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统计数据
常见 微积分 问题
derivative of log_{6}(cot(8x))
d
dx
(
log
6
(
cot
(
8
x
)
)
)
tangent f(x)=sin(sin(x)),\at x=pi
tangent
f
(
x
)
=
sin
(
sin
(
x
)
)
,
at
x
=
π
limit as x approaches 0 of (tan(3x)-sin(3x))/(x^3)
lim
x
→
0
(
tan
(
3
x
)
−
sin
(
3
x
)
x
3
)
derivative of (1-x^2^2)
d
dx
(
(
1
−
x
2
)
2
)
(dy)/(dx)=(y+3)/(x+3)
dy
dx
=
y
+
3
x
+
3
derivative (x^3)/(6x-3)
derivative
x
3
6
x
−
3
面积 3x^2+4,[1,2]
area
3
x
2
+
4
,
[
1
,
2
]
integral of k/(x(ln(x))^b)
∫
k
x
(
ln
(
x
)
)
b
dx
limit as x approaches 0+of (e^{4x})/(3x)
lim
x
→
0
+
(
e
4
x
3
x
)
limit as x approaches 1-of (x^3)/(x^2-1)
lim
x
→
1
−
(
x
3
x
2
−
1
)
斜率 (0,0),(9, 9/7)
slope
(
0
,
0
)
,
(
9
,
9
7
)
integral of (x^3+x+1)/(x^4+2x^2+1)
∫
x
3
+
x
+
1
x
4
+
2
x
2
+
1
dx
derivative 160+3.2x-0.03x^2
derivative
1
6
0
+
3
.
2
x
−
0
.
0
3
x
2
derivative of 9xsin(pix)
d
dx
(
9
x
sin
(
π
x
)
)
sum from n=0 to infinity of (-1/4)^n
∑
n
=
0
∞
(
−
1
4
)
n
tangent f(x)=x-x^2,\at x=-4
tangent
f
(
x
)
=
x
−
x
2
,
at
x
=
−
4
integral of cos(x)cos^2(x)
∫
cos
(
x
)
cos
2
(
x
)
dx
derivative 3x+4
derivative
3
x
+
4
derivative f(x)=((x+2))/((x+4))
derivative
f
(
x
)
=
(
x
+
2
)
(
x
+
4
)
derivative of (e^{2x}+e^{-2x}/4)
d
dx
(
e
2
x
+
e
−
2
x
4
)
derivative of 3x^2-8x
d
dx
(
3
x
2
−
8
x
)
implicit (dy)/(dx),2xy=0
implicit
dy
dx
,
2
xy
=
0
derivative of (pi^2/(x^2+4x))
d
dx
(
π
2
x
2
+
4
x
)
化简 3xy+x^2+y^2
simplify
3
xy
+
x
2
+
y
2
y^{''}+3y^'=(4t+4)sin(4t)
y
′
′
+
3
y
′
=
(
4
t
+
4
)
sin
(
4
t
)
(x^3+y^3)dx-3xy^2dy=0
(
x
3
+
y
3
)
dx
−
3
xy
2
dy
=
0
sum from n=0 to infinity of 2/3 n(1/3)^n
∑
n
=
0
∞
2
3
n
(
1
3
)
n
(\partial)/(\partial x)(16-4x^2-y^2)
∂
∂
x
(
1
6
−
4
x
2
−
y
2
)
y^{''}+y^'+1=0
y
′
′
+
y
′
+
1
=
0
derivative of (2x+3/(x^2-9))
d
dx
(
2
x
+
3
x
2
−
9
)
normal y=x^4+9e^x,(0,5)
normal
y
=
x
4
+
9
e
x
,
(
0
,
5
)
integral of h^{-1/2}
∫
h
−
1
2
dh
(\partial)/(\partial y)(x^2+cos(y))
∂
∂
y
(
x
2
+
cos
(
y
)
)
limit as x approaches 81 of ((sqrt(x)-9))/(x-81)
lim
x
→
8
1
(
(
√
x
−
9
)
x
−
8
1
)
integral of cos^2(x+pi/2)
∫
cos
2
(
x
+
π
2
)
dx
normal y=6xe^x,(0,0)
normal
y
=
6
xe
x
,
(
0
,
0
)
integral of 14xsqrt(7x-3)
∫
1
4
x
√
7
x
−
3
dx
derivative of e^{5xsin(2x})
d
dx
(
e
5
x
sin
(
2
x
)
)
integral of 5cos(x)+3sin(x)
∫
5
cos
(
x
)
+
3
sin
(
x
)
dx
derivative f(x)=2x^2+8x
derivative
f
(
x
)
=
2
x
2
+
8
x
sum from n=1 to infinity of 2(-1/2)^n
∑
n
=
1
∞
2
(
−
1
2
)
n
d/(dt)(1+t)
d
dt
(
1
+
t
)
integral of 8xe^x
∫
8
xe
x
dx
integral of 5csc^4(x)cot^6(x)
∫
5
csc
4
(
x
)
cot
6
(
x
)
dx
derivative of ((x+1^2)/(x-1))
d
dx
(
(
x
+
1
)
2
x
−
1
)
derivative of x^3+x+2
d
dx
(
x
3
+
x
+
2
)
integral of sqrt(x)-2cos(x)
∫
√
x
−
2
cos
(
x
)
dx
derivative of-(x^3/(y^3))
d
dx
(
−
x
3
y
3
)
derivative of (27/x)
