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统计数据
常见 微积分 问题
(\partial)/(\partial t)(s^2t)
∂
∂
t
(
s
2
t
)
sum from n=2 to infinity of e^{3-6n}
∑
n
=
2
∞
e
3
−
6
n
derivative of 3/(2x+7)
d
dx
(
3
2
x
+
7
)
integral from-2 to 2 of (10)/(x^2-2x-24)
∫
−
2
2
1
0
x
2
−
2
x
−
2
4
dx
integral of-e^x
∫
−
e
x
dx
f(x)=1-2cos(x)
f
(
x
)
=
1
−
2
cos
(
x
)
integral of (2x^3)/3
∫
2
x
3
3
dx
integral of cot(x/9)
∫
cot
(
x
9
)
dx
derivative x/((x^2+sqrt(3x))^5)
derivative
x
(
x
2
+
√
3
x
)
5
limit as x approaches-1 of x^2-x-2
lim
x
→
−
1
(
x
2
−
x
−
2
)
limit as x approaches 7 of sec((pix)/6)
lim
x
→
7
(
sec
(
π
x
6
)
)
tangent x^2-2x-3
tangent
x
2
−
2
x
−
3
(dy)/(dx)=(2x)/(x^2-9)
dy
dx
=
2
x
x
2
−
9
(\partial)/(\partial x)(xe^{xy}cos(2x))
∂
∂
x
(
xe
xy
cos
(
2
x
)
)
limit as x approaches infinity of xn(x)
lim
x
→
∞
(
xn
(
x
)
)
integral from 0 to 3.5 of 130x
∫
0
3
.
5
1
3
0
xdx
integral from 0 to 2 of (-x^2+2x)^2
∫
0
2
(
−
x
2
+
2
x
)
2
dx
integral of t^{-2}
∫
t
−
2
dt
laplace变换 2(t-3)^2
laplacetransform
2
(
t
−
3
)
2
tangent f(x)=x^4-3x^2+2,\at x=1
tangent
f
(
x
)
=
x
4
−
3
x
2
+
2
,
at
x
=
1
derivative of 7+cot(x-2csc(x))
d
dx
(
7
+
cot
(
x
)
−
2
csc
(
x
)
)
integral of 2/x+sec^2(x)
∫
2
x
+
sec
2
(
x
)
dx
integral from 0 to 2 of t^2
∫
0
2
t
2
dt
d/(dt)(4/3 pit^3)
d
dt
(
4
3
π
t
3
)
(\partial)/(\partial t)(6e^xt+xt)
∂
∂
t
(
6
e
x
t
+
xt
)
(dy}{dx}=\frac{x^7-2y)/x
dy
dx
=
x
7
−
2
y
x
integral from 0 to 2 of x^3-2x^2
∫
0
2
x
3
−
2
x
2
dx
derivative of (3x/(x+2))
d
dx
(
3
x
x
+
2
)
limit as x approaches 2-of (x+3)/(x-2)
lim
x
→
2
−
(
x
+
3
x
−
2
)
integral of (sin^2(2x))(cos^4(2x))
∫
(
sin
2
(
2
x
)
)
(
cos
4
(
2
x
)
)
dx
derivative x^2-8
derivative
x
2
−
8
integral of (tan^2(x)+cot^2(x)+2)
∫
(
tan
2
(
x
)
+
cot
2
(
x
)
+
2
)
dx
integral of (40)/(x^2+25)
∫
4
0
x
2
+
2
5
dx
derivative of 3x^2cos(x)
d
dx
(
3
x
2
cos
(
x
)
)
(dy)/(dx)=(y-1)^2+0.01
dy
dx
=
(
y
−
1
)
2
+
0
.
