![]() ![]() Step 1: Differentiate the outer function. However, the technique can be applied to a wide variety of functions with any outer exponential function (like x 32 or x 99. ![]() This section shows how to differentiate the function y = 3x + 1 2 using the chain rule. The more times you apply the chain rule to different problems, the easier it becomes to recognize how to apply the rule. That’s it! Chain rule examples: Exponential Functionsĭifferentiating using the chain rule usually involves a little intuition. Step 4: Multiply Step 3 by the outer function’s derivative. The derivative of x 4 – 37 is 4x (4-1) – 0, which is also 4x 3. Step 3: Differentiate the inner function. Step 2:Differentiate the outer function first. The outer function is √, which is also the same as the rational exponent ½. The inner function is the one inside the parentheses: x 4 -37. Step 1: Identify the inner and outer functions.įor an example, let the composite function be y = √(x 4 – 37). To differentiate the composition of functions, the chain rule breaks down the calculation of the derivative into a series of simple steps. This indicates that the function f(x), the inner function, must be calculated before the value of g(x), the outer function, can be found. The composition g (f (x)), which is also written as (g ∘ f) (x), would be (x 2-3) 2. For example, let’s say you had the functions: When you apply one function to the results of another function, you create a composition of functions. What’s needed is a simpler, more intuitive approach! That isn’t much help, unless you’re already very familiar with it. ![]()
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