What is the derivative of x^{52}-1/(x^2) ?

The derivative of x^{52}-1/(x^2) is 52x^{51}+2/(x^3)

What is the first derivative of x^{52}-1/(x^2) ?

The first derivative of x^{52}-1/(x^2) is 52x^{51}+2/(x^3)

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\frac{d}{d x} (x^{52} - \frac{1}{x ^{2}})

52 x^{51} + \frac{2}{x ^{3}}

Solution steps

\frac{d}{d x} (x^{52} - \frac{1}{x ^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{52}) - \frac{d}{d x} (\frac{1}{x ^{2}})

\frac{d}{d x} (x^{52}) = 52 x^{51}

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= 52 x^{51} - (- \frac{2}{x ^{3}})

Simplify

= 52 x^{51} + \frac{2}{x ^{3}}

What is the derivative of x^{52}-1/(x^2) ?
The derivative of x^{52}-1/(x^2) is 52x^{51}+2/(x^3)
What is the first derivative of x^{52}-1/(x^2) ?
The first derivative of x^{52}-1/(x^2) is 52x^{51}+2/(x^3)