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常见 微积分 问题
limit as x approaches 2 of (x^3)/3-7x^2
lim
x
→
2
(
x
3
3
−
7
x
2
)
f(y)=y^4
f
(
y
)
=
y
4
(d^2)/(dx^2)(sec(pi/4))
d
2
dx
2
(
sec
(
π
4
)
)
integral of sec(x)tan(x)-9e^x
∫
sec
(
x
)
tan
(
x
)
−
9
e
x
dx
integral from 1 to 3 of x^2e^x
∫
1
3
x
2
e
x
dx
tangent f(x)=x^2,\at x=-1/4
tangent
f
(
x
)
=
x
2
,
at
x
=
−
1
4
y^'-2xy-8=0
y
′
−
2
xy
−
8
=
0
laplacetransform e^{3(t+1)}
laplacetransform
e
3
(
t
+
1
)
derivative y=x(3x-2)^4
derivative
y
=
x
(
3
x
−
2
)
4
integral of (e^{2x})/(\sqrt[4]{e^x+1)}
∫
e
2
x
4
√
e
x
+
1
dx
integral of x^2(sqrt(4+x^3))
∫
x
2
(
√
4
+
x
3
)
dx
xy^'+y=5xy^2
xy
′
+
y
=
5
xy
2
integral of 1/((6-x^2)^{3/2)}
∫
1
(
6
−
x
2
)
3
2
dx
derivative of 2x-(2000/(x^2))
d
dx
(
2
x
−
2
0
0
0
x
2
)
integral of 6arctan(4y)
∫
6
arctan
(
4
y
)
dy
(\partial)/(\partial x)(2y^{4x})
∂
∂
x
(
2
y
4
x
)
tangent f(x)=sin(x)+1,\at x=-pi/2
tangent
f
(
x
)
=
sin
(
x
)
+
1
,
at
x
=
−
π
2
面积 f(x)=x^2-4,x=-4,x=3
area
f
(
x
)
=
x
2
−
4
,
x
=
−
4
,
x
=
3
integral of 1/(x^2sqrt(a^2-x^2))
∫
1
x
2
√
a
2
−
x
2
dx
limit as x approaches-3 of |x|-2
lim
x
→
−
3
(
|
x
|
−
2
)
laplacetransform e^t
laplacetransform
e
t
tangent f(x)=(5x)/(x+3),2,\at x=2
tangent
f
(
x
)
=
5
x
x
+
3
,
2
,
at
x
=
2
derivative of 2^{arctan(x})
d
dx
(
2
arctan
(
x
)
)
integral of (x+1)^2e^{-2x}
∫
(
x
+
1
)
2
e
−
2
x
dx
(\partial)/(\partial x)(cos^6(x^2y^9))
∂
∂
x
(
cos
6
(
x
2
y
9
)
)
derivative of 3x^2+xy+2x+y
d
dx
(
3
x
2
+
xy
+
2
x
+
y
)
泰勒 cos(x), pi/2
taylor
cos
(
x
)
,
π
2
(\partial)/(\partial y)(x^4y-3x^5y^2)
∂
∂
y
(
x
4
y
−
3
x
5
y
2
)
limit as x approaches 1 of x+1
lim
x
→
1
(
x
+
1
)
integral of xln(3x)
∫
x
ln
(
3
x
)
dx
derivative of x(x-15^2)
d
dx
(
x
(
x
−
1
5
)
2
)
integral of e^{sin(x)}cos(x)
∫
e
sin
(
x
)
cos
(
x
)
dx
integral of 224sin(7x)\sqrt[3]{cos(7x)}
∫
2
2
4
sin
(
7
x
)
3
√
cos
(
7
x
)
dx
integral of 3sin^3(x)cos^3(x)
∫
3
sin
3
(
x
)
cos
3
(
x
)
dx
integral from-1 to 2 of (x-8|x|)
∫
−
1
2
(
x
−
8
|
x
|
)
dx
derivative of x^{4/5}*(x-4^2)
d
dx
(
x
4
5
·
(
x
−
4
)
2
)
integral of 1/(w^2)
∫
1
w
2
dw
integral of x^4*2^{x^5+7}
∫
x
4
·
2
x
5
+
7
dx
integral of (19)/((1-x^2)^{3/2)}
∫
1
9
(
1
−
x
2
)
3
2
dx
integral of cos((nx)/2)
∫
cos
(
nx
2
)
dx
integral of 1/((1+e^{-y))}
∫
1
(
1
+
e
−
y
)
dy
derivative of \sqrt[7]{x}+2sqrt(x^7)
d
dx
(
7
√
x
+
2
√
x
7
)
integral of x^7e^{-x^4}
∫
x
7
e
−
x
4
dx
integral of log_{b}(x)
∫
log
b
(
x
)
dx
面积 y+x=4,36-9x=y^2
area
y
+
x
=
4
,
3
6
−
9
x
=
y
2
d/(dt)(A*(cos(ωt+φ)))
d
dt
(
A
·
(
cos
(
ω
t
+
φ
)
)
)
y^'(x)=(x^2)/(1-y^2),y(4)=2
y
′
(
x
)
=
x
2
1
−
y
2
,
y
(
4
)
=
2
integral of 2sqrt(x)e^{sqrt(x)}
∫
2
√
x
e
√
x
dx
derivative y=(x^2+1)^3
derivative
y
=
(
x
2
+
1
)
3
integral of (1+cos(2x))/(sin^2(2x))
∫
1
+
cos
(
2
x
)
sin
2
(
2
x
)
dx
(\partial)/(\partial y)(x+3y)
∂
∂
y
(
x
+
3
y
)
斜率 (-1.3)(3.5)
slope
(
−
1
.
