Question

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

∫(-9/x⁴)dx= 3/x³ + C
_____ ______
d/dx(3/x³+C)=d/dx(3x______+C)= (_____)x = /x_______

Answer 1

The verification involves taking the derivative of the right side of the equation, applying the power rule for differentiation, and showing that it is equal to the integrand of the left side, confirming that the original statement is correct.

Step-by-step explanation:

To verify the statement, we need to confirm that the derivative of the right side equals the integrand of the left side. The statement in question is ∫(-9/x4)dx = 3/x3 + C. To verify this, let's find the derivative d/dx(3/x3 + C).

Applying the power rule for differentiation, we have:

d/dx(3/x3 + C) = d/dx(3x-3 + C).

Now, differentiating term by term, we get:

d/dx(3x-3) = -9x-4,

and the derivative of the constant C is 0, so:

d/dx(C) = 0.

Therefore, the derivative of the right side is:

d/dx(3/x3 + C) = -9x-4 + 0 = (-9)4.

This shows that the derivative of the right side of the statement is indeed -9/x4, thus verifying that the derivative of the right side equals the integrand of the left side as needed.