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统计数据
常见 微积分 问题
integral of 2/(x^3sqrt(x^4-25))
∫
2
x
3
√
x
4
−
2
5
dx
integral of 1/(x^3sqrt(x^2-4))
∫
1
x
3
√
x
2
−
4
dx
integral of 9x^2-30x+15
∫
9
x
2
−
3
0
x
+
1
5
dx
(\partial)/(\partial x)(x*sin(y-z))
∂
∂
x
(
x
·
sin
(
y
−
z
)
)
d/(dt)((\sqrt[3]{t})/5)
d
dt
(
3
√
t
5
)
(\partial)/(\partial x)(6-(x^2+y^2)^{1/5})
∂
∂
x
(
6
−
(
x
2
+
y
2
)
1
5
)
(\partial)/(\partial y)(x*e^{xy+1})
∂
∂
y
(
x
·
e
xy
+
1
)
derivative y=x^{-1}
derivative
y
=
x
−
1
y^'= 1/(xy)
y
′
=
1
xy
tangent f(x)=8x^2-3,\at x=3
tangent
f
(
x
)
=
8
x
2
−
3
,
at
x
=
3
derivative f(0)=(cos(x))/(x^2-1)
derivative
f
(
0
)
=
cos
(
x
)
x
2
−
1
integral from 1 to 4 of 7e^{sqrt(x)}
∫
1
4
7
e
√
x
dx
sum from n=1 to infinity of (2^n)/(10^n)
∑
n
=
1
∞
2
n
1
0
n
(\partial ^2)/(\partial y^2)(xy^{10}+x^2+y^4)
∂
2
∂
y
2
(
xy
1
0
+
x
2
+
y
4
)
derivative f(x)=x^{-1/2}+x^{1/2}
derivative
f
(
x
)
=
x
−
1
2
+
x
1
2
inverse拉普拉斯 1/(s^3+s^2+s)
inverselaplace
1
s
3
+
s
2
+
s
derivative y=x^3-sqrt(x)
derivative
y
=
x
3
−
√
x
derivative f(x)=cos(sqrt(4t+12))
derivative
f
(
x
)
=
cos
(
√
4
t
+
1
2
)
limit as x approaches 0 of (y^{1-x})/(1-x)
lim
x
→
0
(
y
1
−
x
1
−
x
)
y^{''}-6y^'+2y=0,y(0)=0,y^'(0)=1
y
′
′
−
6
y
′
+
2
y
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
limit as x approaches 5 of sqrt(x^2+4)
lim
x
→
5
(
√
x
2
+
4
)
integral of (3x^2-3)/(x^3-3x)
∫
3
x
2
−
3
x
3
−
3
x
dx
3x(dy)/(dx)+5y=10
3
x
dy
dx
+
5
y
=
1
0
integral of tan^6(9x)sec^4(9x)
∫
tan
6
(
9
x
)
sec
4
(
9
x
)
dx
integral from 0 to 3 of pi(2sqrt(5y))^2
∫
0
3
π
(
2
√
5
y
)
2
dy
normal y=F4x-x^2,(1,3)
normal
y
=
F
4
x
−
x
2
,
(
1
,
3
)
integral of sin^3(1-2x)cos^3(1-2x)
∫
sin
3
(
1
−
2
x
)
cos
3
(
1
−
2
x
)
dx
derivative of 3x-4x^{9/10}
d
dx
(
3
x
−
4
x
9
1
0
)
derivative of 4cos^3(x)
d
dx
(
4
cos
3
(
x
)
)
tangent y=(9x^2-6x+2)(1+2x),\at x=1
tangent
y
=
(
9
x
2
−
6
x
+
2
)
(
1
+
2
x
)
,
at
x
=
1
derivative of asqrt(1+x)
d
dx
(
a
√
1
+
x
)
面积 sqrt(x)+9,0.25x+9
area
√
x
+
9
,
0
.
2
5
x
+
9
derivative of |3x-4|
d
dx
(
|
3
x
−
4
|
)
integral of (x^2)/(sqrt(10-3x^3))
∫
x
2
√
1
0
−
3
x
3
dx
integral of (90x^2sin(2+6x^3))
∫
(
9
0
x
2
sin
(
2
+
6
x
3
)
)
dx
derivative of sqrt((3x+7/(5+2x)))
d
dx
(
√
3
x
+
7
5
+
2
x
)
derivative of (ln(x+1)^2-e^{x^2})
d
dx
(
(
ln
(
x
+
1
)
)
2
−
e
x
2
)
integral of |4y+1|
∫
|
4
y
+
1
|
dy
y^'+7y=t+e^{-6t}
y
′
+
7
y
=
t
+
e
−
6
t
2xdx+dy=0
2
xdx
+
dy
=
0
sum from n=0 to infinity of 5(0.7)^{n-1}
∑
n
=
0
∞
5
(
0
.
7
)
n
−
1
integral of e^{4x}
∫
e
4
x
dx
integral of ((-1)^k)/((2k+1)!)(2x)^{2k}
∫
(
−
1
)
k
(
2
k
+
1
)
!
