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

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

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

Answer

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})