0
1
derivative h(x)=(-3x+2)^4(-2x+3)^3
derivative
h
(
x
)
=
(
−
3
x
+
2
)
4
(
−
2
x
+
3
)
3
integral of t^2sin(β)t
∫
t
2
sin
(
β
)
tdt
integral of csc(x)cot(x)
∫
csc
(
x
)
cot
(
x
)
dx
derivative f(x)=-8xsin(4x^2+1)
derivative
f
(
x
)
=
−
8
x
sin
(
4
x
2
+
1
)
derivative y= 1/(\sqrt[4]{3x^2+7)}
derivative
y
=
1
4
√
3
x
2
+
7
derivative of-{f}(xsin(x)+{g}(x)cos(x))
d
dx
(
−
f
(
x
)
sin
(
x
)
+
g
(
x
)
cos
(
x
)
)
integral of (x+3)/(sqrt(5-4x-x^2))
∫
x
+
3
√
5
−
4
x
−
x
2
dx
(d^2)/(dx^2)(((x+b)(x-a))/((x-b)))
d
2
dx
2
(
(
x
+
b
)
(
x
−
a
)
(
x
−
b
)
)
(cos(x)sin(x)-xy^22)dx+y(1-x^2)dy=0
(
cos
(
x
)
sin
(
x
)
−
xy
2
2
)
dx
+
y
(
1
−
x
2
)
dy
=
0
derivative (3x)/(2-cot(x))
derivative
3
x
2
−
cot
(
x
)
d/(d{z)}(e^{3{x}+4{y}}cos(5{z}))
d
d
z
(
e
3
x
+
4
y
cos
(
5
z
)
)
derivative ((e^x))/(3x^4)
derivative
(
e
x
)
3
x
4
integral of tan^5(5x)(sec^3(5x)-1)
∫
tan
5
(
5
x
)
(
sec
3
(
5
x
)
−
1
)
dx
(\partial)/(\partial x)(y*ln(x^4+y^4+1)-8)
∂
∂
x
(
y
·
ln
(
x
4
+
y
4
+
1
)
−
8
)
limit as x approaches 0 of ((343+x)^{1/3}-7)/((x))
lim
x
→
0
(
(
3
4
3
+
x
)
1
3
−
7
(
x
)
)
integral of (5x+2)/((x-5)(x+5)(x-1))
∫
5
x
+
2
(
x
−
5
)
(
x
+
5
)
(
x
−
1
)
dx
derivative of (xy^3/(x^2+y^2))
d
dx
(
xy
3
x
2
+
y
2
)
integral of sqrt(x^2+4x+5)
∫
√
x
2
+
4
x
+
5
dx
(\partial)/(\partial x)((9x+2y)^5)
∂
∂
x
(
(
9
x
+
2
y
)
5
)
integral from t-1 to t of (1-t+x)*x
∫
t
−
1
t
(
1
−
t
+
x
)
·
xdx
integral from 0 to 1/4 of 2arcsin(4y)
∫
0
1
4
2
arcsin
(
4
y
)
dy
integral of sin((pix^2)/2)
∫
sin
(
π
x
2
2
)
dx
derivative f(x)=(x+3)/(x-3)
derivative
f
(
x
)
=
x
+
3
x
−
3
integral of e^x(x^2-2x+2)
∫
e
x
(
x
2
−
2
x
+
2
)
dx
derivative arctan(x^4)
derivative
arctan
(
x
4
)
derivative y= 1/(x+1)+1
derivative
y
=
1
x
+
1
+
1
derivative of sin(1+x^2)
d
dx
(
sin
(
1
+
x
2
)
)
y^{''}+2y^'+5y=e^{-x}sec(2x)
y
′
′
+
2
y
′
+
5
y
=
e
−
x
sec
(
2
x
)
(d^2)/(dx^2)(6csc(x))
d
2
dx
2
(
6
csc
(
x
)
)
derivative of xsinh(x^2)
d
dx
(
x
sinh
(
x
2
)
)
integral of 1/(x^3sqrt(x^2-16))
∫
1
x
3
√
x
2
−
1
6
dx
derivative f(x)=sin(2x)+2cos(x)
derivative
f
(
x
)
=
sin
(
2
x
)
+
2
cos
(
x
)
limit as x approaches-4-of |x+4|-2x
lim
x
→
−
4
−
(
|
x
+
4
|
−
2
x
)
integral from 120 to 150 of e^{-x/(100)}
∫
1
2
0
1
5
0
e
−
x
1
0
0
dx
integral from 1 to infinity of 2/(x^2)
∫
1
∞
2
x
2
dx
integral of x(x+5)^{21}
∫
x
(
x
+
5
)
2
1
dx
sum from x=0 to infinity of 1/(x^{0.51)}
∑
x
=
0
∞
1
x
0
.
