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统计数据
常见 微积分 问题
derivative of (3x^{6x})
d
dx
(
(
3
x
)
6
x
)
limit as x approaches 0 of x^2cot(x)
lim
x
→
0
(
x
2
cot
(
x
)
)
y-2y^'=0
y
−
2
y
′
=
0
integral of-2ycos(y)
∫
−
2
y
cos
(
y
)
dy
面积 y=tan(5x),y=2sin(5x)
area
y
=
tan
(
5
x
)
,
y
=
2
sin
(
5
x
)
limit as x approaches-1 of 8x^4-3x^3+5x
lim
x
→
−
1
(
8
x
4
−
3
x
3
+
5
x
)
integral of (x+1)sqrt(3-x)
∫
(
x
+
1
)
√
3
−
x
dx
d/(dL)(({K}(L)L)^{1/2})
d
dL
(
(
K
(
L
)
L
)
1
2
)
inverse拉普拉斯 s/(s+5)
inverselaplace
s
s
+
5
tangent f(x)=4x^3-x^2-7,\at x=-1
tangent
f
(
x
)
=
4
x
3
−
x
2
−
7
,
at
x
=
−
1
integral of 8tan(x)sec^3(x)
∫
8
tan
(
x
)
sec
3
(
x
)
dx
derivative y=(x^2+2)^2(x^4+4)^4
derivative
y
=
(
x
2
+
2
)
2
(
x
4
+
4
)
4
integral of 1/(y^3-y)
∫
1
y
3
−
y
dy
tangent h(x)= 7/x ,\at x=5
tangent
h
(
x
)
=
7
x
,
at
x
=
5
derivative of-1/2 e^{-x/4}
d
dx
(
−
1
2
e
−
x
4
)
limit as x approaches 0+of xlog_{e}(x)
lim
x
→
0
+
(
x
log
e
(
x
)
)
展开-8(64e^{-4x^2}x^3-24e^{-4x^2}x)
expand
−
8
(
6
4
e
−
4
x
2
x
3
−
2
4
e
−
4
x
2
x
)
laplace变换 (t^2)/2
laplacetransform
t
2
2
integral of e^{-st}(2t+1)
∫
e
−
st
(
2
t
+
1
)
dt
面积 y= 1/(x^2),y=x,y= 1/8 x
area
y
=
1
x
2
,
y
=
x
,
y
=
1
8
x
derivative of 50e^{-0.5x}-(5/x)
d
dx
(
5
0
e
−
0
.
5
x
−
(
5
x
)
)
(\partial)/(\partial x)(sqrt(x+e^{4y)})
∂
∂
x
(
√
x
+
e
4
y
)
integral of ((3x+4))/((x^2+4)(3-x))
∫
(
3
x
+
4
)
(
x
2
+
4
)
(
3
−
x
)
dx
泰勒-(x)^21
taylor
−
(
x
)
2
1
d/(dt)(-e^{3t})
d
dt
(
−
e
3
t
)
integral of 6x^2cos(x)
∫
6
x
2
cos
(
x
)
dx
tangent f(x)=x^3-3x+2,\at x=2
tangent
f
(
x
)
=
x
3
−
3
x
+
2
,
at
x
=
2
(\partial)/(\partial y)(2e^{2z}xy-2y)
∂
∂
y
(
2
e
2
z
xy
−
2
y
)
泰勒 1/(x^3)
taylor
1
x
3
d/(dt)(cos(t)-sin(t))
d
dt
(
cos
(
t
)
−
sin
(
t
)
)
integral of+(e^{2x})/(1+e^{2x)}
∫
+
e
2
x
1
+
e
2
x
dx
tangent f(x)=sqrt(4x^2-4x+1),\at x=1
tangent
f
(
x
)
=
√
4
x
2
−
4
x
+
1
,
at
x
=
1
(\partial)/(\partial x)(xsin(x+y)-cos(x+y))
∂
∂
x
(
x
sin
(
x
+
y
)
−
cos
(
x
+
y
)
)
y^'=y^4*(4x^2+x)
y
′
=
y
4
·
(
4
x
2
+
x
)
斜率intercept (7,4),(1,-2)
slopeintercept
(
7
,
4
)
,
(
1
,
−
2
)
integral of (x^2-2x)^2
∫
(
x
2
−
2
x
)
2
dx
integral of 3/((4+x^2))
∫
3
(
4
+
x
2
)
dx
derivative 5tsin(4t)
derivative
5
t
sin
(
4
t
)
integral of (7x^2-4)/(x^3+x^2-2x)
∫
7
x
2
−
4
x
3
+
x
2
−
2
x
dx
integral of 3xe^{x^2}
∫
3
xe
x
2
dx
integral from-2 to 0 of 7x^2+7x
∫
−
2
0
7
x
2
+
7
xdx
integral of 1/(1.02^x)
∫
1
1
.
0
2
x
dx
integral of x^4(x^5-1)^{3/4}
∫
x
4
(
x
5
−
1
)
3
4
dx
integral of (sqrt(x-9))/x
∫
√
x
−
9
x
dx
derivative P(x)=-1000+12x+0.0004x^2
derivative
P
(
x
)
=
−
1
0
0
0
+
1
2
x
+
0
.
0
0
0
4
x
2
derivative x^3(x-5)^2
derivative
x
3
(
x
−
5
)
2
泰勒 0.05*x*ln((10)/x),x=1
taylor
0
.
