Question

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

Answer 1

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

Answer 2

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