Question

find f(x). f(x) = 8x^{-7} f(x) = \boxed{}

Explanation:

Step1: Find first derivative \( f'(x) \)

Using power rule \( \frac{d}{dx}(x^n) = nx^{n - 1} \), for \( f(x)=8x^{-7} \), \( f'(x)=8\times(-7)x^{-7 - 1}=-56x^{-8} \)

Step2: Find second derivative \( f''(x) \)

Apply power rule to \( f'(x)=-56x^{-8} \), \( f''(x)=-56\times(-8)x^{-8 - 1}=448x^{-9} \)

Step3: Find third derivative \( f'''(x) \)

Apply power rule to \( f''(x)=448x^{-9} \), \( f'''(x)=448\times(-9)x^{-9 - 1}=-4032x^{-10} \) or \( \frac{-4032}{x^{10}} \)

Answer:

\( -4032x^{-10} \) (or \( \frac{-4032}{x^{10}} \))