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常见 微积分 问题
limit as x approaches 0 of 8/(x^2+x)-8/x
lim
x
→
0
(
8
x
2
+
x
−
8
x
)
derivative of \sqrt[3]{arcsin(x})
d
dx
(
3
√
arcsin
(
x
)
)
limit as x approaches 1 of 1/(ax+2)
lim
x
→
1
(
1
ax
+
2
)
integral from-5 to 1 of |x+2|
∫
−
5
1
|
x
+
2
|
dx
(\partial)/(\partial y)(-4y)
∂
∂
y
(
−
4
y
)
derivative ln((x^2+1)/(x+1))
derivative
ln
(
x
2
+
1
x
+
1
)
integral of sqrt(1+2x^4)(8x^3)
∫
√
1
+
2
x
4
(
8
x
3
)
dx
y^'= x/y
y
′
=
x
y
derivative of x^3+2x^2
d
dx
(
x
3
+
2
x
2
)
(\partial)/(\partial x)(xln(z^4+x^7))
∂
∂
x
(
x
ln
(
z
4
+
x
7
)
)
tangent f(x)=(2x)/(x^2+1),\at x=-1
tangent
f
(
x
)
=
2
x
x
2
+
1
,
at
x
=
−
1
integral of e^{4t}
∫
e
4
t
dt
((x-sqrt(x))*(x+sqrt(x)))^'
(
(
x
−
√
x
)
·
(
x
+
√
x
)
)
′
derivative of 3sin(2x+e^{-x})
d
dx
(
3
sin
(
2
x
)
+
e
−
x
)
inverse拉普拉斯 ((s^4+4))/(s^4-4)
inverselaplace
(
s
4
+
4
)
s
4
−
4
integral of 7^{2x+3}
∫
7
2
x
+
3
dx
(\partial)/(\partial x)(-6y)
∂
∂
x
(
−
6
y
)
derivative of (sqrt(5-2x)/(2x+1))
d
dx
(
√
5
−
2
x
2
x
+
1
)
limit as x approaches 0+of x^{-5}ln(x)
lim
x
→
0
+
(
x
−
5
ln
(
x
)
)
derivative 2x^3-x
derivative
2
x
3
−
x
integral of (3sin(x)-2cos(x))
∫
(
3
sin
(
x
)
−
2
cos
(
x
)
)
dx
sum from n=2 to infinity of 1/(2^{n-1)}
∑
n
=
2
∞
1
2
n
−
1
derivative 45x^8-12x^5
derivative
4
5
x
8
−
1
2
x
5
derivative of (96/x)
d
dx
(
9
6
x
)
11x-4ysqrt(x^2+1)y^'=0
1
1
x
−
4
y
√
x
2
+
1
y
′
=
0
derivative f(x)=11sqrt(x)
derivative
f
(
x
)
=
1
1
√
x
derivative of (x+3/(x-3))
d
dx
(
x
+
3
x
−
3
)
derivative x^2*ln(x)
derivative
x
2
·
ln
(
x
)
integral of (3x^2)/(sqrt(x^2-4))
∫
3
x
2
√
x
2
−
4
dx
integral of sin(2y)(3-cos(2y))^2
∫
sin
(
2
y
)
(
3
−
cos
(
2
y
)
)
2
dy
tangent (x-1)/(x+1)
tangent
x
−
1
x
+
1
integral from 0 to 1 of 6x(1-x)
∫
0
1
6
x
(
1
−
x
)
dx
f(x)=-cos(2x)
f
(
x
)
=
−
cos
(
2
x
)
(\partial)/(\partial x)((z-x)/(z+y))
∂
∂
x
(
z
−
x
z
+
y
)
derivative of (16x/((4-x^2)^2))
d
dx
(
1
6
x
(
4
−
x
2
)
2
)
integral of 1/(2x^2+3x+1)
∫
1
2
x
2
+
3
x
+
1
dx
(\partial)/(\partial x)(4sin(6x-7y))
∂
∂
x
(
4
sin
(
6
x
−
7
y
)
)
integral of-2t^5
∫
−
2
t
5
dt
derivative (x^2-9)^2
derivative
(
x
2
−
9
)
2
integral of (x^2+1/((3x)^2))
∫
(
x
2
+
1
(
3
x
)
2
)
dx
integral of x^3-3x^2+2x
∫
x
3
−
3
x
2
+
2
xdx
integral of (x^3-6x^2+11x-6)/(4x^3-28x^2+56x-32)
∫
x
3
−
6
x
2
+
1
1
x
−
6
4
x
3
−
2
8
x
2
+
5
6
x
−
3
2
dx
integral from-infinity to 0 of e^{5x}
∫
−
∞
0
e
5
x
dx
(\partial)/(\partial x)(5xln(x^2+y))
∂
∂
x
(
5
x
ln
(
x
2
+
y
)
)
limit as x approaches 0 of x^2-6
lim
x
→
0
(
x
2
−
6
)
integral of 2sin(ln(x))
∫
2
sin
(
ln
(
x
)
)
dx
derivative (f(x))/(g(x)+1)
derivative
f
(
x
)
g
(
x
)
+
1
derivative (x^2)/(3+8x)
derivative
x
2
3
+
8
x
integral of 3sqrt(t+1)
∫
3
√
t
+
1
dt
derivative of x^3-3x^2+5x-2
d
dx
(
x
3
−
3
x
2
+
5
x
−
2
)
derivative of ae^x+b/x+c/(x^2)
d
dx
(
ae
x
+
b
x
+
c
x
2
)
tangent f(x)=7x^2-x^3,\at x=1
