What is the derivative of \sqrt[3]{x}*(x-2)/(x+1) ?

The derivative of \sqrt[3]{x}*(x-2)/(x+1) is (x-2)/(3x^{2/3)(x+1)}+(3\sqrt[3]{x})/((x+1)^2)

What is the first derivative of \sqrt[3]{x}*(x-2)/(x+1) ?

The first derivative of \sqrt[3]{x}*(x-2)/(x+1) is (x-2)/(3x^{2/3)(x+1)}+(3\sqrt[3]{x})/((x+1)^2)

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derivative of

3 x \cdot \frac{x - 2}{x + 1}

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

Solution steps

\frac{d}{d x} (3 x \frac{x - 2}{x + 1})

Apply the Product Rule:

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

f = 3 x, g = \frac{x - 2}{x + 1}

= \frac{d}{d x} (3 x) \frac{x - 2}{x + 1} + \frac{d}{d x} (\frac{x - 2}{x + 1}) 3 x

\frac{d}{d x} (3 x) = \frac{1}{3 x ^{\frac{2}{3}}}

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

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

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} \cdot \frac{x - 2}{x + 1} + \frac{3}{( x + 1 ) ^{2}} 3 x : \frac{x - 2}{3 x ^{\frac{2}{3}} ( x + 1 )} + \frac{3 3 x}{( x + 1 ) ^{2}}

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

\int 2 x^{3} x^{2} - 2 d x

2 x - \frac{1}{x}

\frac{d y}{d t} = y^{2} - 2 y - 2

\frac{\partial}{\partial x} (y^{4} cos (6 x))

\int \frac{x ^{2}}{x ^{2} + x + 2} d x

What is the derivative of \sqrt[3]{x}*(x-2)/(x+1) ?
The derivative of \sqrt[3]{x}*(x-2)/(x+1) is (x-2)/(3x^{2/3)(x+1)}+(3\sqrt[3]{x})/((x+1)^2)
What is the first derivative of \sqrt[3]{x}*(x-2)/(x+1) ?
The first derivative of \sqrt[3]{x}*(x-2)/(x+1) is (x-2)/(3x^{2/3)(x+1)}+(3\sqrt[3]{x})/((x+1)^2)