cos to the third power x sin to the third power x to find the monotonic interval

f(x)=cos³x+sin³x，f'(x)=3cos²x(-sinx)+3sin²x(cosx)=3sinxcosx(sinx-cosx)，f'(x)=0, i.e. x=k+2, or x=k+4, kz, x (2k, 4+2k), sinx>0, cosx>0, sinx-cosx<0, so f'(x) <0, f(x) monotonically decreasing;

x ( 4+2k , 2+2k ), sinx>0, cosx>0, sinx-cosx>0, so f'(x) >0, f(x) monotonically increasing;

x ( 2+2k , 2k ), sinx>0, cosx<0, sinx-cosx>0, so f'(x) <0, f(x) monotonically decreasing;

x ( 2k ,5 4+2k ),sinx<0,cosx<0,sinx-cosx>0,so f'(x) >0, f(x) monotonically increasing;

x(5 4+2k ,3 2+2k ),sinx<0,cosx<0,sinx-cosx<0, so f'(x) <0, f(x) monotonically decreasing;

x(3 2+2k ,2 +2k ),sinx<0,cosx>0,sinx-cosx<0,so f'(x) >0, f(x) monotonically increasing;

y=(sinx)^4+(cosx)^4

sinx)^2+(cosx)^2]^2-2(sinxcosx)^2

1-1/2*(sin2x)^2

1-1/4*2(sin2x)^2

1-1/4(1-cos4x)

3 source tremor 4+1 4*cos4x

When 4x [2k - 2k ],x [(2k-1) volt only 4,k 2], the monotonous hail hall defeat increases.

y=(sinx)^4+(cosx)^4

sinx)^2+(cosx)^2]^2-2(sinxcosx)^2

1-1 Jean Oak 2*(sin2x) 2

1-1/4*2(sin2x)^2

1-1 Frank 4 (1-cos4x).

3/4+1/4*cos4x

When 4x [2k - 2k], x [(2k-1) 4, k 2], the single Ruchang tone increases.

sinx 4-cosx 4=(sinx 2+cosx 2):auspicious*(lead sinx 2-cosx 2)=sinx 2-cosx 2=-cos2x

This function increments the Huai drain on (- 2+2k, 2k) (k z).

Derivative, obtainable (cos(sinx)).'sin(sinx)cosxwhen x (2k, 2k), sinx>0, sin(sinx)>0 when beats nucleus x (-2k, 2k), sinx "zen only 0, sin(sinx)<0

When x (-2+2k, 2+2k), cosx>0, when x (2+2k, 3 2+2k), cosx<0 can be combined to get the result (it is too troublesome to type out - just understand the idea.

y=x-x^3

y'=1-3x 2=-3(x+root3 3)(x-root3 3)when-root3 3 x root3 chainfield 3, y'0, monotonous increase;

When x-root number 3 canopy shouts 3, or x root number 3 3, y'0, monotonous minus bright hall.

y=sinx+cosxy'=cosx-sinx= 2[ 2cosx- 2 2sinx]= 2cos(x+ 4) Find the monotonically increasing interval y below'>=0,2k - 2 x + 4 2k + 2 2k -3 4 x 2k + 4 monotonically increasing band cultivation interval [2k -3 4 ,2k + stupid only 4] The following is the monotonically decreasing interval.