What is the derivative of 4x^{1/2} ?

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

What is the first derivative of 4x^{1/2} ?

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

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derivative of

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

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

Solution steps

\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}}}

9 y^{^{''}} + 42 y^{^{'}} + 49 y = 0

\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

x \to 7 lim (- 11)

x^{- \frac{1}{9}}

\frac{\partial}{\partial x} (5 x y^{4})

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