Question

h(x)=(4x + 1)^2
how would you rewrite h(x) so it can be differentiated usi
power rule?
choose 1 answer:
a 16x^2 + 8x + 1
b (4x + 1)/((4x + 1)^-1)
c (4x + 1)(4x + 1)
d this is not possible.

Explanation:

Step1: Expand the expression

Use the formula \((a + b)^2=a^{2}+2ab + b^{2}\), where \(a = 4x\) and \(b = 1\).

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