Basic Formulas for Differentiation in Calculus:
1.)Constant Rule: The derivative of a constant function, such as f(x) = c, where c is a constant, is zero: f'(x) = 0.
2.)Power Rule: The derivative of a function raised to a power, such as f(x) = x^n, where n is a constant, is given by: f'(x) = nx^(n-1).
3.)Sum Rule: The derivative of the sum of two functions, such as f(x) = g(x) + h(x), is equal to the sum of their derivatives: f'(x) = g'(x) + h'(x).
4.)Product Rule: The derivative of the product of two functions, such as f(x) = g(x)h(x), is given by: f'(x) = g'(x)h(x) + g(x)h'(x).
5.)Quotient Rule: The derivative of the quotient of two functions, such as f(x) = g(x)/h(x), is given by: f'(x) = (h(x)g'(x) - g(x)h'(x))/(h(x))^2.
6.)Chain Rule: The chain rule states that the derivative of a composite function, such as f(x) = g(h(x)), is given by: f'(x) = g'(h(x))h'(x).
These basic formulas for differentiation provide a foundation for further study in calculus and are used to find the derivatives of a wide range of functions in various fields, including physics, engineering, and economics. Understanding these formulas is important for solving optimization problems, finding maximum and minimum points, and solving differential equations.