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Popular Calculus >

derivative of sqrt(x)+\sqrt[8]{x}

Solution

derivative of

x + 8 x

Solution

\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}}

Solution steps

\frac{d}{d x} (x + 8 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (8 x)

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

\frac{d}{d x} (8 x) = \frac{1}{8 x ^{\frac{7}{8}}}

= \frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+\sqrt[8]{x} ?
The derivative of sqrt(x)+\sqrt[8]{x} is 1/(2sqrt(x))+1/(8x^{7/8)}
What is the first derivative of sqrt(x)+\sqrt[8]{x} ?
The first derivative of sqrt(x)+\sqrt[8]{x} is 1/(2sqrt(x))+1/(8x^{7/8)}