3
)
(
3
.
5
)
derivative g(x)=ln^3(x)
derivative
g
(
x
)
=
ln
3
(
x
)
tangent y=(5x)/(2^x),\at x=2
tangent
y
=
5
x
2
x
,
at
x
=
2
(\partial)/(\partial y)(ln(x^2+3y))
∂
∂
y
(
ln
(
x
2
+
3
y
)
)
derivative of (6x^5-7x/(x^4-8))
d
dx
(
6
x
5
−
7
x
x
4
−
8
)
integral of (6e^{-0.2x})
∫
(
6
e
−
0
.
2
x
)
dx
面积 5-x,25-x^2
area
5
−
x
,
2
5
−
x
2
integral of 1/(x^2)arctan(x)
∫
1
x
2
arctan
(
x
)
dx
limit as x approaches 4+of sqrt(x-4)
lim
x
→
4
+
(
√
x
−
4
)
derivative f(x)=0.6x^{1.5}
derivative
f
(
x
)
=
0
.
6
x
1
.
5
(dy)/(dx)=9.8-0.196y
dy
dx
=
9
.
8
−
0
.
1
9
6
y
y^{''}-4y^'-21y=0
y
′
′
−
4
y
′
−
2
1
y
=
0
integral of sec^4(u)tan(u)
∫
sec
4
(
u
)
tan
(
u
)
du
2x(y+1)dx-ydy=0
2
x
(
y
+
1
)
dx
−
ydy
=
0
limit as x approaches 0 of arccos(x)
lim
x
→
0
(
arccos
(
x
)
)
limit as x approaches infinity of 6x
lim
x
→
∞
(
6
x
)
integral of 5sin^3(x)cos^2(x)
∫
5
sin
3
(
x
)
cos
2
(
x
)
dx
derivative f(x)=arcsin(6x+1)
derivative
f
(
x
)
=
arcsin
(
6
x
+
1
)
integral of y^2z^3
∫
y
2
z
3
dx
(\partial)/(\partial x)(4ln((3xy)/(7z)))
∂
∂
x
(
4
ln
(
3
xy
7
z
)
)
integral of-cos(2y)
∫
−
cos
(
2
y
)
dy
derivative 4sqrt(x)-3/(x^6)
derivative
4
√
x
−
3
x
6
integral of 2x^2-4
∫
2
x
2
−
4
dx
integral of 4/(sqrt(x+4)+\sqrt{x)}
∫
4
√
x
+
4
+
√
x
dx
limit as x approaches-1 of 4x^3-2m
lim
x
→
−
1
(
4
x
3
−
2
m
)
limit as x approaches 0-of (x^2)/2-1/x
lim
x
→
0
−
(
x
2
2
−
1
x
)
integral of 1/(sec(x)+1)
∫
1
sec
(
x
)
+
1
dx
tangent y=sqrt(x),(49,7)
tangent
y
=
√
x
,
(
4
9
,
7
)
integral of (25)/(x^{3/2)}
∫
2
5
x
3
2
dx
integral of x*2^{x^2}
∫
x
·
2
x
2
dx
f'(x)
f
′
(
x
)
integral of xsec^2(4x)
∫
x
sec
2
(
4
x
)
dx
tangent f(x)=(x^2-15)^7,\at x=4
tangent
f
(
x
)
=
(
x
2
−
1
5
)
7
,
at
x
=
4
x(dy)/(dx)+2y=6x^2sqrt(y)
x
dy
dx
+
2
y
=
6
x
2
√
y
derivative of acos^3(x)
d
dx
(
a
cos
3
(
x
)
)
derivative y=x^2ln(3x)
derivative
y
=
x
2
ln
(
3
x
)
y^'=((1-y)^2)/(x+1),y(0)=5
y
′
=
(
1
−
y
)
2
x
+
1
,
y
(
0
)
=
5
derivative of ln(ln(sec(x)))
d
dx
(
ln
(
ln
(
sec
(
x
)
)
)
)
sum from n=1 to infinity of 1-7/(4^n)
∑
n
=
1
∞
1
−
7
4
n
(\partial)/(\partial x)(8-x^2-y^2)
∂
∂
x
(
8
−
x
2
−
y
2
)
24y^{''}-2y^'-15y=0
2
4
y
′
′
−
2
y
′
−
1
5
y
=
0
d/(dt)(cos^2(e^{cos^2(t)}))
d
dt
(
cos
2
(
e
cos
2
(
t
)
)
)
limit as x approaches-2 of 5x^2
lim
x
→
−
2
(
5
x
2
)
(dy)/(dx)=(cos(16x))/(e^{16y)}
dy
dx
=
cos
(
1
6
x
)
e
1
6
y
derivative of tan(xsec^2(x))
d
dx
(
tan
(
x
)
sec
2
(
x
)
)
integral from 2 to 3 of (31)/(sqrt(3-x))
∫
2
3
3
1
√
3
−
x
dx
(tsin(t))^'
(
t
sin
(
t
)
)
′
(\partial)/(\partial x)(e^{xz}y^3-ln(x))
∂
∂
x
(
e
xz
y
3
−
ln
(
x
)
)
derivative of arctan(11x)
d
dx
(
arctan
(
1
1
x
)
)
1
..
10
11
12
13
14
..
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