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

The derivative of f(x)=3sqrt(x^3) is (9sqrt(x))/2

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

The first derivative of f(x)=3sqrt(x^3) is (9sqrt(x))/2

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derivative of

f (x) = 3 x^{3}

\frac{9 x}{2}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{9 x}{2}

\int_{0}^{8} - x^{2} + 2 x + 4 d x

f (x) = \frac{4 x}{x + 1}, at x = 3

x \to - 4 lim (\frac{∣ x + 4 ∣}{x + 4})

y = (e^{4 x} - 3)^{8}

\frac{d ^{3}}{d x ^{3}} (2 x^{3} - 4 x^{2} + 2)

What is the derivative of f(x)=3sqrt(x^3) ?
The derivative of f(x)=3sqrt(x^3) is (9sqrt(x))/2
What is the first derivative of f(x)=3sqrt(x^3) ?
The first derivative of f(x)=3sqrt(x^3) is (9sqrt(x))/2