What is the derivative of 48x^{1/2} ?

The derivative of 48x^{1/2} is (24)/(x^{1/2)}

What is the first derivative of 48x^{1/2} ?

The first derivative of 48x^{1/2} is (24)/(x^{1/2)}

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\frac{d}{d x} (48 x^{\frac{1}{2}})

\frac{24}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (48 x^{\frac{1}{2}})

Take the constant out:

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

= 48 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 48 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

48 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{24}{x ^{\frac{1}{2}}}

= \frac{24}{x ^{\frac{1}{2}}}

What is the derivative of 48x^{1/2} ?
The derivative of 48x^{1/2} is (24)/(x^{1/2)}
What is the first derivative of 48x^{1/2} ?
The first derivative of 48x^{1/2} is (24)/(x^{1/2)}