Question

Найти производную сложной функции у=(7х^4-5х^3+2х)^2

Answer 1

$y=(7x^4-5x^3+2x)^2=u^2\\u=u(x); ,; ; (u^2)'=2ucdot u'; ,; ; u=7x^4-5x^3+2x\\y'=2(7x^4-5x^3+2)cdot (7x^4-5x^3+2x)'=\\=2(7x^4-5x^3+2x)cdot (28x^3-15x^2+2)$

Answer 2

$y=left(7x^4-5x^3+2xright)^2\ y'=2cdotleft(7x^4-5x^3+2xright)cdotleft(28x^3-15x^2+2right)=\ =2left(196x^7-105x^6+14x^4-140x^6+75x^5-10x^3+56x^3-30x^2+4xright)=\ =2cdotleft(196x^7-245x^6+75x^5+14x^4+46x^3-30x^2+4xright)=\ =392x^7-490x^6+150x^5+28x^4+92x^3-60x^2+8x$