Question

What is the first derivative of this function?

Should the quotient rule be used as well as product rule?

(It is 8x^5 +3, in case it’s not clear above)

Answer 1

`\bf \cfrac{-9x^2}{8x^5+3}\implies \stackrel{\textit{using the quotient rule}}{\cfrac{(-18x)(8x^5+3)~~-~~(-9x^2)(40x^4)}{(8x^5+3)^2}} \\\\\\ \cfrac{(-144x^6-54x)~~-~~(-360x^6)}{(8x^5+3)^2}\implies \cfrac{-144x^6-54x~~+~~360x^6}{(8x^5+3)^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{216x^6-54x}{64x^(10)+48x^5+9}~\hfill`