0
5
·
x
·
ln
(
1
0
x
)
,
x
=
1
inverse拉普拉斯 (5s)/(s^2+2s+5)
inverselaplace
5
s
s
2
+
2
s
+
5
integral of 3cos^2(x)sin^2(x)
∫
3
cos
2
(
x
)
sin
2
(
x
)
dx
limit as x approaches 0 of x^{3x}
lim
x
→
0
(
x
3
x
)
integral from 1 to 2 of (4+u^2)/(u^3)
∫
1
2
4
+
u
2
u
3
du
(dy}{dx}=\frac{x^2)/y
dy
dx
=
x
2
y
(dx)/(dt)=2(x^2+1),x(pi/4)=1
dx
dt
=
2
(
x
2
+
1
)
,
x
(
π
4
)
=
1
integral of (x^2-2x-1)/(sqrt(x))
∫
x
2
−
2
x
−
1
√
x
dx
laplace变换 e^{1-t}
laplacetransform
e
1
−
t
xy^'sin^2(y/x)=x+ysin^2(y/x)
xy
′
sin
2
(
y
x
)
=
x
+
y
sin
2
(
y
x
)
(\partial)/(\partial x)(8y^7cos(8x))
∂
∂
x
(
8
y
7
cos
(
8
x
)
)
derivative 1/(b^{2/7)}
derivative
1
b
2
7
limit as x approaches 2 of 3/(x^2-4)
lim
x
→
2
(
3
x
2
−
4
)
(dx)/x-y^2dy=0
dx
x
−
y
2
dy
=
0
integral from-4 to 0 of (sqrt(16-x^2))
∫
−
4
0
(
√
1
6
−
x
2
)
dx
derivative of sqrt(x^2+1)+2xe^x
d
dx
(
√
x
2
+
1
+
2
xe
x
)
(\partial)/(\partial x)(7e^{x/y})
∂
∂
x
(
7
e
x
y
)
integral of (x^2sin(3x))
∫
(
x
2
sin
(
3
x
)
)
dx
integral of 1/(x^2sqrt(1-\frac{1){x^2)}}
∫
1
x
2
√
1
−
1
x
2
dx
tangent y^2=5x^4-x^2,(1,2)
tangent
y
2
=
5
x
4
−
x
2
,
(
1
,
2
)
limit as x approaches 0 of (e^x-1)/(12x)
lim
x
→
0
(
e
x
−
1
1
2
x
)
integral of (5sin(x)+2sec(x))/(tan(x))
∫
5
sin
(
x
)
+
2
sec
(
x
)
tan
(
x
)
dx
laplace变换 e^{3t}sin(2t)
laplacetransform
e
3
t
sin
(
2
t
)
integral from 0 to 0.6 of 600x
∫
0
0
.
6
6
0
0
xdx
integral of 1/500 e^{-1/500 t}
∫
1
5
0
0
e
−
1
5
0
0
t
dt
(\partial)/(\partial y)(8x+6x^2y+2y^2)
∂
∂
y
(
8
x
+
6
x
2
y
+
2
y
2
)
derivative 1/8
derivative
1
8
integral of sin(4x)cos(5x)
∫
sin
(
4
x
)
cos
(
5
x
)
dx
integral from 1 to 2 of (2-x)^{(-2)/3}
∫
1
2
(
2
−
x
)
−
2
3
dx
integral of 1/(1-2y)
∫
1
1
−
2
y
dy
d/(dv)((v^3-2vsqrt(v))/v)
d
dv
(
v
3
−
2
v
√
v
v
)
derivative 7e^y
derivative
7
e
y
integral of ((x^2))/(sqrt(6x^2-49))
∫
(
x
2
)
√
6
x
2
−
4
9
dx
derivative (1-x)cos(2x)
derivative
(
1
−
x
)
cos
(
2
x
)
integral of (1-1/(x^2))sqrt(x)
∫
(
1
−
1
x
2
)
√
x
dx
derivative of (x+y/(sqrt(x^2+y^2)))
d
dx
(
x
+
y
√
x
2
+
y
2
)
laplace变换 e^{-3t}sin(2t)
laplacetransform
e
−
3
t
sin
(
2
t
)
derivative of (x^2/9)
d
dx
(
x
2
9
)
y^{''}+4y=2csc^2(2t)
y
′
′
+
4
y
=
2
csc
2
(
2
t
)
d/(dy)(2y^2e^{xy^2})
d
dy
(
2
y
2
e
xy
2
)
面积 y=x^2,y=sqrt(x)
area
y
=
x
2
,
y
=
√
x
(\partial)/(\partial y)(sin(x^2))
∂
∂
y
(
sin
(
x
2
)
)
斜率intercept (0,-14),(-7,0)
slopeintercept
(
0
,
−
1
4
)
,
(
−
7
,
0
)
integral of (ln(x))x^2
∫
(
ln
(
x
)
)
x
2
dx
limit as x approaches 1/2 of x^3-x^2-x+1
lim
x
→
1
2
(
x
3
−
x
2
−
x
+
1
)
integral from 0 to 3 of x^2-4
∫
0
3
x
2
−
4
dx
f(t)=3cos(2t)
f
(
t
)
=
3
cos
(
2
t
)
sum from n=0 to infinity of 3^{-n}
∑
n
=
0
∞
3
−
n
limit as x approaches-4-of (-5x)/(x+4)
lim
x
→
−
4
−
(
−
5
x
x
+
4
)
(dy)/(dx)+1/x y=x^2y^3
dy
dx
+
1
x
y
=
x
2
y
3
(\partial)/(\partial x)(1/(4-3x))
∂
∂
x
(
1
4
−
3
x
)
limit as x approaches 0 of ((3^x-5^x))/x
lim
x
→
0
(
(
3
x
−
5
x
)
x
)
derivative of (ln(2x)^4)
d
dx
(
(
ln
(
2
x
)
)
4
)
integral from 4 to 9 of 6sqrt(x)
∫
4
9
6
√
x
dx
1
..
1211
1212
1213
1214
1215
..
2459