Deferenciate x3-2/x3-2

May 15, 2026Mathematics

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Answer

\frac{dy}{dx} = 3x^2 + \frac{6}{x^4}

3 steps

To differentiate $y = x^3 - \frac{2}{x^3} - 2$ with respect to $x$ , we can rewrite the expression using negative exponents.

Rewrite the function.
$y = x^3 - 2x^{-3} - 2$
Apply the power rule for differentiation, $\frac{d}{dx}(x^n) = nx^{n-1}$ , and the rule that the derivative of a constant is 0.
$\frac{dy}{dx} = \frac{d}{dx}(x^3) - \frac{d}{dx}(2x^{-3}) - \frac{d}{dx}(2)$ $\frac{dy}{dx} = 3x^{3-1} - 2(-3)x^{-3-1} - 0$ $\frac{dy}{dx} = 3x^2 + 6x^{-4}$
Rewrite the term with the negative exponent as a fraction.
$\frac{dy}{dx} = \boxed{3x^2 + \frac{6}{x^4}}$