What is the derivative of In\sqrt[3]{6x+4} ?

The derivative of In\sqrt[3]{6x+4} is (2nI)/((6x+4)^{2/3)}

What is the first derivative of In\sqrt[3]{6x+4} ?

The first derivative of In\sqrt[3]{6x+4} is (2nI)/((6x+4)^{2/3)}

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\frac{d}{d x} (I n 3 6 x + 4)

\frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (I n 3 6 x + 4)

Treat

n, I

as a constant

Take the constant out:

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

= I n \frac{d}{d x} (3 6 x + 4)

Apply the chain rule:

\frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x + 4)

= \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x + 4)

\frac{d}{d x} (6 x + 4) = 6

= I n \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \cdot 6

Simplify

I n \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \cdot 6 : \frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

= \frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

What is the derivative of In\sqrt[3]{6x+4} ?
The derivative of In\sqrt[3]{6x+4} is (2nI)/((6x+4)^{2/3)}
What is the first derivative of In\sqrt[3]{6x+4} ?
The first derivative of In\sqrt[3]{6x+4} is (2nI)/((6x+4)^{2/3)}