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

The derivative of 3/5 x^{5/3} is x^{2/3}

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

The first derivative of 3/5 x^{5/3} is x^{2/3}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

1 + x

\frac{d}{d x} (\frac{e ^{x} + 1}{e ^{x} + 2})

x \to 2 lim (\frac{x ^{3} - 8}{x - 2})

\frac{d}{d t} (e^{2 t} cos (t))

y = \frac{ln ( 9 x )}{9 x}

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