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常见 微积分 问题
(dy)/(dx)=((x^2+y^2))/(xy)
dy
dx
=
(
x
2
+
y
2
)
xy
derivative 8x^4+7sin(x)
derivative
8
x
4
+
7
sin
(
x
)
面积 5cos(3x),5-5cos(3x),0, pi/3
area
5
cos
(
3
x
)
,
5
−
5
cos
(
3
x
)
,
0
,
π
3
y^'= x/(18y)
y
′
=
x
1
8
y
integral of-4x(3x^2-1)^7
∫
−
4
x
(
3
x
2
−
1
)
7
dx
derivative of log_{2}(3x)
d
dx
(
log
2
(
3
x
)
)
implicit (dy)/(dx),y^3=2x
implicit
dy
dx
,
y
3
=
2
x
tangent f(x)=2x^3+3x^2-12x+9
tangent
f
(
x
)
=
2
x
3
+
3
x
2
−
1
2
x
+
9
derivative of (x+3/(x^2))
d
dx
(
x
+
3
x
2
)
integral from-2 to 1 of (4-x^2)-(x+2)
∫
−
2
1
(
4
−
x
2
)
−
(
x
+
2
)
dx
derivative f(x)=(5x^2-8x)e^x
derivative
f
(
x
)
=
(
5
x
2
−
8
x
)
e
x
derivative 3/(sqrt(6x+8))
derivative
3
√
6
x
+
8
面积 12-x^2,x^2-6
area
1
2
−
x
2
,
x
2
−
6
面积 y=x,y=x^2
area
y
=
x
,
y
=
x
2
limit as x approaches 4 of (x+2)/(4x-16)
lim
x
→
4
(
x
+
2
4
x
−
1
6
)
derivative y=e^{mx}
derivative
y
=
e
mx
tangent x^2-5(-4.11)
tangent
x
2
−
5
(
−
4
.
1
1
)
derivative of (x(x-2)/((x-1)^2))
d
dx
(
x
(
x
−
2
)
(
x
−
1
)
2
)
derivative of (x+4/(9x^2e^x))
d
dx
(
x
+
4
9
x
2
e
x
)
derivative of-(250x/((25x^2+1)^2))
d
dx
(
−
2
5
0
x
(
2
5
x
2
+
1
)
2
)
derivative of (x-1e^{x^2-4})
d
dx
(
(
x
−
1
)
e
x
2
−
4
)
(\partial)/(\partial x)(-ysec^2(x))
∂
∂
x
(
−
y
sec
2
(
x
)
)
integral from 1 to 4 of (sqrt(x))/(x-9)
∫
1
4
√
x
x
−
9
dx
derivative of 1/82 e^x
d
dx
(
1
8
2
e
x
)
integral of (x+1)/(x^2(x-1))
∫
x
+
1
x
2
(
x
−
1
)
dx
derivative of (sqrt(x)/(2+x))
d
dx
(
√
x
2
+
x
)
(\partial)/(\partial x)(3/(x^2+z^2))
∂
∂
x
(
3
x
2
+
z
2
)
(\partial)/(\partial x)(x^3y-y^3)
∂
∂
x
(
x
3
y
−
y
3
)
derivative d(x)(55)/(0.01x^2+1)
derivative
d
(
x
)
5
5
0
.
0
1
x
2
+
1
integral from 1 to 2 of 1/(x^6)
∫
1
2
1
x
6
dx
integral of (2x+1)/(x^2)
∫
2
x
+
1
x
2
dx
derivative of (6x^{-5})
d
dx
(
(
6
x
)
−
5
)
derivative of x+3/x
d
dx
(
x
+
3
x
)
y^{''}+25y=tsin(5t)
y
′
′
+
2
5
y
=
t
sin
(
5
t
)
(x^2-xy)dx+x^2dy=0
(
x
2
−
xy
)
dx
+
x
2
dy
=
0
sum from n=1 to infinity of (11n)/(n!)
∑
n
=
1
∞
1
1
n
n
!
