Question

Найти производную функции:

1) (√x)sin4x

2) (1+cosx)/sinx

3) (√3x)/3^x+1

4)(x²-2x+3)/x²+4x+1

Answer 1

1)sin4x/2√x +4√x *cos4x=(sin4x+8x*cos4x)/2√x
2)(-sin²x-six-sincosx)/sin²x=-1-1/sinx-ctgx
3)[38(3^x +1)/2√3x - 3^x *√3x]/(3^x +1)²=3(3^x +1-6x*3^x)/2√3x(3^x +1)²
4)[(2x-2)(x²+4x+1)-(2x+4)(x²-2x+3)]/(x²+4x+1)²=
=(2x³+8x²+2x-2x²-8x-2-2x³+4x²-6x-4x²+8x-12)/(x²+4x+1)²=(6x²-4x-14)/(x²+4x+1)²