tangent
f
(
x
)
=
7
x
2
−
x
3
,
at
x
=
1
integral from 0 to 1 of ln(4+x^2)
∫
0
1
ln
(
4
+
x
2
)
dx
integral of-ucos(2u)
∫
−
u
cos
(
2
u
)
du
integral of 1/([(x^2+9)^2])
∫
1
[
(
x
2
+
9
)
2
]
dx
derivative of (7^x/(x^3))
d
dx
(
7
x
x
3
)
integral of (e^{2x}-1)/(e^{2x)+3}
∫
e
2
x
−
1
e
2
x
+
3
dx
limit as x approaches 3 of (x+1)/(x^2-9)
lim
x
→
3
(
x
+
1
x
2
−
9
)
integral of 1/(-1+x^2)
∫
1
−
1
+
x
2
dx
derivative of-1/64 sin(x/8)
d
dx
(
−
1
6
4
sin
(
x
8
)
)
d/(dt)(acos(wt)+bsin(wt))
d
dt
(
a
cos
(
wt
)
+
b
sin
(
wt
)
)
integral of (e^{5x})(cos(-2x))
∫
(
e
5
x
)
(
cos
(
−
2
x
)
)
dx
(dy)/(dx)=y-x,y(0)= 2/3
dy
dx
=
y
−
x
,
y
(
0
)
=
2
3
integral of (2x+1)/((x-1)(x+3))
∫
2
x
+
1
(
x
−
1
)
(
x
+
3
)
dx
derivative of (x^2-x+5/(4x-1))
d
dx
(
x
2
−
x
+
5
4
x
−
1
)
(\partial)/(\partial y)(e^{-2y}cos(x))
∂
∂
y
(
e
−
2
y
cos
(
x
)
)
derivative of (x-1(x^2-8x+7))
d
dx
(
(
x
−
1
)
(
x
2
−
8
x
+
7
)
)
面积 y=5cos(2x),y=5sin(4x),x=0,x= pi/4
area
y
=
5
cos
(
2
x
)
,
y
=
5
sin
(
4
x
)
,
x
=
0
,
x
=
π
4
laplace变换 cos(t/2)
laplacetransform
cos
(
t
2
)
inverse拉普拉斯 (22.96)/((s+10.7))
inverselaplace
2
2
.
9
6
(
s
+
1
0
.
7
)
limit as x approaches 2 of (sin(x))/x
lim
x
→
2
(
sin
(
x
)
x
)
derivative of ln(1/4 e^x+3/4 e^{-x})
d
dx
(
ln
(
1
4
e
x
+
3
4
e
−
x
)
)
derivative of ln|x-1|
d
dx
(
ln
|
x
−
1
|
)
f^'(x)=cos(x),f(0)=-5
f
′
(
x
)
=
cos
(
x
)
,
f
(
0
)
=
−
5
derivative of sin^2(-3x+6)
d
dx
(
sin
2
(
−
3
x
+
6
)
)
斜率intercept (-10,3),(-8,-8)
slopeintercept
(
−
1
0
,
3
)
,
(
−
8
,
−
8
)
sum from n=0 to infinity of (1/5)^{n+1}
∑
n
=
0
∞
(
1
5
)
n
+
1
integral of (e^x+2x)^2
∫
(
e
x
+
2
x
)
2
dx
integral of (x^3)/(sqrt(1-x^4))
∫
x
3
√
1
−
x
4
dx
derivative f(x)=sqrt(5-3x)
derivative
f
(
x
)
=
√
5
−
3
x
integral from-1 to 1 of (x^2-x)
∫
−
1
1
(
x
2
−
x
)
dx
integral of 4r
∫
4
rdr
integral of 1/(x-9)
∫
1
x
−
9
dx
implicit y/(x-5y)=x^7+9
implicit
y
x
−
5
y
=
x
7
+
9
xe^y(dy)/(dx)=2(e^y+x^3e^{2x})
xe
y
dy
dx
=
2
(
e
y
+
x
3
e
2
x
)
(dy)/(dx)=e^{5x}+10y
dy
dx
=
e
5
x
+
1
0
y
integral from 0 to 1 of (1+e^x)/(e^x)
∫
0
1
1
+
e
x
e
x
dx
(\partial)/(\partial x)((-x-6y)/(y^2+5x^2))
∂
∂
x
(
−
x
−
6
y
y
2
+
5
x
2
)
(\partial)/(\partial x)(sqrt(2-x^2))
∂
∂
x
(
√
2
−
x
2
)
inverse拉普拉斯 1/(s^2+4)
inverselaplace
1
s
2
+
4
integral of 1/(x\sqrt[8]{x)}
∫
1
x
8
√
x
dx
7t*(dy)/(dt)-4y=sqrt(t)
7
t
·
dy
dt
−
4
y
=
√
t
derivative of 1-sin(3x)
d
dx
(
1
−
sin
(
3
x
)
)
inverse拉普拉斯 (e^{-5s})/(s^2)
inverselaplace
e
−
5
s
s
2
limit as x approaches 3+of ((x^2))/(x-3)
lim
x
→
3
+
(
(
x
2
)
x
−
3
)
integral from 0 to 1 of 2pi(2-y)(5y^2)
∫
0
1
2
π
(
2
−
y
)
(
5
y
2
)
dy
(\partial)/(\partial y)(2ye^{-x})
∂
∂
y
(
2
ye
−
x
)
derivative of (3x/(x^2+3)+98.6)
d
dx
(
3
x
x
2
+
3
+
9
8
.
6
)
化简 (3x^2)^{2x}*(x^2+2x)^2
simplify
(
3
x
2
)
2
x
·
(
x
2
+
2
x
)
2
integral of (2x^4)/(sqrt(7-6x^5))
∫
2
x
4
√
7
−
6
x
5
dx
1
..
797
798
799
800
801
..
2459