Find the derivative of the function. Use Example 7 as a model. Function Rewrite Diff

step 1 In this question we have to differentiate the function that is y equals to x square plus 2x divi

Find the derivative of the function. Use Example 7 as a...

Find the derivative of the function. Use Example 7 as a model.
$$\begin{array}{ll}{\text { Function }} & {\text { Rewrite}} & {\text { Differentiate}} & {\text { Simplify}} \\{y=\frac{x^{2}+2 x}{x}} \end{array}$$

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Key Concepts

Linearity of Differentiation

The linearity of differentiation states that the derivative of the sum or difference of functions is equal to the sum or difference of their derivatives. Additionally, a constant factor can be taken outside the differentiation process. This principle simplifies the calculation of derivatives for functions expressed as combinations of simpler functions.

Differentiation

Differentiation is the process of finding the derivative of a function, which represents the rate at which the function's value changes with respect to changes in its independent variable. This concept is central to calculus and is used to analyze the behavior of functions.

Algebraic Manipulation

Algebraic manipulation involves rewriting and simplifying expressions before applying calculus techniques. By decomposing a complex expression into simpler parts or canceling common factors, one can make the process of differentiation more straightforward.

Power Rule

The power rule is a basic rule in differentiation used to differentiate functions of the form x raised to a power. It states that the derivative of x^n is n multiplied by x raised to the power of (n-1), and is one of the most frequently used methods when dealing with polynomial terms.

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