-(14)/(x^2)+7