What is the derivative of x^{1/3}(x^2-4) ?

The derivative of x^{1/3}(x^2-4) is (7x^2-4)/(3x^{2/3)}

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

The first derivative of x^{1/3}(x^2-4) is (7x^2-4)/(3x^{2/3)}

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\frac{d}{d x} (x^{\frac{1}{3}} (x^{2} - 4))

\frac{7 x ^{2} - 4}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (x^{\frac{1}{3}} (x^{2} - 4))

Apply the Product Rule:

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

f = x^{\frac{1}{3}}, g = x^{2} - 4

= \frac{d}{d x} (x^{\frac{1}{3}}) (x^{2} - 4) + \frac{d}{d x} (x^{2} - 4) x^{\frac{1}{3}}

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

\frac{d}{d x} (x^{2} - 4) = 2 x

= \frac{1}{3 x ^{\frac{2}{3}}} (x^{2} - 4) + 2 x x^{\frac{1}{3}}

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} (x^{2} - 4) + 2 x x^{\frac{1}{3}} : \frac{7 x ^{2} - 4}{3 x ^{\frac{2}{3}}}

= \frac{7 x ^{2} - 4}{3 x ^{\frac{2}{3}}}

5 + 4 e - 2 t

\frac{\partial}{\partial x} (x^{3} y + x y^{2} + x y + x)

\frac{d}{d x} (\frac{- 200 ln ( \frac{x}{40} )}{x + 20})

\int_{0}^{15} 2 π x (15 x - x^{2}) d x

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

What is the derivative of x^{1/3}(x^2-4) ?
The derivative of x^{1/3}(x^2-4) is (7x^2-4)/(3x^{2/3)}
What is the first derivative of x^{1/3}(x^2-4) ?
The first derivative of x^{1/3}(x^2-4) is (7x^2-4)/(3x^{2/3)}