h(x)=(4x + 1)^2\nhow would you rewrite h(x) so it can be differentiated usi\npower rule?\nchoose 1…

Explanation:

Step1: Expand the expression

Use the formula ((a + b)^2=a^{2}+2ab + b^{2}), where (a = 4x) and (b = 1). [ \begin{align*} (4x + 1)^2&=(4x)^2+2\times(4x)\times1+1^2\ &=16x^{2}+8x + 1 \end{align*} ]

Step2: Check power - rule applicability

The power rule for differentiation is (\frac{d}{dx}(x^{n})=nx^{n - 1}). For the function (y=16x^{2}+8x + 1), we can differentiate each term separately. The derivative of (16x^{2}) using the power rule is (16\times2x^{2-1}=32x), the derivative of (8x) is (8\times1x^{1 - 1}=8) and the derivative of the constant (1) is (0).

Answer:

A. (16x^{2}+8x + 1)