What is the derivative of y=2x^{3/2} ?

The derivative of y=2x^{3/2} is 3x^{1/2}

What is the first derivative of y=2x^{3/2} ?

The first derivative of y=2x^{3/2} is 3x^{1/2}

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} y^{3} - 4 y)

\frac{d y}{d x}, 4 x y = 8

\int \frac{2}{x ^{3} - 5 x ^{2} + 3 x + 9} d x

\frac{\partial}{\partial x} (x^{y} + y^{x})

\frac{\partial}{\partial x} (2 x^{3} + y)

What is the derivative of y=2x^{3/2} ?
The derivative of y=2x^{3/2} is 3x^{1/2}
What is the first derivative of y=2x^{3/2} ?
The first derivative of y=2x^{3/2} is 3x^{1/2}