What is the derivative of f(x)=4x\sqrt[3]{x} ?

The derivative of f(x)=4x\sqrt[3]{x} is (16\sqrt[3]{x})/3

What is the first derivative of f(x)=4x\sqrt[3]{x} ?

The first derivative of f(x)=4x\sqrt[3]{x} is (16\sqrt[3]{x})/3

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derivative of

Solution steps

Simplify

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

f (x) = (3 x + 7)^{2}

\frac{d}{d x} f (x) = (5 x - 5 x^{3}) (7 + x)

x \frac{d y}{d x} + y = \frac{1}{y ^{2}}

\frac{d}{d x} (30 - 80 e^{- 0.8 x})

y d x + (e^{- y} + x) d y = 0

What is the derivative of f(x)=4x\sqrt[3]{x} ?
The derivative of f(x)=4x\sqrt[3]{x} is (16\sqrt[3]{x})/3
What is the first derivative of f(x)=4x\sqrt[3]{x} ?
The first derivative of f(x)=4x\sqrt[3]{x} is (16\sqrt[3]{x})/3