d
dx
(
2
7
x
)
tangent 12sqrt(x)
tangent
1
2
√
x
integral of (5x+2)^{-3}
∫
(
5
x
+
2
)
−
3
dx
derivative of 3pix
d
dx
(
3
π
x
)
integral of tan(4x+1)
∫
tan
(
4
x
+
1
)
dx
integral of (3t-1)^3
∫
(
3
t
−
1
)
3
dt
(dy)/(dt)+2y=3
dy
dt
+
2
y
=
3
integral of (cos^2(y))/(1-sin(y))
∫
cos
2
(
y
)
1
−
sin
(
y
)
dy
integral of (x^3)/((sqrt(x^2+1)))
∫
x
3
(
√
x
2
+
1
)
dx
integral of 3cos(x)
∫
3
cos
(
x
)
dx
integral of (x+6)/(x^3+3x)
∫
x
+
6
x
3
+
3
x
dx
xdx+ye^{-x}dy=0
xdx
+
ye
−
x
dy
=
0
integral of ((x^2)/(sqrt(9-x^2)))
∫
(
x
2
√
9
−
x
2
)
dx
derivative of ((2x^3+ax+a)/(x^2-1))
d
dx
(
(
2
x
3
+
ax
+
a
)
x
2
−
1
)
integral of 4x^2e^{x^3}
∫
4
x
2
e
x
3
dx
normal y=-2x^3+6/x ,\at x=-1
normal
y
=
−
2
x
3
+
6
x
,
at
x
=
−
1
integral of (x^3)/(2x^4+x^2-1)
∫
x
3
2
x
4
+
x
2
−
1
dx
derivative of (x^4+3/(3x))
d
dx
(
x
4
+
3
3
x
)
derivative of (x^2/(8-8x))
d
dx
(
x
2
8
−
8
x
)
integral of x^2sqrt((x^3+1))
∫
x
2
√
(
x
3
+
1
)
dx
limit as x approaches 0 of sin(x)+cos(x)
lim
x
→
0
(
sin
(
x
)
+
cos
(
x
)
)
derivative y=(x^3+8)/x
derivative
y
=
x
3
+
8
x
integral of (16)/(16+e^x)
∫
1
6
1
6
+
e
x
dx
f(u)= 1/u
f
(
u
)
=
1
u
sum from n=1 to infinity of (((-1)^n))/n
∑
n
=
1
∞
(
(
−
1
)
n
)
n
integral of (v+1)/(v^2+1)
∫
v
+
1
v
2
+
1
dv
integral of (10)/((x^2+9)(x-1))
∫
1
0
(
x
2
+
9
)
(
x
−
1
)
dx
derivative g(x)=tan(2x)*sin(2x)
derivative
g
(
x
)
=
tan
(
2
x
)
·
sin
(
2
x
)
(2y^2x-y)dx+xdy=0
(
2
y
2
x
−
y
)
dx
+
xdy
=
0
derivative y=sqrt(2x-x^2)
derivative
y
=
√
2
x
−
x
2
(\partial)/(\partial x)((10000x)/(y^2))
∂
∂
x
(
1
0
0
0
0
x
y
2
)
sum from n=1 to infinity of (8/5)^{n-1}
∑
n
=
1
∞
(
8
5
)
n
−
1
(t^2+1)f^'(t)+[f(t)]^2+1=0,f(4)=e
(
t
2
+
1
)
f
′
(
t
)
+
[
f
(
t
)
]
2
+
1
=
0
,
f
(
4
)
=
e
integral of (x^3)/x
∫
x
3
x
dx
integral from 0 to 2 of 5x^3sqrt(x^2+4)
∫
0
2
5
x
3
√
x
2
+
4
dx
limit as x approaches 3-of cx^2+4x
lim
x
→
3
−
(
cx
2
+
4
x
)
integral of (x^2+5x+1)/((x^2+1)^2)
∫
x
2
+
5
x
+
1
(
x
2
+
1
)
2
dx
derivative (-1)/((1+x)^2)
derivative
−
1
(
1
+
x
)
2
limit as x approaches 0 of (sin(x))^x
lim
x
→
0
(
(
sin
(
x
)
)
x
)
derivative of x^{cos(2pix})
d
dx
(
x
cos
(
2
π
x
)
)
d/(dt)((4t^2+7t^5)/(sqrt(t)))
d
dt
(
4
t
2
+
7
t
5
√
t
)
integral of x*sin(npix)
∫
x
·
sin
(
n
π
x
)
dx
d/(dθ)(2+2sin(θ))
d
d
θ
(
2
+
2
sin
(
θ
)
)
integral of x/(sqrt(49+x^2))
∫
x
√
4
9
+
x
2
dx
integral of cos^2(pit)sin(pit)
∫
cos
2
(
π
t
)
sin
(
π
t
)
dt
derivative of (3x/(x+1))
d
dx
(
3
x
x
+
1
)
derivative x^2e^{-7x}
derivative
x
2
e
−
7
x
(\partial)/(\partial v)(2usin(v))
∂
∂
v
(
2
u
sin
(
v
)
)
derivative of x^3-2x+2
d
dx
(
x
3
−
2
x
+
2
)
integral of 1/(4x-2)
∫
1
4
x
−
2
dx
limit as x approaches 3 of 2/x+1
lim
x
→
3
(
2
x
+
1
)
面积 y=5x,y= 5/x ,x=5
area
y
=
5
x
,
y
=
5
x
,
x
=
5
1
..
1487
1488
1489
1490
1491
..
2459