Question

$\frac{d}{dx}12\ln(x) =$

Explanation:

Step1: Apply the constant multiple rule

The constant multiple rule states that if \(y = k\cdot f(x)\), then \(y^\prime=k\cdot f^\prime(x)\). Here \(k = 12\) and \(f(x)=\ln(x)\). So, \(\frac{d}{dx}[12\ln(x)]=12\frac{d}{dx}[\ln(x)]\).

Step2: Differentiate \(\ln(x)\)

The derivative of \(\ln(x)\) with respect to \(x\) is \(\frac{1}{x}\). So, \(12\frac{d}{dx}[\ln(x)] = 12\times\frac{1}{x}\).

Answer:

\(\frac{12}{x}\)