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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

f (x) = 3 x cos (x), at x = π

\frac{\partial}{\partial x} (x^{2} + 3)

9 y^{^{''}} + 9 y = 0

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

f (x) = \frac{cos ( x )}{x ^{2} - 1}

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