What is the derivative of x-3x^{1/3} ?

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

What is the first derivative of x-3x^{1/3} ?

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

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

1 - \frac{1}{x ^{\frac{2}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

= 1 - \frac{1}{x ^{\frac{2}{3}}}

\frac{d}{d x} (cos (3 x) \cdot 3)

f (x) = \frac{x ^{3}}{3}

f (x) = x - e^{x}

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

\int_{5}^{8} (x - 6)^{2} d x

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