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Popular >

derivative of f(x)=sqrt(x)+\sqrt[9]{x}

Solution

derivative of

f (x) = x + 9 x

Solution

\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}}

Solution steps

\frac{d}{d x} (x + 9 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (9 x)

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (9 x) = \frac{1}{9 x ^{\frac{8}{9}}}

= \frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)+\sqrt[9]{x} ?
The derivative of f(x)=sqrt(x)+\sqrt[9]{x} is 1/(2sqrt(x))+1/(9x^{8/9)}
What is the first derivative of f(x)=sqrt(x)+\sqrt[9]{x} ?
The first derivative of f(x)=sqrt(x)+\sqrt[9]{x} is 1/(2sqrt(x))+1/(9x^{8/9)}