What is the derivative of ab\sqrt[5]{x^3} ?

The derivative of ab\sqrt[5]{x^3} is (3ab)/(5x^{2/5)}

What is the first derivative of ab\sqrt[5]{x^3} ?

The first derivative of ab\sqrt[5]{x^3} is (3ab)/(5x^{2/5)}

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\frac{3 ab}{5 x ^{\frac{2}{5}}}

Solution steps

Take the constant out:

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

Apply the chain rule:

\frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{3})

= \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{3})

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

= ab \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \cdot 3 x^{2}

Simplify

ab \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \cdot 3 x^{2} : \frac{3 ab}{5 x ^{\frac{2}{5}}}

= \frac{3 ab}{5 x ^{\frac{2}{5}}}

What is the derivative of ab\sqrt[5]{x^3} ?
The derivative of ab\sqrt[5]{x^3} is (3ab)/(5x^{2/5)}
What is the first derivative of ab\sqrt[5]{x^3} ?
The first derivative of ab\sqrt[5]{x^3} is (3ab)/(5x^{2/5)}