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

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

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

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

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

\frac{4 x - 1}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

\frac{4 x ^{\frac{1}{3}}}{3} - \frac{1}{3 x ^{\frac{2}{3}}} : \frac{4 x - 1}{3 x ^{\frac{2}{3}}}

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

f (x) = (7 - x) (\frac{5}{x ^{2}} - 8)

\frac{d y}{d x}, y = x^{2} + 1

\int e^{6 θ} sin (7 θ) d θ

x \to \infty lim ((3)^{x})

n = 1 \sum \infty \frac{n}{( n + 2 )}

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