What is the derivative of 4/5 x^{3/2} ?

The derivative of 4/5 x^{3/2} is (6x^{1/2})/5

What is the first derivative of 4/5 x^{3/2} ?

The first derivative of 4/5 x^{3/2} is (6x^{1/2})/5

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\frac{d}{d x} (\frac{4}{5} x^{\frac{3}{2}})

\frac{6 x ^{\frac{1}{2}}}{5}

Solution steps

\frac{d}{d x} (\frac{4}{5} x^{\frac{3}{2}})

Take the constant out:

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

= \frac{4}{5} \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= \frac{4}{5} \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

\frac{4}{5} \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{6 x ^{\frac{1}{2}}}{5}

= \frac{6 x ^{\frac{1}{2}}}{5}

\int x^{2} 2 + x d x

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

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

x \frac{d y}{d x} + 2 y = 10 x^{2}

\int (1 + x^{2})^{2} d x

What is the derivative of 4/5 x^{3/2} ?
The derivative of 4/5 x^{3/2} is (6x^{1/2})/5
What is the first derivative of 4/5 x^{3/2} ?
The first derivative of 4/5 x^{3/2} is (6x^{1/2})/5