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统计数据
常见 微积分 问题
(\partial)/(\partial x)(cos(w+x)sin(y-z))
∂
∂
x
(
cos
(
w
+
x
)
sin
(
y
−
z
)
)
d/(dt)(3t-2)
d
dt
(
3
t
−
2
)
integral from 0 to 1 of 1/((x+1)(x+2))
∫
0
1
1
(
x
+
1
)
(
x
+
2
)
dx
tangent f(x)=17tan(x),\at x= pi/4
tangent
f
(
x
)
=
1
7
tan
(
x
)
,
at
x
=
π
4
derivative 5x^4sqrt(25-x^2)
derivative
5
x
4
√
2
5
−
x
2
derivative f(x)=(x+2)sqrt(2x-3)
derivative
f
(
x
)
=
(
x
+
2
)
√
2
x
−
3
(\partial)/(\partial y)(((x+y))/((y+z)))
∂
∂
y
(
(
x
+
y
)
(
y
+
z
)
)
(\partial)/(\partial x)(x/(x^6-y^3))
∂
∂
x
(
x
x
6
−
y
3
)
(dy)/(dx)=4x+y,y(0)=9
dy
dx
=
4
x
+
y
,
y
(
0
)
=
9
derivative of x^{16}
d
dx
(
x
1
6
)
y^{''}-2y^'=sin(x)
y
′
′
−
2
y
′
=
sin
(
x
)
integral of x^2(2x-1)^5
∫
x
2
(
2
x
−
1
)
5
dx
derivative of cos(x^6)
d
dx
(
cos
(
x
6
)
)
integral of (\sqrt[3]{x}+sqrt(x^5))/x
∫
3
√
x
+
√
x
5
x
dx
derivative u^4
derivative
u
4
tangent f(x)=(1-x)(x^2-3)^2,\at x=2
tangent
f
(
x
)
=
(
1
−
x
)
(
x
2
−
3
)
2
,
at
x
=
2
limit as x approaches 2+of (2-x)^{x-2}
lim
x
→
2
+
(
(
2
−
x
)
x
−
2
)
3y^{''}-5y^'-14y=0
3
y
′
′
−
5
y
′
−
1
4
y
=
0
integral from 4 to 7 of (x-6)^2
∫
4
7
(
x
−
6
)
2
dx
limit as x approaches 5 of (x^2-9)/(x-3)
lim
x
→
5
(
x
2
−
9
x
−
3
)
y^'-2y=4
y
′
−
2
y
=
4
derivative sin(tan(e^{x^2}))
derivative
sin
(
tan
(
e
x
2
)
)
integral of 1/((s^2+1)^3)
∫
1
(
s
2
+
1
)
3
ds
y^{''}-4y^'+5y=0,y(0)=1,y^'(0)=-1
y
′
′
−
4
y
′
+
5
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
−
1
integral of (x^2)/(x^3+2)
∫
x
2
x
3
+
2
dx
derivative of tan(x^2+1)
d
dx
(
tan
(
x
2
+
1
)
)
derivative 7
derivative
7
y^'+ay+b=0
y
′
+
ay
+
b
=
0
((2-2x)/(2x-x^2+3))^'
(
2
−
2
x
2
x
−
x
2
+
3
)
′
integral of 1/((z^2+x^2)^{3/2)}
∫
1
(
z
2
+
x
2
)
3
2
dx
integral of (100)/(x^2)
∫
1
0
0
x
2
dx
derivative x^2+3x+14
derivative
x
2
+
3
x
+
1
4
integral of x/(sqrt(8+x^2))
∫
x
√
8
+
x
2
dx
面积 y=x,y=x^4,(0,1)
area
y
=
x
,
y
=
x
4
,
(
0
,
1
)
sum from n=1 to infinity of 1/n-1/(n+3)
∑
n
=
1
∞
1
n
−
1
n
+
3
体积about y=0,y=2x^2,y=12x-4x^2,[0,2]
volumeabout
y
=
0
,
y
=
2
x
2
,
y
=
1
2
x
−
4
x
2
,
[
0
,
2
]
((6x+1)y^2)(dy)/(dx)+3x^2+2y^3=0
(
(
6
x
+
1
)
y
2
)
dy
dx
+
3
x
2
+
2
y
3
=
0
limit as x approaches-4 of 0
lim
x
→
−
4
(
0
)
integral from 4 to infinity of e^{3x}
∫
4
∞
e
3
x
dx
integral of tan^5(x)sec^{10}(x)
∫
tan
5
(
x
)
sec
1
0
(
x
)
dx
(dy)/(dx)=(e^{3x})/(y^6)
dy
dx
=
e
3
x
y
6
inverse拉普拉斯 1/(s(s+3))
inverselaplace
1
s
(
s
+
3
)
x^{''}-kx=0
x
′
′
−
kx
=
0
(\partial)/(\partial t)(e^{-2t}cos(pix))
∂
∂
t
(
e
−
2
t
cos
(
π
x
)
)
integral of (13^x)
∫
(
1
3
x
)
dx
limit as x approaches-2 of 3x^3+6x^2+4
lim
x
→
−
2
(
3
x
3
+
6
x
2
+
4
)
5x*(dy)/(dx)=2xe^x-5y+6x^2
5
x
·
dy
dx
=
2
xe
x
−
5
y
+
6
x
2
integral of 3x-sqrt(x)
∫
3
x
−
√
x
dx
integral from 1 to 4 of integral from 1 to sqrt(x of)2ye^{-x}
∫
1
4
∫
1
√
x
2
ye
−
x
dydx
integral of x(x^2+3)^{12}
∫
x
(
x
2
+
3
)
1
