What is the derivative of f(x)=4sqrt(x^3) ?

The derivative of f(x)=4sqrt(x^3) is 6sqrt(x)

What is the first derivative of f(x)=4sqrt(x^3) ?

The first derivative of f(x)=4sqrt(x^3) is 6sqrt(x)

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derivative of

f (x) = 4 x^{3}

6 x

Solution steps

\frac{d}{d x} (4 x^{3})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{3})

Apply radical rule:

n a^{m} = a^{\frac{m}{n}}

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

Apply the Power Rule:

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

= 4 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

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

= 6 x

\frac{d}{d x} (ln (1 + x y))

\int 30 (x + 7) (x + 5)^{4} d x

x \to 8 lim (\frac{8 x}{x - 8})

y^{^{'}} = (1 - 2 t) y^{2}, y (0) = - \frac{1}{6}

\int x^{3} x^{2} + 24 d x

What is the derivative of f(x)=4sqrt(x^3) ?
The derivative of f(x)=4sqrt(x^3) is 6sqrt(x)
What is the first derivative of f(x)=4sqrt(x^3) ?
The first derivative of f(x)=4sqrt(x^3) is 6sqrt(x)