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

The derivative of x^{2/3}(x+2) is (5x+4)/(3x^{1/3)}

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

The first derivative of x^{2/3}(x+2) is (5x+4)/(3x^{1/3)}

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

\frac{5 x + 4}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x + 2) + 1 \cdot x^{\frac{2}{3}} : \frac{5 x + 4}{3 x ^{\frac{1}{3}}}

= \frac{5 x + 4}{3 x ^{\frac{1}{3}}}

\frac{\partial}{\partial y} (\frac{1}{2 - x + y})

x^{2} + 3 y \cdot \frac{d y}{d x} = 0

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

\int_{0}^{2} x + 2 - x^{2} d x

\frac{d}{d t} (\frac{t ^{3}}{4 - 3 t + 5})

What is the derivative of x^{2/3}(x+2) ?
The derivative of x^{2/3}(x+2) is (5x+4)/(3x^{1/3)}
What is the first derivative of x^{2/3}(x+2) ?
The first derivative of x^{2/3}(x+2) is (5x+4)/(3x^{1/3)}