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

The derivative of ((x+2)/x)(7-2x^3) is (-6x^4-8x^3-14)/(x^2)

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

The first derivative of ((x+2)/x)(7-2x^3) is (-6x^4-8x^3-14)/(x^2)

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derivative of

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

\frac{- 6 x ^{4} - 8 x ^{3} - 14}{x ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- \frac{2}{x ^{2}}) (7 - 2 x^{3}) + (- 6 x^{2}) \frac{x + 2}{x} : \frac{- 6 x ^{4} - 8 x ^{3} - 14}{x ^{2}}

= \frac{- 6 x ^{4} - 8 x ^{3} - 14}{x ^{2}}

\int \frac{5}{( 5 x + 4 ) ln ( 5 x + 4 )} d x

\int 6 x^{2} - 2 x + 1 d x

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What is the derivative of ((x+2)/x)(7-2x^3) ?
The derivative of ((x+2)/x)(7-2x^3) is (-6x^4-8x^3-14)/(x^2)
What is the first derivative of ((x+2)/x)(7-2x^3) ?
The first derivative of ((x+2)/x)(7-2x^3) is (-6x^4-8x^3-14)/(x^2)