Question

let ( g(x)=3 x^{4}-7 ln (x) ).
( g^{prime}(x)= )

Explanation:

Step1: Differentiate \(3x^4\)

Using the power rule \((x^n)^\prime = nx^{n - 1}\), for \(y = 3x^4\), we have \(y^\prime=3\times4x^{4 - 1}=12x^3\).

Step2: Differentiate \(-7\ln(x)\)

Using the formula \((\ln x)^\prime=\frac{1}{x}\), for \(y=-7\ln(x)\), we have \(y^\prime=-7\times\frac{1}{x}=-\frac{7}{x}\).

Answer:

\(12x^3-\frac{7}{x}\)