Find y^' (a) by applying the Product Rule and (b) by multiplying the factors to produce a sum of

step 1 In this question we are given the y equal to x square plus 1 times with the x plus 5 and plus 1

Find y^' (a) by applying the Product Rule and (b) by...

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Key Concepts

Product Rule

The product rule is a fundamental technique in differentiation used when computing the derivative of a product of two functions. It states that the derivative of f(x)g(x) is f'(x)g(x) + f(x)g'(x), allowing one to handle situations where two functions multiply together.

Algebraic Expansion

Algebraic expansion refers to the process of multiplying out products to rewrite an expression as a sum of simpler terms. This method simplifies differentiation because once the expression is expanded, each term can be differentiated independently using basic differentiation rules.

Power Rule

The power rule is a basic rule in differentiation that applies to functions of the form x^n. It states that the derivative of x^n is n*x^(n-1). This rule is essential for differentiating polynomial terms and expressions involving powers of x.

Linearity of Differentiation

The principle of linearity in differentiation indicates that the derivative operator distributes over sums and differences. This means that the derivative of a sum is equal to the sum of the derivatives, which simplifies the process of differentiating functions term by term after expansion.

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