What is (\partial)/(\partial x)(sqrt(3)x^{1/2}) ?

The answer to (\partial)/(\partial x)(sqrt(3)x^{1/2}) is (sqrt(3))/(2x^{1/2)}

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(\partial)/(\partial x)(sqrt(3)x^{1/2})

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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f (x) = 2 x^{3} - 3 x^{2} - 36 x + 5

What is (\partial)/(\partial x)(sqrt(3)x^{1/2}) ?
The answer to (\partial)/(\partial x)(sqrt(3)x^{1/2}) is (sqrt(3))/(2x^{1/2)}