integral from-2 to 0 of sqrt(2x^2+3x+3)
∫
−
2
0
√
2
x
2
+
3
x
+
3
dx
derivative of (2x^2-3^2)
d
dx
(
(
2
x
2
−
3
)
2
)
limit as x approaches 3 of 4x+|x-3|
lim
x
→
3
(
4
x
+
|
x
−
3
|
)
泰勒 1/(sqrt(4-x))
taylor
1
√
4
−
x
integral of θcos^2(θ)
∫
θ
cos
2
(
θ
)
d
θ
derivative y=((sqrt(x))/7+9)^{3/2}
derivative
y
=
(
√
x
7
+
9
)
3
2
derivative of (x-1/(x^2+x-2))
d
dx
(
x
−
1
x
2
+
x
−
2
)
(dy)/(dx)=x+xy
dy
dx
=
x
+
xy
derivative f(x)=2ln(x)
derivative
f
(
x
)
=
2
ln
(
x
)
inverse拉普拉斯 (-s-1)/(s^2+s+1)
inverselaplace
−
s
−
1
s
2
+
s
+
1
面积 y=e^x,y=e^{-x},[0,1]
area
y
=
e
x
,
y
=
e
−
x
,
[
0
,
1
]
derivative of cos(sin^2(3x))
d
dx
(
cos
(
sin
2
(
3
x
)
)
)
integral of cot(pix)
∫
cot
(
π
x
)
dx
integral of e^{x+8e^x}
∫
e
x
+
8
e
x
dx
integral from 0 to 1 of 1/(sqrt(4+x^2))
∫
0
1
1
√
4
+
x
2
dx
sum from n=0 to infinity of 1/(2^n+n)
∑
n
=
0
∞
1
2
n
+
n
integral of (x-ln^2(x))/x
∫
x
−
ln
2
(
x
)
x
dx
integral of (4-4cos(x))^2
∫
(
4
−
4
cos
(
x
)
)
2
dx
tangent y=4x-x^2,\at x=a
tangent
y
=
4
x
−
x
2
,
at
x
=
a
derivative of 2x(4x+9^{1/2}+12)
d
dx
(
2
x
(
4
x
+
9
)
1
2
+
1
2
)
derivative of (x^2+x*(tan(x)))
d
dx
(
(
x
2
+
x
)
·
(
tan
(
x
)
)
)
derivative of arcsin(-x)
d
dx
(
arcsin
(
−
x
)
)
derivative of 6sec(x^2)
d
dx
(
6
sec
(
x
2
)
)
derivative (410t)/((t^2+5)^3)
derivative
4
1
0
t
(
t
2
+
5
)
3
derivative of (4-3x-x^2/(x-2))
d
dx
(
4
−
3
x
−
x
2
x
−
2
)
limit as x approaches-1 of F(x)
lim
x
→
−
1
(
F
(
x
)
)
integral of log_{e}(2y+1)
∫
log
e
(
2
y
+
1
)
dy
integral of-3/5 e^x
∫
−
3
5
e
x
dx
integral of 4-6x-40x^3
∫
4
−
6
x
−
4
0
x
3
dx
integral from 0 to 2 of sqrt(1+e^{-2x)}
∫
0
2
√
1
+
e
−
2
x
dx
sum from n=1 to infinity of 3/((-2)^n)
∑
n
=
1
∞
3
(
−
2
)
n
integral from 0 to infinity of 1/(5+x)
∫
0
∞
1
5
+
x
dx
derivative f(x)=sqrt(x^2)
derivative
f
(
x
)
=
√
x
2
derivative 5arcsin((x-1)/(x+1))
derivative
5
arcsin
(
x
−
1
x
+
1
)
derivative y=(2x^2+8x+4)/(sqrt(x))
derivative
y
=
2
x
2
+
8
x
+
4
√
x
limit as x approaches infinity+of x^0
lim
x
→
∞
+
(
x
0
)
3^'
3
′
xy^'+y=x^2
xy
′
+
y
=
x
2
derivative arctan(8t)
derivative
arctan
(
8
t
)
integral of x/(x^4+6)
∫
x
x
4
+
6
dx
(\partial)/(\partial x)(y(1-e^{-x}))
∂
∂
x
(
y
(
1
−
e
−
x
)
)
integral of 2x+4sin(x)
∫
2
x
+
4
sin
(
x
)
dx
integral from 0 to infinity of x*e^{-2x}
∫
0
∞
x
·
e
−
2
x
dx
(dy)/(dx)=y*tan(x)+1
dy
dx
=
y
·
tan
(
x
)
+
1
(d^2)/(dx^2)(2^{x^2+1})
d
2
dx
2
(
2
x
2
+
1
)
(dy)/(dx)=e^{5y}
dy
dx
=
e
5
y
derivative of e^{-2x}sin(x)
d
dx
(
e
−
2
x
sin
(
x
)
)
limit as x approaches-1 of (|x|)/x
lim
x
→
−
1
(
|
x
|
x
)
(dP)/(dt)=P(1/t-P)
dP
dt
=
P
(
1
t
−
P
)
limit as x approaches 2 of x^2+x
lim
x
→
2
(
x
2
+
x
)
(\partial)/(\partial v)(e^{{u}(v)}cos(v))
∂
∂
v
(
e
u
(
v
)
cos
(
v
)
)
derivative y=e^{-12x}
derivative
y
=
e
−
1
2
x
integral of (1/2 sec(x)tan(x))
∫
(
1
2
sec
(
x
)
tan
(
x
)
)
dx
limit as x approaches 0 of x/(x+3)
lim
x
→
0
(
x
x
+
3
)
integral from 1 to 2 of 3ln(4x)
∫
1
2
3
ln
(
4
x
)
dx
integral of-3x^{-2}
∫
−
3
x
−
2
dx
tangent f(x)=(2x^3+1)^2,(-1,1)
tangent
f
(
x
)
=
(
2
x
3
+
1
)
2
,
(
−
1
,
1
)
limit as x approaches 0 of ((ee^{-ax}-e^{-bx}))/x
lim
x
→
0
(
(
ee
−
ax
−
e
−
bx
)
x
)
derivative f(x)=x^3-3x+1
derivative
f
(
x
)
=
x
3
−
3
x
+
1
面积 x=36-y^2,x=y^2-36
area
x
=
3
6
−
y
2
,
x
=
y
2
−
3
6
integral of t-cos(t)
∫
t
−
cos
(
t
)
dt
derivative of (3x^2-18x+25/(x^2-6x+8))
d
dx
(
3
x
2
−
1
8
x
+
2
5
x
2
−
6
x
+
8
)
integral of (4x-2)/((4x^2-4x+2)^4)
∫
4
x
−
2
(
4
x
2
−
4
x
+
2
)
4
dx
inverse拉普拉斯 (1-e^{-2s})/(6s^2)
inverselaplace
1
−
e
−
2
s
6
s
2
1
..
1213
1214
1215
1216
1217
..
2459