What is the derivative of (3sqrt(x)/2) ?

The derivative of (3sqrt(x)/2) is 3/(4sqrt(x))

What is the first derivative of (3sqrt(x)/2) ?

The first derivative of (3sqrt(x)/2) is 3/(4sqrt(x))

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

\frac{3}{4 x}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

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

Simplify

\frac{3}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3}{4 x}

= \frac{3}{4 x}

x^{2} y^{^{'}} + 2 x y = 13 cos^{2} (x)

y^{^{'}} + 3 x^{2} y = 6 x^{2}

\int - cot (2 x) d x

\int x (a - x)^{2} d x

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

What is the derivative of (3sqrt(x)/2) ?
The derivative of (3sqrt(x)/2) is 3/(4sqrt(x))
What is the first derivative of (3sqrt(x)/2) ?
The first derivative of (3sqrt(x)/2) is 3/(4sqrt(x))