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

The derivative of 3x^{3/2} is (9x^{1/2})/2

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

The first derivative of 3x^{3/2} is (9x^{1/2})/2

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derivative of

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

\frac{9 x ^{\frac{1}{2}}}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{9 x ^{\frac{1}{2}}}{2}

= \frac{9 x ^{\frac{1}{2}}}{2}

s l o p e (2, 3), (7, - 6)

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

t an g e n t f (x) = \frac{1}{x + 1}, (0, 1)

a re a y = 6 e^{x}, y = 6 e^{- x}, x = 1

\int \frac{1}{y ^{2} - 9} d y

What is the derivative of 3x^{3/2} ?
The derivative of 3x^{3/2} is (9x^{1/2})/2
What is the first derivative of 3x^{3/2} ?
The first derivative of 3x^{3/2} is (9x^{1/2})/2