What is the (3sqrt(x))^' ?

The (3sqrt(x))^' is 3/(2sqrt(x))

What is the first (3sqrt(x))^' ?

The first (3sqrt(x))^' is 3/(2sqrt(x))

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(3 x)^{^{'}}

\frac{3}{2 x}

Solution steps

(3 x)^{'}

Take the constant out:

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

= 3 (x)^{^{'}}

Apply radical rule:

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

= 3 (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{3}{2 x}

\frac{\partial}{\partial x} (y^{2} cos (y))

x \to - 2 lim (x^{3} + 4 x^{2} - 5 x + 1)

n = 2 \sum \infty \frac{1}{4 n ^{2} - 1}

\frac{\partial}{\partial y} (y e^{3 x})