Find the rules for the composite functionsfogandgof f(x)=5x2+7x+9;g(x)=x+10 fog= gof= Composite Function: The formation of a new function by the combination of two functions is called the composite function. The composition of two function...
The chain rule of differentiation means creating a chain of derivatives. This rule is applied to the composition of functions. The composite function can be made from two or more than two functions. The chain rule formula for composite function {eq}f(g(x)) {/eq} is written as: $$\dfr...
Applying the Rules of Differentiation to Calculate Derivatives: If a function is in a product of two-factor form, then we apply the product rule of differentiation to find the derivative function. For example, if we have a function like {eq}u(x)\cdot v(x){/eq}, then...
The power rule states: {eq}(x^n)' = nx^{n-1} {/eq} The chain rule states: {eq}\left( f(g(x) \right)' = f'(g(x)) \cdot g'(x) {/eq} Answer and Explanation: Learn more about this topic: Applying the Rules of Differentiation to Calculate Derivatives ...
Using the rules of finding domain, the domain of f(x) is obtained by solving x - 1 ≥ 0. Then we get x ≥ 1. Thus, the domain is [1, ∞). Range of a square root is always the set of all non-negative numbers. Thus, the range is [0, ∞). ...
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