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

The derivative of-x^{2/3}(x-4) is -(5x-8)/(3x^{1/3)}

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

The first derivative of-x^{2/3}(x-4) is -(5x-8)/(3x^{1/3)}

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

- \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (x - 4) = 1

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

Simplify

- (\frac{2}{3 x ^{\frac{1}{3}}} (x - 4) + 1 \cdot x^{\frac{2}{3}}) : - \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

= - \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

\int \frac{3}{2} x d x

\int (2 x - x^{2})^{2} d x

\frac{d}{d x} (2 a x - x^{2})

x = \frac{( y - 3 ) ^{2}}{5}, x = 13 - y

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

What is the derivative of-x^{2/3}(x-4) ?
The derivative of-x^{2/3}(x-4) is -(5x-8)/(3x^{1/3)}
What is the first derivative of-x^{2/3}(x-4) ?
The first derivative of-x^{2/3}(x-4) is -(5x-8)/(3x^{1/3)}