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

The derivative of f(x)=x^5+1/(x^5) is 5x^4-5/(x^6)

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

The first derivative of f(x)=x^5+1/(x^5) is 5x^4-5/(x^6)

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derivative of

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

5 x^{4} - \frac{5}{x ^{6}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

= 5 x^{4} - \frac{5}{x ^{6}}

What is the derivative of f(x)=x^5+1/(x^5) ?
The derivative of f(x)=x^5+1/(x^5) is 5x^4-5/(x^6)
What is the first derivative of f(x)=x^5+1/(x^5) ?
The first derivative of f(x)=x^5+1/(x^5) is 5x^4-5/(x^6)