What is the derivative of f(x)=x^{1/5}+8 ?

The derivative of f(x)=x^{1/5}+8 is 1/(5x^{4/5)}

What is the first derivative of f(x)=x^{1/5}+8 ?

The first derivative of f(x)=x^{1/5}+8 is 1/(5x^{4/5)}

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derivative of

f (x) = x^{\frac{1}{5}} + 8

\frac{1}{5 x ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{1}{5}} + 8)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{1}{5}}) + \frac{d}{d x} (8)

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

\frac{d}{d x} (8) = 0

= \frac{1}{5 x ^{\frac{4}{5}}} + 0

Simplify

= \frac{1}{5 x ^{\frac{4}{5}}}

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What is the derivative of f(x)=x^{1/5}+8 ?
The derivative of f(x)=x^{1/5}+8 is 1/(5x^{4/5)}
What is the first derivative of f(x)=x^{1/5}+8 ?
The first derivative of f(x)=x^{1/5}+8 is 1/(5x^{4/5)}