Understanding the Basics | Four Derivative Rules in Calculus for Calculating Rates of Change

What are the four basic derivative rules?

The four basic derivative rules in calculus are:

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The four basic derivative rules in calculus are:

1. Power Rule: This rule is used when taking the derivative of a function with a variable raised to a power. If we have a function f(x) = x^n, where n is a constant, then the derivative f'(x) is given by f'(x) = nx^(n-1). For example, if f(x) = x^2, then f'(x) = 2x.

2. Constant Rule: This rule is used when taking the derivative of a constant value. If a function f(x) = c, where c is a constant, then the derivative f'(x) is equal to 0. Any constant value has a derivative of zero since it does not change with respect to x.

3. Sum/Difference Rule: This rule is used when taking the derivative of a sum or difference of functions. If we have two functions f(x) and g(x), then the derivative of their sum or difference f(x) ± g(x) is equal to the sum or difference of their derivatives, respectively. Mathematically, (f ± g)'(x) = f'(x) ± g'(x).

4. Product Rule: This rule is used when taking the derivative of a product of two functions. If we have two functions f(x) and g(x), then the derivative of their product f(x)g(x) is given by the product rule as (f(x)g(x))’ = f'(x)g(x) + f(x)g'(x).

These four basic derivative rules are crucial in the field of calculus as they allow us to find the rate of change of a function, which helps in solving a variety of real-life problems.

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