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csc2x
y= lncosx/ sinx的导数是什么?
答:
-2
csc2x
解题过程如下:y=lncotx =lncosx/sinx =lncosx-lnsinx =-sinx/cosx-cosx/sinx =-(sin^2x+cosx^2)/sinxcosx =-1/sinxcosx =-2/2sinxcosx =-2/sin2x =-2csc2x
∫sec^4x dx ∫sec^
2x
tan^2x dx
答:
sec^4x =sec^
2x
*(1/cos^2x )=sec^2x *tan^2x *(1/sin^2x )=sec^2x *tan^2x *
csc
^2x 所以原题∫sec^4x dx =∫sec^2x tan^2x *csc^2x dx
tanx分之secx^2的积分怎么求
答:
因为 sec²x * dx = d(tanx),那么:∫sec²x * dx/tanx =∫d(tanx)/tanx =ln|tanx| + C
二重积分比大小,x+y=4这条切线怎么算出
答:
∫ cos2x / (sin²x * cos²x) dx = ∫ cos2x / (1/2 * sin2x)² dx = 4∫ cos2x / (sin²2x) dx = 4∫
csc2x
* cot2x dx = -2∫ csc2x * cot2x d(2x)= -2csc2x + C = -2/(sin2x) + C = -secx*cscx + C ...
1/cosxsinxdx不定积分
答:
∫ dx/(cosxsinx) dx = ∫ dx/[(1/2)sin2x]= ∫
csc2x
d(2x)= ∫ cscz dz,z = 2x = ∫ cscz * (cscz - cotz)/(cscz - cotz) dz = ∫ (csc²z - csczcotz)/(cscz - cotz) dz = ∫ d(cscz - cotz)/(cscz - cotz)= ln| cscz - cotz | + C = ln| csc...
求证: sina/(
csc
^
2x
-1)=1
答:
(1)sin^
2x
/(sec^2x-1)+cos^2x/(
csc
^2x-1)=sin^2x/tan^2x+cos^2x/cot^2x =cos^2x+sin^2x =1 (2)题目出错了,不等于1的 (3)①cos(A+B)=cos(π-C)=-cosC ②sin(2A+2B)=sin[2(A+B)]=sin[2(π-C)]=sin(2π-2C)=-sin2C ③cos(2A+2B)=cos[2(A+B)]=cos...
f(sinx+1/sinx)=
csc
^
2x
-cos^2x 求f(x)
答:
f(sinx+1/sinx)=
csc
^
2x
-cos^2x =1/sin^2x-cos^2x =1/sin^2x-(1-sin^2x)=1/sin^2x+sin^2x-1 =1/sin^2x+2+sin^2x-1-2 =(sinx+1/sinx)^2-3 f(x)=x^2-3
已知函数f(x)=2sinx+cosx-2
csc
^
2x
求f(x)=?
答:
-2
csc
^
2x
cotx y′=(csc^2x)′=[(sinx)^-2]′=-2(sinx)^-3*sinx′=-2(sinx)^-3*cosx =-2(sinx)^-2*cotx =-2csc^2xcotx
tanx*(-
csc
^
2x
)/(1/x)求导 答案是x/cosx*sinx
答:
y=tanx*(-(cscx)^2)/(1/x)=xtanx*(-(tanx)^2-1)=-x(tanx)^3-xtanx y'=-(tanx)^3-3x(tanx)^2(secx)^2-tanx-x(secx)^2
已知函数f(x)=sin^
2x
+
csc
^2x+cos^2x+sec^2x+tan...
答:
f(x)=sin^
2x
+
csc
^2x+cos^2x+sec^2x+tan^2x+7cot^2x = sin^2x+cos^2x+tan^2x+7cot^2x+sec^2x+csc^2x =1+ tan^2x+7cot^2x+1+ tan^2x+1+ cot^2x =3+2 tan^2x+8cot^2x =3+2 tan^2x+8/ tan^2x 设tan^2x=t,x∈(0,π/4]则t∈(0,1].2 tan^2x+8/ tan^2x=2t...
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