3.3 Derivatives of Composite Functions: The Chain Rule
faculty.atu.edu › mfinan › 2243where f(x) and g(x) are two di erentiable functions. Theorem 3.3.1 If f and g are di erentiable then f(g(x)) is di erentiable with derivative given by the formula d dx f(g(x)) = f 0(g(x)) g (x): This result is known as the chain rule. Thus, the derivative of f(g(x)) is the derivative of f(x) evaluated at g(x) times the derivative of g(x): Proof ...
8.2 Derivatives of Combinations of Functions
math.mit.edu › classes › 18Now suppose g(f(x)) = 0 over an interval containing x. We can then apply the chain rule to find (g(f(x)))' = 0' = 0 = g'(f) * f '(x), and this equation will determine f ' in terms of f. This is actually the general idea used above to evaluate the derivatives both of and h-1 (the reciprocal and the inverse functions to h).
Product rule - Math
https://www.math.net/product-ruleGiven the product of two functions, f (x)g (x), the derivative of the product of those two functions can be denoted as (f (x)·g (x))'. Another way that the derivative is denoted is . The function does not necessarily have to be a function of x, so these are often abbreviated as (f · g)' or , where the apostrophe (') indicates a derivative:
Derivative Rules - mathsisfun.com
https://www.mathsisfun.com/calculus/derivatives-rules.htmlThe Derivative tells us the slope of a function at any point.. There are rules we can follow to find many derivatives.. For example: The slope of a constant value (like 3) is always 0; The slope of a line like 2x is 2, or 3x is 3 etc; and so on. Here are useful rules to help you work out the derivatives of many functions (with examples below).Note: the little mark ’ means derivative of, and ...