Find the derivative of the function f by using the rules of differentiation. f(x)=(1+2 x^2)^2+2

step 1 Now, let's solve exercise 20. In this exercise, we want to find the derivative of the function o

Find the derivative of the function f by using the rules of...

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Key Concepts

Power Rule

The power rule is a fundamental differentiation technique used to find the derivative of functions in the form f(x) = x^n, where n is any real number. Its rule states that the derivative is n*x^(n-1), allowing an easy and direct computation of derivatives for polynomial terms.

Chain Rule

The chain rule is used to differentiate composite functions, where one function is nested inside another. It states that the derivative of a composite function f(g(x)) is f'(g(x)) multiplied by g'(x). This rule is essential for handling cases where functions are raised to a power or composed with other functions.

Sum Rule

The sum rule in differentiation states that the derivative of the sum of two or more functions is equal to the sum of their individual derivatives. This rule simplifies the process of differentiation when dealing with functions that are added together.

Constant Multiple Rule

The constant multiple rule indicates that if a function is multiplied by a constant, its derivative is simply that constant multiplied by the derivative of the function. This allows constants to be factored out before the differentiation process, streamlining the calculation.

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