Question

Вычислите производную
Ln(x^3+4x^2-9/2x^4)

Answer 1

(Ln(x^3+4x^2-9/2x^4))' = (2x^4)/(x^3+4x^2-9) * (x^3+4x^2-9/2x^4)'=
 = (2x^4)/(x^3+4x^2-9) *( (3х² +8х)*2х^4 - (x^3 +4x^2 -9)*8x³ )/4x^8=
= (2x^4)/(x^3+4x^2-9) * (6x^6 +16x^5 -8x^6 -32x^5 +72x^3)/4x^8=
=  (2x^4)/(x^3+4x^2-9) *( -2x^6 -16x^5 +72x^3)/4x^8