What is the derivative of 4*\sqrt[3]{x+8} ?

The derivative of 4*\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}

What is the first derivative of 4*\sqrt[3]{x+8} ?

The first derivative of 4*\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}

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\frac{d}{d x} (4 \cdot 3 x + 8)

\frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (4 3 x + 8)

Take the constant out:

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

= 4 \frac{d}{d x} (3 x + 8)

Apply the chain rule:

\frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (x + 8)

= \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 4 \cdot \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \cdot 1

Simplify

4 \cdot \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \cdot 1 : \frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

= \frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

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

\int \frac{3 x}{π} cos (n x) d x

x \to 0 lim (e^{x} + 7)

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

\int sin^{2} (x) cos^{4} (x) d x

What is the derivative of 4*\sqrt[3]{x+8} ?
The derivative of 4*\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}
What is the first derivative of 4*\sqrt[3]{x+8} ?
The first derivative of 4*\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}