What is the derivative of 8(x-3^{2/3}) ?

The derivative of 8(x-3^{2/3}) is (16)/(3(x-3)^{1/3)}

What is the first derivative of 8(x-3^{2/3}) ?

The first derivative of 8(x-3^{2/3}) is (16)/(3(x-3)^{1/3)}

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

\frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x - 3) = 1

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

Simplify

8 \cdot \frac{2}{3 ( x - 3 ) ^{\frac{1}{3}}} \cdot 1 : \frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

= \frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

What is the derivative of 8(x-3^{2/3}) ?
The derivative of 8(x-3^{2/3}) is (16)/(3(x-3)^{1/3)}
What is the first derivative of 8(x-3^{2/3}) ?
The first derivative of 8(x-3^{2/3}) is (16)/(3(x-3)^{1/3)}