What is the derivative of (5x^{1/2}) ?

The derivative of (5x^{1/2}) is (5^{1/2})/(2x^{1/2)}

What is the first derivative of (5x^{1/2}) ?

The first derivative of (5x^{1/2}) is (5^{1/2})/(2x^{1/2)}

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\frac{d}{d x} ((5 x)^{\frac{1}{2}})

\frac{5 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((5 x)^{\frac{1}{2}})

Simplify

(5 x)^{\frac{1}{2}} : 5^{\frac{1}{2}} x^{\frac{1}{2}}

= \frac{d}{d x} (5^{\frac{1}{2}} x^{\frac{1}{2}})

Take the constant out:

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

= 5^{\frac{1}{2}} \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 5^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

5^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{5 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

= \frac{5 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

What is the derivative of (5x^{1/2}) ?
The derivative of (5x^{1/2}) is (5^{1/2})/(2x^{1/2)}
What is the first derivative of (5x^{1/2}) ?
The first derivative of (5x^{1/2}) is (5^{1/2})/(2x^{1/2)}