Mathematics

The key is to test the claim by differentiating—if $F(x)$ is truly an antiderivative of $f(x)$, then $F'(x)$ must equal $f(x)$. Use the power rule or quotient rule to find the derivative of $\frac{1}{x}$ and compare it to $\frac{1}{x^2}$. If they don't match, you'll need to adjust $F(x)$ and verify your correction by differentiating again.

The key is to test the claim by differentiating—if $F(x)$ is truly an antiderivative of $f(x)$, then $F'(x)$ must equal $f(x)$. Use the power rule or quotient rule to find the derivative of $\frac{1}{x}$ and compare it to $\frac{1}{x^2}$. If they don't match, you'll need to adjust $F(x)$ and verify your correction by differentiating again.