2
dx
(\partial)/(\partial y)(x^2-3xy)
∂
∂
y
(
x
2
−
3
xy
)
30y^{''}-25y^'=0
3
0
y
′
′
−
2
5
y
′
=
0
integral of xe^{sqrt(x)}
∫
xe
√
x
dx
integral from 0 to 1 of (e^z+1)/(e^z+z)
∫
0
1
e
z
+
1
e
z
+
z
dz
(dy)/(dx)=40-3y
dy
dx
=
4
0
−
3
y
integral of x^3cos(x^4+1)
∫
x
3
cos
(
x
4
+
1
)
dx
integral of (6+x^9)^5x^8
∫
(
6
+
x
9
)
5
x
8
dx
limit as h approaches infinity of (3h+2xh^2+x^2+h^3)/(4-3xh-2x^3h^3)
lim
h
→
∞
(
3
h
+
2
xh
2
+
x
2
+
h
3
4
−
3
xh
−
2
x
3
h
3
)
derivative of e^{6xsin(2x})
d
dx
(
e
6
x
sin
(
2
x
)
)
limit as x approaches 3 of sin(1/(x-3))
lim
x
→
3
(
sin
(
1
x
−
3
)
)
derivative of (x^2+5^{1/2})
d
dx
(
(
x
2
+
5
)
1
2
)
derivative cos^4(t)-sin^4(t)
derivative
cos
4
(
t
)
−
sin
4
(
t
)
y^'+3y=18x
y
′
+
3
y
=
1
8
x
derivative of-(a^2x/(b^2y))
d
dx
(
−
a
2
x
b
2
y
)
derivative of e^{ax^2}
d
dx
(
e
ax
2
)
integral from 0 to 9 of piy^2
∫
0
9
π
y
2
dy
(\partial)/(\partial x)(x+1/y)
∂
∂
x
(
x
+
1
y
)
((y^4-x^2)dy)/(dx)=-xy
(
y
4
−
x
2
)
dy
dx
=
−
xy
integral of (9+t+t^2)/(sqrt(t))
∫
9
+
t
+
t
2
√
t
dt
integral of sin(x)*e^{cos(x)}
∫
sin
(
x
)
·
e
cos
(
x
)
dx
derivative of (30/(x^4))
d
dx
(
3
0
x
4
)
derivative y=x^2(4x^4+5x^3-16)
derivative
y
=
x
2
(
4
x
4
+
5
x
3
−
1
6
)
(\partial)/(\partial y)(1+x^3+y^3)
∂
∂
y
(
1
+
x
3
+
y
3
)
integral from 1 to 4 of 2/(x^3)
∫
1
4
2
x
3
dx
derivative f(x)=5cot(x/8)
derivative
f
(
x
)
=
5
cot
(
x
8
)
limit as x approaches 0 of x^5ln(x)
lim
x
→
0
(
x
5
ln
(
x
)
)
d/(dy)(x^{y^2})
d
dy
(
x
y
2
)
integral of (3x^2+10x)(x^3+5x^2+6)
∫
(
3
x
2
+
1
0
x
)
(
x
3
+
5
x
2
+
6
)
dx
(dy)/(dx)=(y-x+1)^2+1
dy
dx
=
(
y
−
x
+
1
)
2
+
1
limit as x approaches 0 of 0/(x^3)
lim
x
→
0
(
0
x
3
)
y^'=3-y/(1000)
y
′
=
3
−
y
1
0
0
0
derivative y=49.99sin(x/(5.0073))+49.99
derivative
y
=
4
9
.
9
9
sin
(
x
5
.
0
0
7
3
)
+
4
9
.
9
9
derivative of ((2-x^2)/((2+x)))
d
dx
(
(
2
−
x
)
2
(
2
+
x
)
)
limit as x approaches 0 of 1/(x^2+x)-1/x
lim
x
→
0
(
1
x
2
+
x
−
1
x
)
limit as x approaches-5 of ((x^2+6x+5))/(x^2+4x-5)
lim
x
→
−
5
(
(
x
2
+
6
x
+
5
)
x
2
+
4
x
−
5
)
y^'=3y+2
y
′
=
3
y
+
2
integral of y(x+y)
∫
y
(
x
+
y
)
dy
integral of 1/((121-x^2)^{3/2)}
∫
1
(
1
2
1
−
x
2
)
3
2
dx
limit as x approaches 0+of x^{8/x}
lim
x
→
0
+
(
x
8
x
)
derivative x^2sin(8x)
derivative
x
2
sin
(
8
x
)
y^{''}-4y=0
y
′
′
−
4
y
=
0
integral of (x^{3/2}+6)^8sqrt(x)
∫
(
x
3
2
+
6
)
8
√
x
dx
(\partial)/(\partial x)(10sqrt(xy))
∂
∂
x
(
1
0
√
xy
)
derivative of |x^2-4|
d
dx
(
|
x
2
−
4
|
)
derivative of sin(xsin(y)sin(x+y))
d
dx
(
sin
(
x
)
sin
(
y
)
sin
(
x
+
y
)
)
limit as x approaches 2 of x^3f(x)
lim
x
→
2
(
x
3
f
(
x
)
)
sum from n=1 to infinity of ((-1)^n)/(5(2^{n+2))}
∑
n
=
1
∞
(
−
1
)
n
5
(
2
n
+
2
)
limit as x approaches 1+of 7/(1-x)
lim
x
→
1
+
(
7
1
−
x
)
derivative y=4-3x
derivative
y
=
4
−
3
x
(\partial)/(\partial x)(e^{-2x}cos(8y))
∂
∂
x
(
e
−
2
x
cos
(
8
y
)
)
1
..
1216
1217
1218
1219
1220
..
2459