Question

f(x)=2x^4+8/3x^3 найти производную функции

Answer 1

$f(x)=\frac{2x^{4}+8 }{3x^{3} }\\\\f'(x)=\frac{(2x^{4}+8)'*3x^{3}-(2x^{4}+8)*(3x^{3})'}{(3x^{3})^{2}}=\frac{8x^{3}*3x^{3} -(2x^{4}+8)*9x^{2}}{9x^{6} }=\frac{24x^{3}-18x^{6}-72x^{2}}{9x^{6}}=\frac{3x^{2}(8x-6x^{4}-24)}{9x^{6} }=\frac{8x-6x^{4}-24 }{3x^{4} }$