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

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

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

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

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derivative of

\frac{3 x}{x}

\frac{3}{2 x}

Solution steps

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

Simplify

\frac{3 x}{x} : 3 x

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

Take the constant out:

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

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

Apply radical rule:

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

= 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{3}{2 x}

\int - x^{3} - 8 x + 5 d x

x \to 0 lim (\frac{1}{x + x ^{5}})

2 x^{2} - x^{3}, y = 0

\int - \frac{3}{2} x^{2} d x

\int (tan (\frac{x}{18}))^{5} d x

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