MATH 1P97 Lecture Notes - Lecture 10: Constant Function, Power Rule, Differentiable Function

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P97
• Professor: Sandra Yee

Document Summary

Differentiation is used to find the derivative of a function without doing the tedious work of using the definition of the derivative. This is done by using the notation d/dx [f(x)] The derivative of f " w/ respect to x at x. The derivative of a constant function is always equal to zero. B/c if f(n) is a straight line, the slope is 0, therefore the tangent line would also be equal to zero. If n is any real number, then d/dx (x^n)= nx^n-1. Rule 4: the derivative of a constant multiple of a function. The derivative of a constant multiplied by a differentiable function, is equal to the constant multiplied by the derivative of the function. The derivative of the sum (difference) of two differentiable functions, is equal to the sum (difference) of their derivatives. If f(x)= x^3 - 3x^2 + 1.