Найдите производную функции: y=(5x^3)/(4-x^2)

Question

Найдите производную функции: y=(5x^3)/(4-x^2)

Answer 1

y=(5x^3)/(4-x^2);
y'=((5x^3)'(4-x^2)-(5x^3)(4-x^2)')/(4-x^2)^2=((15x^2)(4-x^2)-(5x^3)(-2x))/(4-x^2)^2=(60x^2-15x^4+10x^4)/(4-x^2)^2=(60x^2-5x^4)/(4-x^2)^2=x^2(60-5x^2)/(4-x^2)^2=-x^2(5x^2-60)/(x^4-8x^2+16)