given the function ( f(x)=7x^{2}-7ln x ), find ( f(x) ).\nanswer\n( f(x)= )

Explanation:

Step1: Differentiate (7x^{2})

Using the power rule ((x^n)^\prime = nx^{n - 1}), for (y = 7x^{2}), we have (y^\prime=7\times2x^{2 - 1}=14x).

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}).

Step3: Combine the derivatives

By the sum - difference rule ((u\pm v)^\prime = u^\prime\pm v^\prime), where (u = 7x^{2}) and (v = 7\ln x), (f^\prime(x)=(7x^{2})^\prime-(7\ln x)^\prime).

Answer:

(f^\prime(x)=14x-\frac{7}{x})