# Find the derivative of $x^5(3-6x^{-9})$

By Leibnitz product rule
$f'(x) =x^5 \large\frac{d}{dx}$$(3-6x^{-9})+(3-6x^{-9}) \large\frac{d}{dx}$$(x^5)$
$= x^5 \{0-6(-9)x^{-9-1} \}+ (3-6x^{-9})(5x^4)$
$= x^5 (54x^{-10})+15x^4-30x^{-5}$
$= 54x^{-5}+15x^4-30x^{-5}$
$= 24x^{-5}+15x^4$
$= 15x^4+ \large\frac{24}{x^5}$