What is the derivative of (x-1/(x^2)^5) ?

The derivative of (x-1/(x^2)^5) is 5(x-1/(x^2))^4(1+2/(x^3))

What is the first derivative of (x-1/(x^2)^5) ?

The first derivative of (x-1/(x^2)^5) is 5(x-1/(x^2))^4(1+2/(x^3))

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\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

5 (x - \frac{1}{x ^{2}})^{4} (1 + \frac{2}{x ^{3}})

Solution steps

\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

Apply the chain rule:

5 (x - \frac{1}{x ^{2}})^{4} \frac{d}{d x} (x - \frac{1}{x ^{2}})

= 5 (x - \frac{1}{x ^{2}})^{4} \frac{d}{d x} (x - \frac{1}{x ^{2}})

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

= 5 (x - \frac{1}{x ^{2}})^{4} (1 + \frac{2}{x ^{3}})

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What is the derivative of (x-1/(x^2)^5) ?
The derivative of (x-1/(x^2)^5) is 5(x-1/(x^2))^4(1+2/(x^3))
What is the first derivative of (x-1/(x^2)^5) ?
The first derivative of (x-1/(x^2)^5) is 5(x-1/(x^2))^4(1+2/(x^3))