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统计数据
常见 微积分 问题
面积 y=10x,y=x^2-11
area
y
=
1
0
x
,
y
=
x
2
−
1
1
integral of x(2x+1)
∫
x
(
2
x
+
1
)
dx
(\partial)/(\partial y)(msin(2(mx+ny)))
∂
∂
y
(
m
sin
(
2
(
mx
+
ny
)
)
)
tangent y= 1/(3t),(2, 1/6)
tangent
y
=
1
3
t
,
(
2
,
1
6
)
integral of x*cos^2(x)
∫
x
·
cos
2
(
x
)
dx
麦克劳林 g(x)= x/(x-1)
maclaurin
g
(
x
)
=
x
x
−
1
f^{''}(x)= 6/x
f
′
′
(
x
)
=
6
x
limit as x approaches 0 of 1-2sin^2(x/2)
lim
x
→
0
(
1
−
2
sin
2
(
x
2
)
)
limit as x approaches 1+of sqrt(2x-2)-2
lim
x
→
1
+
(
√
2
x
−
2
−
2
)
integral of (6x+5)/(sqrt(3x^2+5x))
∫
6
x
+
5
√
3
x
2
+
5
x
dx
integral from 3 to 5 of 1/(sqrt(x^2-9))
∫
3
5
1
√
x
2
−
9
dx
derivative f(x)=(x^3-10x)(3x^2+4x)
derivative
f
(
x
)
=
(
x
3
−
1
0
x
)
(
3
x
2
+
4
x
)
面积 y=x^2ln(x),y=4ln(x)
area
y
=
x
2
ln
(
x
)
,
y
=
4
ln
(
x
)
derivative of (e^{2x}\sqrt[3]{x^3+1})
d
dx
(
(
e
2
x
)
3
√
x
3
+
1
)
derivative of e^{(x+2/(x-2)})
d
dx
(
e
x
+
2
x
−
2
)
integral from-8 to 8 of (4x^9+7x^5)
∫
−
8
8
(
4
x
9
+
7
x
5
)
dx
tangent y=((x+5)^5)/(7x-5)
tangent
y
=
(
x
+
5
)
5
7
x
−
5
integral from 0 to 6 of 2pix(6x-x^2)
∫
0
6
2
π
x
(
6
x
−
x
2
)
dx
derivative of cos^2(x-cos(x))
d
dx
(
cos
2
(
x
)
−
cos
(
x
)
)
derivative of m(m-1x^{m-2})
d
dx
(
m
(
m
−
1
)
x
m
−
2
)
derivative of arctan(1)
d
dx
(
arctan
(
1
)
)
integral of (1-x^{3/2})^{5/3}*sqrt(x)
∫
(
1
−
x
3
2
)
5
3
·
√
x
dx
derivative of sin((5x^2+8^8))
d
dx
(
sin
(
(
5
x
2
+
8
)
8
)
)
limit as x approaches infinity of 5x-1
lim
x
→
∞
(
5
x
−
1
)
derivative sqrt(2t^2-t)
derivative
√
2
t
2
−
t
derivative of x-inx
d
dx
(
x
−
inx
)
laplace变换 te^{-0.003t}cos(10t)
laplacetransform
te
−
0
.
0
0
3
t
cos
(
1
0
t
)
integral from 0 to 1 of 1/((x+1)(x^2+1))
∫
0
1
1
(
x
+
1
)
(
x
2
+
1
)
dx
tangent f(x)=x^4+8x^3+2x+2,\at x=1
tangent
f
(
x
)
=
x
4
+
8
x
3
+
2
x
+
2
,
at
x
=
1
(\partial)/(\partial x)((12x)/(x+y))
∂
∂
x
(
1
2
x
x
+
y
)
derivative f(x)=(-x^3+x^2+x)cos(x)
derivative
f
(
x
)
=
(
−
x
3
+
x
2
+
x
)
cos
(
x
)
integral of x^2-2x+1
∫
x
2
−
2
x
+
1
dx
integral of x^{2k}
∫
x
2
k
dx
integral of 1/(x+6)
∫
1
x
+
6
dx
(\partial)/(\partial x)(x^{-2})
∂
∂
x
(
x
−
2
)
integral of x^{-0.9}
∫
x
−
0
.
9
dx
泰勒 (1-x)e^{x+(x^2)/2+(x^3)/3}
taylor
(
1
−
x
)
e
x
+
x
2
2
+
x
3
3
integral of sin(ln(u))
∫
sin
(
ln
(
u
)
)
du
y^{''}-y=5sin(2t)(0)1
y
′
′
−
y
=
5
sin
(
2
t
)
(
0
)
1
泰勒 1/(2+3x)
taylor
1
2
+
3
x
y^'=y+x,y(0)=-1
y
′
=
y
+
x
,
y
(
0
)
=
−
1
derivative r/(sqrt(r^2+1))
derivative
r
√
r
2
+
1
integral of (-0.5x+450)
∫
(
−
0
.
