Possible derivation:
d/dx(y) = d/dx(1/2 cos(2 x)-x)
The derivative of y is zero:
0 = d/dx(-x+1/2 cos(2 x))
Differentiate the sum term by term and factor out constants:
0 = (d/dx(cos(2 x)))/2-d/dx(x)
The derivative of x is 1:
0 = 1/2 (d/dx(cos(2 x)))-1
Using the chain rule, d/dx(cos(2 x)) = ( dcos(u))/( du) ( du)/( dx), where u = 2 x and ( d)/( du)(cos(u)) = -sin(u):
0 = -1+1/2-d/dx(2 x) sin(2 x)
Factor out constants:
0 = -1-1/2 sin(2 x) 2 d/dx(x)
Simplify the expression:
0 = -1-(d/dx(x)) sin(2 x)
The derivative of x is 1:
Answer: |
| 0 = -1-1 sin(2 x)
Вектор АВ(9;-3) длина √(81+9)=√90
Вектор АС(7;-9)
S = 1/2 ABxAC= 1/2*|(9*(-9)-(-3)*7)|=30
Она же равна СD * AB /2
CD= 60/√90=2√10
Cos6x+√2cos(3π/2-3x)=1
1-2sin²3x-√2sin3x-1=0
2sin²3x+√2sin3x=0
sin3x*(2sin3x+√2)=0
sin3x=0⇒3x=πn⇒x=πn/3
sin3x=-√2/2⇒3x=(-1)^(n+1)*π/4+πk⇒x=(-1)^(n+1)*π/12+πk/3,k∈z
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