What is the derivative of x^7+1/(x^7+7x+7/x+7) ?

The derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7

What is the first derivative of x^7+1/(x^7+7x+7/x+7) ?

The first derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7

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\frac{d}{d x} (x^{7} + \frac{1}{x ^{7}} + 7 x + \frac{7}{x} + 7)

7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

Solution steps

\frac{d}{d x} (x^{7} + \frac{1}{x ^{7}} + 7 x + \frac{7}{x} + 7)

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

\frac{d}{d x} (7 x) = 7

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{x ^{2}}

\frac{d}{d x} (7) = 0

= 7 x^{6} - \frac{7}{x ^{8}} + 7 - \frac{7}{x ^{2}} + 0

Simplify

= 7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

What is the derivative of x^7+1/(x^7+7x+7/x+7) ?
The derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7
What is the first derivative of x^7+1/(x^7+7x+7/x+7) ?
The first derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7