Question

calcule as derivadas a seguir aplicando a regra sa cadeia: y=(5x²-18x³+4x)^7

Answer 1

derivada de $\boxed{\boxed{(u^n )^' = n*u^{n-1} * u'}}$

aplicando isso
$]y = (5x^2-18x^3+4x)^7\\\\y' = 7*(5x^2-18x^3+4x)^{7-1}*(5x^2-18x^3+4x)'\\\\y'=7*(5x^2-18x^3+4x)^6 *(5*2x^{2-1}-18*3x^{3-1}+4x^{1-1})\\\\ y'=7*(5x^2-18x^3+4x)^6*(10x-54x^2+4)\\\\ \boxed{\boxed{y'=(5x^2-18x^3+4x)^6*(70x-738x^2+14)}}$