5
1
integral of sin(7x)cos(2x)
∫
sin
(
7
x
)
cos
(
2
x
)
dx
(\partial)/(\partial y)(x-x^2y^2)
∂
∂
y
(
x
−
x
2
y
2
)
integral of 8x^4-5x^3+4x^2+C
∫
8
x
4
−
5
x
3
+
4
x
2
+
Cdx
derivative \sqrt[3]{t^2}+2sqrt(t^3)
derivative
3
√
t
2
+
2
√
t
3
integral from 0 to 1 of (2x)/((x^2+2)^2)
∫
0
1
2
x
(
x
2
+
2
)
2
dx
(\partial)/(\partial y)(8e^xln(y))
∂
∂
y
(
8
e
x
ln
(
y
)
)
(\partial)/(\partial x)(7e^{5x})
∂
∂
x
(
7
e
5
x
)
f(x)=e^{x^2-4}
f
(
x
)
=
e
x
2
−
4
limit as x approaches 2 of (x+3)^2
lim
x
→
2
(
(
x
+
3
)
2
)
derivative ln(x+e)
derivative
ln
(
x
+
e
)
(\partial)/(\partial v)(13.12+0.6215T-11.37v^{0.16}+0.3965Tv^{0.16})
∂
∂
v
(
1
3
.
1
2
+
0
.
6
2
1
5
T
−
1
1
.
3
7
v
0
.
1
6
+
0
.
3
9
6
5
Tv
0
.
1
6
)
(\partial)/(\partial x)(x^2+y^2-4y)
∂
∂
x
(
x
2
+
y
2
−
4
y
)
limit as x approaches 2 of 5^2-4x+1
lim
x
→
2
(
5
2
−
4
x
+
1
)
sum from n=0 to infinity of 2*(4/5)^n
∑
n
=
0
∞
2
·
(
4
5
)
n
面积 y=9-x^2,y=-8x
area
y
=
9
−
x
2
,
y
=
−
8
x
derivative (2x)/(x^2-4)
derivative
2
x
x
2
−
4
derivative of \sqrt[3]{1-x}
d
dx
(
3
√
1
−
x
)
integral of (5x)/(sqrt(5x^2+4y^2))
∫
5
x
√
5
x
2
+
4
y
2
dx
integral of-8x^{-9}
∫
−
8
x
−
9
dx
integral of 0.733xe^{-0.27x}
∫
0
.
7
3
3
xe
−
0
.
2
7
x
dx
integral of 18xcos(3x)
∫
1
8
x
cos
(
3
x
)
dx
xy+y^2-x^2*(dy)/(dx)=0
xy
+
y
2
−
x
2
·
dy
dx
=
0
limit as x approaches-1 of \sqrt[3]{-1}
lim
x
→
−
1
(
3
√
−
1
)
integral of sqrt(x+x^2)
∫
√
x
+
x
2
dx
integral of 8cot(e^{4x})e^{4x}
∫
8
cot
(
e
4
x
)
e
4
x
dx
limit as x approaches 3 of sqrt(x-3)
lim
x
→
3
(
√
x
−
3
)
derivative of (1+x^{-1/2})
d
dx
(
(
1
+
x
)
−
1
2
)
y^'=-sin(x)-sin(x)y,y(0)=8
y
′
=
−
sin
(
x
)
−
sin
(
x
)
y
,
y
(
0
)
=
8
1
..
1383
1384
1385
1386
1387
..
2459