Question

найдите производную функции y=x^7-4/x^6

Answer 1

$1)\; \; y=x^7-\frac{4}{x^6}\\\\y'=7x^6-\frac{-4\cdot (x^6)'}{(x^6)^2}=7x^6+\frac{4\cdot 6x^5}{x^{12}}=7x^6+\frac{24}{x^7}\\\\\\2)\; \; y=\frac{x^7-4}{x^6}\\\\y'=\frac{7x^6\cdot x^6-(x^7-4)\cdot 6x^5}{(x^6)^2}=\frac{7x^{12}-6x^{12}+24x^5}{x^{12}}=\frac{x^{12}+24x^5}{x^{12}}=\frac{x^7+24}{x^7}=1+\frac{24}{x^7}$