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

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

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

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

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

- \frac{3}{2 x}

Solution steps

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

Simplify

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

Simplify

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

= - \frac{3}{2 x}

- \frac{8}{x ^{2}} - \frac{8}{x}

\int_{2}^{3} \frac{20}{3 - x} d x

\frac{\partial}{\partial x} (3 cos (x y))

\frac{1}{( 1 - 3 \cdot x ^{3} ) ^{3}}

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