What is the derivative of 6sqrt(x^3) ?

The derivative of 6sqrt(x^3) is 9sqrt(x)

What is the first derivative of 6sqrt(x^3) ?

The first derivative of 6sqrt(x^3) is 9sqrt(x)

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\frac{d}{d x} (6 x^{3})

9 x

Solution steps

\frac{d}{d x} (6 x^{3})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{3})

Apply radical rule:

= 6 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= 6 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

6 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : 9 x

= 9 x

2 x y \frac{d y}{d x} = x^{2} + 2 y^{2}

\int sin (\frac{1}{x}) d x

f (x) = cot^{3} (x)

y = 2 x, y = 3 x - 4, y = 0

x \to 2 lim (\frac{2 x}{3 x + 1})

What is the derivative of 6sqrt(x^3) ?
The derivative of 6sqrt(x^3) is 9sqrt(x)
What is the first derivative of 6sqrt(x^3) ?
The first derivative of 6sqrt(x^3) is 9sqrt(x)