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GATE 2023 CH – Question 48

Engineering Mathematics · Calculus: Definite and improper integrals, partial and total derivatives, maxima and minima · 2 marks · Numerical answer

The first derivative of the function $U(r) = 4\left[\left(\frac{1}{r}\right)^{12} - \left(\frac{1}{r}\right)^6\right]$ evaluated at $r = 1$ is ______ (in integer).

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Correct answer: -24

Explanation

$U'(r) = 4\left[-12r^{-13} + 6r^{-7}\right]$. At $r = 1$: $4(-12 + 6) = -24$.