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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= \frac{2}{5} \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Simplify

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

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

\int (x^{3} - 2 x^{\frac{1}{2}} + 4)^{2} d x

\frac{d}{d x} (\frac{1}{y - 5 x ^{2}})

y^{^{'}} - y = 2 t

x^{2} y^{^{'}} + 2 x y = 25 cos^{2} (x)

\frac{- 8 x}{x ^{2} + 1}

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