5
x
+
4
5
0
)
dx
(dy)/(dx)=4x-5
dy
dx
=
4
x
−
5
limit as x approaches 0 of (x)^{tan(x)}
lim
x
→
0
(
(
x
)
tan
(
x
)
)
(\partial)/(\partial x)(y/(x^2+y^2+z^2))
∂
∂
x
(
y
x
2
+
y
2
+
z
2
)
斜率 y=sqrt(7x+1),(5,6)
slope
y
=
√
7
x
+
1
,
(
5
,
6
)
(\partial)/(\partial x)(xye^{x-2z})
∂
∂
x
(
xye
x
−
2
z
)
(\partial)/(\partial x)(A+B*cos(x)sin(y))
∂
∂
x
(
A
+
B
·
cos
(
x
)
sin
(
y
)
)
(dx)/(dt)=x^{2/3}
dx
dt
=
x
2
3
inverse拉普拉斯 1/(4s^2)
inverselaplace
1
4
s
2
y^'-y=3te^{2t},y(0)=1
y
′
−
y
=
3
te
2
t
,
y
(
0
)
=
1
derivative 2sin(t)
derivative
2
sin
(
t
)
(\partial)/(\partial x)(ye^{(x/y)})
∂
∂
x
(
ye
(
x
y
)
)
(d^2)/(dx^2)((x^2-4x)/(x+1))
d
2
dx
2
(
x
2
−
4
x
x
+
1
)
derivative of 3x^2sqrt(5x+3)
d
dx
(
3
x
2
√
5
x
+
3
)
tangent f(x)=sqrt(2-10x),\at x=-1
tangent
f
(
x
)
=
√
2
−
1
0
x
,
at
x
=
−
1
integral of (7x)
∫
(
7
x
)
dx
derivative of \sqrt[3]{sin(x})
d
dx
(
3
√
sin
(
x
)
)
integral of 1/(1+u^2)
∫
1
1
+
u
2
du
integral of (x^3)/((1+x^4))
∫
x
3
(
1
+
x
4
)
dx
limit as x approaches 0 of x^2+x-3
lim
x
→
0
(
x
2
+
x
−
3
)
integral from 0 to 1 of 2piy(y-y^2)
∫
0
1
2
π
y
(
y
−
y
2
)
dy
(\partial)/(\partial x)(sin(pixy))
∂
∂
x
(
sin
(
pixy
)
)
integral of (2+5x^4)x^3
∫
(
2
+
5
x
4
)
x
3
dx
integral of 1/(xsqrt(400x^2-400))
∫
1
x
√
4
0
0
x
2
−
4
0
0
dx
integral of 1/(x^3-8)
∫
1
x
3
−
8
dx
derivative f(x)=(7x^2-11x)e^x
derivative
f
(
x
)
=
(
7
x
2
−
1
1
x
)
e
x
(\partial)/(\partial z)(x-z-arctan(yz))
∂
∂
z
(
x
−
z
−
arctan
(
yz
)
)
integral of 6xsec(x)tan(x)
∫
6
x
sec
(
x
)
tan
(
x
)
dx
derivative of 60x^4-180x^3+180x^2-60x
d
dx
(
6
0
x
4
−
1
8
0
x
3
+
1
8
0
x
2
−
6
0
x
)
derivative of ln(x^2+10)
d
dx
(
ln
(
x
2
+
1
0
)
)
d/(dt)(10000(12+t)e^{-0.05t})
d
dt
(
1
0
0
0
0
(
1
2
+
t
)
e
−
0
.
0
5
t
)
integral of 5/((3x-1))
∫
5
(
3
x
−
1
)
dx
derivative of e^{60x+50x^2}
d
dx
(
e
6
0
x
+
5
0
x
2
)
(dy)/(dx)=(y^3-x^3)/(xy^2)
dy
dx
=
y
3
−
x
3
xy
2
derivative 2log_{5}(x)
derivative
2
log
5
(
x
)
limit as x approaches 6 of (10)(-5)
lim
x
→
6
(
(
1
0
)
(
−
5
)
)
integral of 1/(sqrt(3))
∫
1
√
3
integral of 1/2 x^{-2}
∫
1
2
x
−
2
dx
derivative 8cos(4x)
derivative
8
cos
(
4
x
)
integral of a^{nx}
∫
a
nx
dx
derivative of e^{x+6}
d
dx
(
e
x
+
6
)
f(x)=ln(x^2+5)
f
(
x
)
=
ln
(
x
2
+
5
)
y^{''}-36y=e^{6x}
y
′
′
−
3
6
y
=
e
6
x
derivative of tan(x^2+tan^2(x))
d
dx
(
tan
(
x
2
)
+
tan
2
(
x
)
)
y^'-2y=e^{3t}
y
′
−
2
y
=
e
3
t
derivative-6/x
derivative
−
6
x
sum from n=0 to infinity of ((-1)x^n)/n
∑
n
=
0
∞
(
−
1
)
x
n
n
(\partial)/(\partial v)(v/2)
∂
∂
v
(
v
2
)
2sin(2x)dx+3e^{3y}dy=2xdx
2
sin
(
2
x
)
dx
+
3
e
3
y
dy
=
2
xdx
integral from-2 to-1 of x^2-x-2
∫
−
2
−
1
x
2
−
x
−
2
dx
(dy)/(dx)=(3x+2y)/(3x+2y+2)
dy
dx
=
3
x
+
2
y
3
x
+
2
y
+
2
y^{''}+7y^'+10y=-4sin(3t)
y
′
′
+
7
y
′
+
1
0
y
=
−
4
sin
(
3
t
)
derivative sin^2(3x)
derivative
sin
2
(
3
x
)
tangent f(x)=(6x-2)^{1/4},\at x=1
tangent
f
(
x
)
=
(
6
x
−
2
)
1
4
,
at
x
=
1
derivative 8/t
derivative
8
t
integral of xsin(x)cos(x)
∫
x
sin
(
x
)
cos
(
x
)
dx
derivative of (2-x^2)
d
dx
(
(
2
−
x
)
2
)
(\partial)/(\partial x)(4xy-10x^2y^2z+5z^2)
∂
∂
x
(
4
xy
−
1
0
x
2
y
2
z
+
5
z
2
)
1
..
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1224
1225
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1227
..
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