What is the derivative of 4x\sqrt[3]{x^4} ?

The derivative of 4x\sqrt[3]{x^4} is 4(x\sqrt[3]{x}+(4x^{4/3})/3)

What is the first derivative of 4x\sqrt[3]{x^4} ?

The first derivative of 4x\sqrt[3]{x^4} is 4(x\sqrt[3]{x}+(4x^{4/3})/3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 3 x^{4}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (3 x^{4}) = \frac{4 x ^{\frac{1}{3}}}{3}

= 4 (1 \cdot 3 x^{4} + \frac{4 x ^{\frac{1}{3}}}{3} x)

Simplify

4 (1 \cdot 3 x^{4} + \frac{4 x ^{\frac{1}{3}}}{3} x) : 4 (x 3 x + \frac{4 x ^{\frac{4}{3}}}{3})

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

\int \frac{x ^{2}}{( 9 - 25 x ^{2} ) ^{\frac{5}{2}}} d x

\frac{1 - x}{1 + x}

\frac{d}{d x} (\frac{1}{5} e^{x})

x \to 2 lim (\frac{2 ^{x} - 4}{x - 2})

y = e^{x}, y = x, x = 0, x = 2

What is the derivative of 4x\sqrt[3]{x^4} ?
The derivative of 4x\sqrt[3]{x^4} is 4(x\sqrt[3]{x}+(4x^{4/3})/3)
What is the first derivative of 4x\sqrt[3]{x^4} ?
The first derivative of 4x\sqrt[3]{x^4} is 4(x\sqrt[3]{x}+(4x^{4/3})/3)