Найти производную сложной функции y =5sin²x
ответ: 5sin2x
Объяснение: y =5sin²x u =sinx y =5u²
y'ₓ = y'u *u'ₓ = 5*2u*(sinx) '=10u*cosx= 10sinx*cosx = 5sin2x
- - - - - - - или ( усложняем )
y =5sin²x = 5(1 -cos2x) /2 = 5/2 - (5/2) cos2x
y ' = (5/2 - (5/2)cos2x) = (5/2) ' - (5/2)*(cos2x) ' = - (5/2)*(cos2x) '
нужно найти (cos2x) '
y₁ =cosu u =2x y₁'ₓ = y'u *u'ₓ = (-sinu)*(2x)ₓ' = - 2sinu = -2sin2x
y ' = (-5/2)*(-2sin2x) = 5sin2x
1) ac2-ad+c3-cd-bc2+bd= = (ac2 – ad) + (c3 –
bc2) + (bd – cd) = a·(c2 – d) + c2·(c – b) + d·(b – c) = a·(c2 – d) +
c2·(c – b) – d·(c – b) = a·(c2 – d) + c2·(c – b) – d·(c – b) = a·(c2 –
d) + (c – b)·(c2 – d) = (c2 – d)·(a + c – b)
2) mx2+my2-nx2-ny2+n-m= x2 ( m - n ) + y2 ( m - n ) - ( m - n ) = ( m-n ) (x2 + y2 - 1 )
3) am2+cm2-an+an2-cn+cn2= m2 (a + c ) + n2 ( a + c ) - n ( a + c ) = ( a+ c) ( m2 + n2 - n)
4) xy2-ny2-mx+mn+m2x-m2n= y2 ( x - n ) + m2 ( x - n) - m ( x - n ) = ( x-n) ( y2 + m2 - m )
5) a2b+a+ab2+b+2ab+2=ab ( a + b + 2 ) + ( a+ b+ 2 ) = 2 ( a+ b + 2 )
6) x2-xy+x-xy2+y3-y2= x ( x – y + 1) – y 2 ( x – y + 1)=( x – y + 1)( x – y 2 ).