(
2
x
)
2
k
dx
(dx)/(dt)=x+t
dx
dt
=
x
+
t
derivative 3/(sqrt((45+36)^3))
derivative
3
√
(
4
5
+
3
6
)
3
derivative e^{x^7}
derivative
e
x
7
derivative of x 2/3
d
dx
(
x
2
3
)
integral of 1/(xsqrt(4x^2-9))
∫
1
x
√
4
x
2
−
9
dx
limit as x approaches 0 of (e^x-1)/(x^5)
lim
x
→
0
(
e
x
−
1
x
5
)
(\partial)/(\partial x)(ln(x^2+y^2+1))
∂
∂
x
(
ln
(
x
2
+
y
2
+
1
)
)
(\partial)/(\partial y)(ln(x+z))
∂
∂
y
(
ln
(
x
+
z
)
)
derivative y=2x-4
derivative
y
=
2
x
−
4
derivative of 1/(sqrt(x^2+5))
d
dx
(
1
√
x
2
+
5
)
limit as x approaches 1 of (x^5-1)/(x-1)
lim
x
→
1
(
x
5
−
1
x
−
1
)
derivative f(x)=xsin(2^x)
derivative
f
(
x
)
=
x
sin
(
2
x
)
1/x e^ytan(y)y^'=e^{x+y}
1
x
e
y
tan
(
y
)
y
′
=
e
x
+
y
(\partial)/(\partial y)((4x)/(x^2+y^2))
∂
∂
y
(
4
x
x
2
+
y
2
)
integral of 1/2 (cos(x))^2
∫
1
2
(
cos
(
x
)
)
2
dx
tangent f(x)=(40)/x ,(1,40)
tangent
f
(
x
)
=
4
0
x
,
(
1
,
4
0
)
integral of ((x+1)/(sqrt(x)))
∫
(
x
+
1
√
x
)
dx
integral of 1/2 x^5
∫
1
2
x
5
dx
limit as x approaches pi/2+of 2e^{tan(x)}
lim
x
→
π
2
+
(
2
e
tan
(
x
)
)
tangent f(x)=3x^4-8x^2,(-1,5)
tangent
f
(
x
)
=
3
x
4
−
8
x
2
,
(
−
1
,
5
)
(\partial)/(\partial x)(-3xyln(xy))
∂
∂
x
(
−
3
xy
ln
(
xy
)
)
(\partial)/(\partial x)((xy^2)/(z^3))
∂
∂
x
(
xy
2
z
3
)
y^{''}=-y
y
′
′
=
−
y
integral of x-7
∫
x
−
7
dx
limit as x approaches+0 of (e^{x^2}-1)/x
lim
x
→
+
0
(
e
x
2
−
1
x
)
derivative of (x^2+25/x)
d
dx
(
x
2
+
2
5
x
)
(\partial)/(\partial z)(ln(1+z^2))
∂
∂
z
(
ln
(
1
+
z
2
)
)
integral of-(6000)/((3x+50)^2)
∫
−
6
0
0
0
(
3
x
+
5
0
)
2
dx
limit as x approaches 15 of sqrt(2)
lim
x
→
1
5
(
√
2
)
泰勒 e^{2x},1
taylor
e
2
x
,
1
(\partial)/(\partial x)(x^2-4y)
∂
∂
x
(
x
2
−
4
y
)
y(dy)/(dx)-e^{y^2}*x*cos(x)=0
y
dy
dx
−
e
y
2
·
x
·
cos
(
x
)
=
0
derivative of-(50/(x^3)+5/(x^2))
d
dx
(
−
5
0
x
3
+
5
x
2
)
integral of 4x^2sin(2x)
∫
4
x
2
sin
(
2
x
)
dx
(\partial)/(\partial x)(ln(1+x^2+y^2-z^2))
∂
∂
x
(
ln
(
1
+
x
2
+
y
2
−
z
2
)
)
(d^3y)/(dx^3)-cos(x)=0
d
3
y
dx
3
−
cos
(
x
)
=
0
integral from 6 to 8 of (28)/((x-6)^3)
∫
6
8
2
8
(
x
−
6
)
3
dx
integral of r^3
∫
r
3
dr
integral of (2x^2+5x+18)/(x(x^2+9))
∫
2
x
2
+
5
x
+
1
8
x
(
x
2
+
9
)
dx
斜率intercept (-9,-9),(-6,0)
slopeintercept
(
−
9
,
−
9
)
,
(
−
6
,
0
)
derivative 7*5^x
derivative
7
·
5
x
derivative of 5x^{-5}
d
dx
(
5
x
−
5
)
integral from 0 to 1 of sqrt(1+\sqrt{x)}
∫
0
1
√
1
+
√
x
dx
integral from 1 to 3 of (2x-1/x)^2
∫
1
3
(
2
x
−
1
x
)
2
dx
(6/x)^'
(
6
x
)
′
(dy)/(dx)-y=2e^x
dy
dx
−
y
=
2
e
x
limit as x approaches infinity of (5)^x
lim
x
→
∞
(
(
5
)
x
)
(\partial)/(\partial x)(e^{sin(x)}cos(x))
∂
∂
x
(
e
sin
(
x
)
cos
(
x
)
)
f(x)=7x^{-6}-5x^{-3}
f
(
x
)
=
7
x
−
6
−
5
x
−
3
面积 y=x,(0,1),x^2
area
y
=
x
,
(
0
,
1
)
,
x
2
2sqrt(x)((dy)/(dx))=cos^2(y)
2
√
x
(
dy
dx
)
=
cos
2
(
y
)
integral of 1/((x^2+21)^3)
∫
1
(
x
2
+
2
1
)
3
dx
integral of 3/(x+1)
∫
3
x
+
1
dx
xln(x)=y(1+sqrt(24+y^2))y^'(x),y(1)=1
x
ln
(
x
)
=
y
(
1
+
√
2
4
+
y
2
)
y
′
(
x
)
,
y
(
1
)
=
1
integral of sqrt((2x+2))
∫
√
(
2
x
+
2
)
dx
derivative f(x)=x^n
derivative
f
(
x
)
=
x
n
sum from n=0 to infinity of (1/2)^n
∑
n
=
0
∞
(
1
2
)
n
1
..
1201
1202
1203
1204
1205
..
2459