Question

find f(x).
f(x) = -15 ln x + 8x² - 7
f(x) = \square

Explanation:

Step1: Differentiate each term separately

Use the rules: \((\ln x)'=\frac{1}{x}\), \((x^n)' = nx^{n - 1}\), and \((c)'=0\) (where \(c\) is a constant).
For \(-15\ln x\): \((-15\ln x)'=-15\times\frac{1}{x}\)
For \(8x^{2}\): \((8x^{2})'=8\times2x\)
For \(-7\): \((-7)' = 0\)

Step2: Combine the derivatives

\(f'(x)=(-15\ln x)'+(8x^{2})'+(-7)'\)
\(f'(x)=-\frac{15}{x}+16x+0\)

Answer:

\(f'(x)=16x-\frac{15}{x}\)