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

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

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

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

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derivative of

(3 x)^{\frac{1}{2}}

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

Solution steps

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

Simplify

(3 x)^{\frac{1}{2}} : 3^{\frac{1}{2}} x^{\frac{1}{2}}

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

Take the constant out:

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

= 3^{\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}

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

Simplify

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

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

d er i v a t i v e y = ln (x) sec^{3} (x)

\frac{d}{d t} (15 + 300 t)

d er i v a t i v e x^{9} - 10 x^{5} + 2 x^{2} - 10

d er i v a t i v e \frac{y}{( x - y ) 2}

\frac{d}{d x} (3 ∣ sin (x) x ∣ - 4 ∣ cos (x) ∣)

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