What is the derivative of f(x)=(4x^{3/2})/x ?

The derivative of f(x)=(4x^{3/2})/x is 2/(x^{1/2)}

What is the first derivative of f(x)=(4x^{3/2})/x ?

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

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derivative of

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

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

Solution steps

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

Simplify

\frac{4 x ^{\frac{3}{2}}}{x} : 4 x^{\frac{1}{2}}

= \frac{d}{d x} (4 x^{\frac{1}{2}})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

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

Simplify

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

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

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