Question

Verify the statement by showing that the derivative of the right side equals the integrand of the left side.

∫(-6/x⁴) dx = 2/x³ + C

Answer 1

The derivative of the right side (-6/x^4) is indeed equal to the integrand on the left side, which is -6/x^4. To verify the statement, we need to find the derivative of the right side and check if it is equal to the integrand on the left side.

Step-by-step explanation:

To verify the statement, we need to find the derivative of the right side and check if it is equal to the integrand on the left side.

The right side of the equation is 2/x³ + C. To find its derivative, we use the power rule: d/dx (x^n) = nx^(n-1).

d/dx(2/x³ + C) = d/dx(2x^(-3) + C) = -6x^(-4) = -6/x^4.

We can see that the derivative of the right side (-6/x^4) is indeed equal to the integrand on the left side, which is -6/x^4.