What is the derivative of x^{5/3}-5x^{2/3} ?

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (5 x^{\frac{2}{3}}) = \frac{10}{3 x ^{\frac{1}{3}}}

= \frac{5 x ^{\frac{2}{3}}}{3} - \frac{10}{3 x ^{\frac{1}{3}}}

Simplify

\frac{5 x ^{\frac{2}{3}}}{3} - \frac{10}{3 x ^{\frac{1}{3}}} : \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

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

\frac{d}{d x} (tan (x) + \frac{1}{x})

y = 8 x

x \to π - lim (csc (x))

\int_{0}^{1} \frac{1}{4 - t ^{2}} d t

y = \frac{5}{x ^{3}}

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