An Introduction to the Derivative Difference Rule in Calculus – Finding the Derivative of the Difference of Two Functions

derivative difference rule, h(x)= f(x) – g(x)

The derivative difference rule is a differentiation rule that allows us to find the derivative of a function that is the difference of two other functions

The derivative difference rule is a differentiation rule that allows us to find the derivative of a function that is the difference of two other functions. Suppose we have two functions, f(x) and g(x), and we want to find the derivative of their difference h(x) = f(x) – g(x).

To find the derivative of h(x), we can apply the derivative rules for sums and differences. According to these rules, the derivative of a sum or difference of two functions is equal to the sum or difference of their individual derivatives.

So, using the derivative rules, we can write:

h'(x) = (f(x) – g(x))’

Now, to find the derivative of f(x) – g(x), we differentiate each term separately. The derivative of f(x) with respect to x is denoted as f'(x), and the derivative of g(x) with respect to x is denoted as g'(x).

Therefore, we can rewrite the above equation as:

h'(x) = f'(x) – g'(x)

So, the derivative of h(x) = f(x) – g(x) is h'(x) = f'(x) – g'(x).

In simpler words, when you have two functions subtracted from each other, the derivative of their difference is the difference of their derivatives.

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