Question

1)y=3cos^2(x)  - ctg (x/2)+5

2)y=(1/4) * x^4 - 5x^2+2*sqrt(2x+5) (sqrt - корень)
Надо найти производную функции)

Answer 1

1)y`=(3cos²x - ctg (x/2)+5)`=3·2·cosx·(cosx)`-(-1/sin²(x/2))·(x/2)`+(5)`=

= - 6·sinx·cosx+(1/(2·sin²(x/2)))+0=-3sin2x + (1/(2sin²(x/2)))

2)y`=((1/4)· x⁴ - 5x²+2·√(2x+5))`=(1/4)·( x⁴)`-5(x²)`+2·(√(2x+5))`=

=(1/4)·4x³-5·2x+2·(1/2√(2x+5))·(2x+5)`=x³-10x+2/√(2x+5).