Answer:
[tex]f'(x)=2x+\dfrac{12}{x^4}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2-\dfrac{4}{x^3}+9[/tex]
Apply exponent rule [tex]\dfrac{1}{a^b}=a^{-b}[/tex]:
[tex]\implies f(x)=x^2-4x^{-3}+9[/tex]
Differentiate using the power rule [tex]\frac{d}{dx}(x^a)=a \cdot x^{a-1}[/tex] :
[tex]\implies f'(x)=2 \cdot x^{2-1}-(-3)4x^{-3-1}+0[/tex]
[tex]\implies f'(x)=2x+12x^{-4}[/tex]
[tex]\implies f'(x)=2x+\dfrac{12}{x^4}[/tex]
