Formulas we find in introductory differential calculus
1. Derivative of a constant: The derivative of a constant function is 0. If f(x) = c, where c is a constant, then f'(x) = 0.
2. Power rule: The derivative of a function of the form f(x) = x^n, where n is a constant, is given by f'(x) = nx^(n-1). This rule can be extended to handle functions that involve a constant multiple as well, such as f(x) = cx^n, where c is a constant.
3. Sum/Difference rule: The derivative of a sum or difference of functions is equal to the sum or difference of their derivatives. If f(x) and g(x) are two functions, then (f(x) + g(x))' = f'(x) + g'(x) and (f(x) - g(x))' = f'(x) - g'(x).
4. Product rule: The derivative of a product of two functions is given by the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function. If f(x) and g(x) are two functions, then (f(x) * g(x))' = f'(x)g(x) + f(x)g'(x).
5. Quotient rule: The derivative of a quotient of two functions is given by the denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all divided by the square of the denominator. If f(x) and g(x) are two functions where g(x) is not equal to 0, then (f(x) / g(x))' = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2.
6. Chain rule: The chain rule allows us to find derivatives of composite functions. If h(x) = f(g(x)), where f(x) and g(x) are differentiable functions, then h'(x) = f'(g(x)) * g'(x).
These are some of the basic formulas and rules in introductory differential calculus. There are also rules for trigonometric functions, exponential functions, logarithmic functions, and other more advanced topics.