What is the derivative of a\sqrt[n]{x}+b\sqrt[3]{x} ?

The derivative of a\sqrt[n]{x}+b\sqrt[3]{x} is (ax^{(1-n)/n})/(n)+b/(3x^{2/3)}

What is the first derivative of a\sqrt[n]{x}+b\sqrt[3]{x} ?

The first derivative of a\sqrt[n]{x}+b\sqrt[3]{x} is (ax^{(1-n)/n})/(n)+b/(3x^{2/3)}

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العربية

\frac{a x ^{\frac{1 - n}{n}}}{n} + \frac{b}{3 x ^{\frac{2}{3}}}

Solution steps

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{a x ^{\frac{1 - n}{n}}}{n} + \frac{b}{3 x ^{\frac{2}{3}}}

What is the derivative of a\sqrt[n]{x}+b\sqrt[3]{x} ?
The derivative of a\sqrt[n]{x}+b\sqrt[3]{x} is (ax^{(1-n)/n})/(n)+b/(3x^{2/3)}
What is the first derivative of a\sqrt[n]{x}+b\sqrt[3]{x} ?
The first derivative of a\sqrt[n]{x}+b\sqrt[3]{x} is (ax^{(1-n)/n})/(n)+b/(3x^{2/3)}