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

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

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

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

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\frac{d}{d x} (\frac{9 x ^{\frac{3}{2}}}{3})

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

Solution steps

\frac{d}{d x} (\frac{9 x ^{\frac{3}{2}}}{3})

Simplify

\frac{9 x ^{\frac{3}{2}}}{3} : 3 x^{\frac{3}{2}}

= \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}

(a x^{2} + b x + c) e^{- \frac{x}{6}}

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

x \cdot e^{- x + 1}

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

\frac{d}{d x} ((5 x^{2} + x + 9) tan (7 x))

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