Question

1.Найти прозводную функции: а)3x+1; б)4x^2-6x; в)(4x+3x)^6; г)x^2+5/x-2; д)2x^3-1/x; е)e^x*sinx

Answer 1

1) f'(x) = 3
2) f'(x) = 8x - 6
3) f'(x) = 6(4x + 3x)^5 * (4x + 3x)' = 6(4x + 3x)^5 * 7 = 42(4x + 3x)^5
4) f'(x) = 2x + ((5')(x - 2) - (x - 2)'5)/(x - 2)^2 = 2x - 5/(x - 2)^2
5) f'(x) = 6x^2 + 1/x^2
6) f'(x) = (e^x)'(sinx) + (sinx)'(e^x) = e^x(sinx + cosx)

Answer 2

а)3
б)8х-6
в)6(4x+3x)^5(4+3)
г) 2х-5/(х-2)^2
д)6x^2+1/x^2
e) хз)