Answer
Find the integral of the equation on the left (Left side / LS). Then differentiate the equation on the right (Reft side / RS). Ensure integrating the equation on the left is equal to differentiating the equation on the right.
$f(x) = \frac{2}{x^{3}}+C$
$f'(x) = -\frac{6}{x^{4}}$
Work Step by Step
1. Left side (integrate)
$\int (-\frac{6}{x^{4}})dx$
$\int (-6x^{-4})dx$
$f(x) = \frac{-6x^{(-4)+(1)}}{(-4)+(1)}$
$f(x) =\frac{-6x^{-3}}{-3}$
$f(x) =2x^{-3}$
$f(x) = \frac{2}{x^{3}}+C$
Therefore, $RS = LS$
2. Right side (derivative)
$f(x) = \frac{2}{x^{3}} + C$
$f(x) = 2x^{-3} + C$
$f'(x) = (-3)(2x^{(-3)-(1)}) + 0$
$f'(x) = -6x^{-4}$
$f'(x) = -\frac{6}{x^{4}}$
Therefore, $LS = RS$
