Understanding the Negative 1 in L'Hospital's Rule Differentiation

[MathewsMD]

When using L'Hospital's rule to differentiate this function, why does the second term have a negative 1 multiplying it? Is it not already negative? Is it because of the -h in the expression?

 

[Mark44]

When using L'Hospital's rule to differentiate this function, why does the second term have a negative 1 multiplying it? Is it not already negative? Is it because of the -h in the expression?

Since the limit is on h, that's the variable used in differentiation. So, yes, the -1 comes about from differentiating f(x - h) with respect to h.