What is the derivative of f(x)=-x^{2/3}(x-5) ?

The derivative of f(x)=-x^{2/3}(x-5) is -(5x-10)/(3x^{1/3)}

What is the first derivative of f(x)=-x^{2/3}(x-5) ?

The first derivative of f(x)=-x^{2/3}(x-5) is -(5x-10)/(3x^{1/3)}

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derivative of

f (x) = - x^{\frac{2}{3}} (x - 5)

- \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (- x^{\frac{2}{3}} (x - 5))

Take the constant out:

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

= - \frac{d}{d x} (x^{\frac{2}{3}} (x - 5))

Apply the Product Rule:

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

f = x^{\frac{2}{3}}, g = x - 5

= - (\frac{d}{d x} (x^{\frac{2}{3}}) (x - 5) + \frac{d}{d x} (x - 5) x^{\frac{2}{3}})

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

\frac{d}{d x} (x - 5) = 1

= - (\frac{2}{3 x ^{\frac{1}{3}}} (x - 5) + 1 \cdot x^{\frac{2}{3}})

Simplify

- (\frac{2}{3 x ^{\frac{1}{3}}} (x - 5) + 1 \cdot x^{\frac{2}{3}}) : - \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

= - \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

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

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

\int_{0}^{2} x^{3} (2 - x)^{2} d x

x \to 0 lim (\frac{e ^{x}}{ln ( x )})

\frac{3 x ^{2} + x}{- x ^{2} + 3 x - 3}

What is the derivative of f(x)=-x^{2/3}(x-5) ?
The derivative of f(x)=-x^{2/3}(x-5) is -(5x-10)/(3x^{1/3)}
What is the first derivative of f(x)=-x^{2/3}(x-5) ?
The first derivative of f(x)=-x^{2/3}(x-5) is -(5x-10)/(3x^{1/3)}