Question

Производная сложной функции
1) f(x)=$(3x^{2} -6x)cosx$
2) f(x)=$\frac{6 x^{2} -8}{3 x^{2} +4}$

Answer 1

1)f`(x)=(6x-6)cosx-(3x²-6xsinx
2)f`(x)=[12x(3x²+4)-6x(6x²-8)]/(3x²+4)²=(36x³+48x-36x³+48x)/(3x²+4)²=96x/(3x²+4)²

Answer 2

1) (3x*2-6x)'cosx+(3x*2-6x)cos'X=(6x-6)cosx-sinx(3x*2-6x)
2)(6x*2-8)'(3x*2+4)-(6x*2-8)(3x*2+4)'/(3x*2+4)*2=12x(3x*2+4)-6x(6x*2-8)/3x*2+4)*2=36x*3+48x-36x*3+48x/3x*2+4)*2=96x/(3x*2+4)*2