Question

1. if $f(x)=3x^{2}+2x$, then $f(x)=$

Explanation:

Step1: Apply power rule

The power rule states that if \(y = ax^{n}\), then \(y^\prime=anx^{n - 1}\). For the term \(3x^{2}\), where \(a = 3\) and \(n=2\), its derivative is \(3\times2x^{2 - 1}=6x\). For the term \(2x\), where \(a = 2\) and \(n = 1\), its derivative is \(2\times1x^{1 - 1}=2\).

Step2: Sum the derivatives

Since \(f(x)=3x^{2}+2x\), by the sum rule of derivatives \((u + v)^\prime=u^\prime+v^\prime\) (where \(u = 3x^{2}\) and \(v = 2x\)), we have \(f^\prime(x)=(3x^{2})^\prime+(2x)^\prime\).

Answer:

\(6x + 2\)