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常见 微积分 问题
limit as x approaches 30 of (x^2)/6-5/x
lim
x
→
3
0
(
x
2
6
−
5
x
)
derivative of (4x-5/(3x+2))
d
dx
(
4
x
−
5
3
x
+
2
)
(\partial)/(\partial x)(e^{-3x^2-5y^2})
∂
∂
x
(
e
−
3
x
2
−
5
y
2
)
integral of (-2ln(x))/(x^2)
∫
−
2
ln
(
x
)
x
2
dx
integral of (e^{-x}(3-3xln(x)))/(2x)
∫
e
−
x
(
3
−
3
x
ln
(
x
)
)
2
x
dx
integral of 1/(3-(x-2)^2)
∫
1
3
−
(
x
−
2
)
2
dx
integral of 4-|x|
∫
4
−
|
x
|
dx
integral from-1 to 1 of sqrt(x+1)-1
∫
−
1
1
√
x
+
1
−
1
dx
integral from-3 to 2 of |x+1|
∫
−
3
2
|
x
+
1
|
dx
limit as x approaches 1 of (2x)/(ln(x))
lim
x
→
1
(
2
x
ln
(
x
)
)
斜率 (2.9)(9.7)
slope
(
2
.
9
)
(
9
.
7
)
derivative f(x)=sqrt(6-x)
derivative
f
(
x
)
=
√
6
−
x
integral from 0 to 2 of e^{x/2}
∫
0
2
e
x
2
dx
(dy)/(dx)=(xy^3)/(sqrt(1+x^2))
dy
dx
=
xy
3
√
1
+
x
2
integral of 4-4x
∫
4
−
4
xdx
(dy)/y-4xdx=0
dy
y
−
4
xdx
=
0
derivative f(x)=xln(x)
derivative
f
(
x
)
=
x
ln
(
x
)
面积 x^3,x^2+x,-1,1.5
area
x
3
,
x
2
+
x
,
−
1
,
1
.
5
泰勒 (x^2+1/4)^{3/2}
taylor
(
x
2
+
1
4
)
3
2
derivative of ln(2x^2+3)
d
dx
(
ln
(
2
x
2
+
3
)
)
integral of 8x^{3/5}+7x^{-4/5}
∫
8
x
3
5
+
7
x
−
4
5
dx
laplace变换 1+e^{-t}
laplacetransform
1
+
e
−
t
derivative (4x-3)/(sqrt(x))
derivative
4
x
−
3
√
x
y^{''}-3/x y^'-4/(x^2)y=0
y
′
′
−
3
x
y
′
−
4
x
2
y
=
0
(\partial)/(\partial x)(17x^3y^2)
∂
∂
x
(
1
7
x
3
y
2
)
derivative of e^x(5x^2-2x+3)
d
dx
(
e
x
(
5
x
2
−
2
x
+
3
)
)
(dy)/(dx)=(ysin(x))/(1-2y)
dy
dx
=
y
sin
(
x
)
1
−
2
y
y^'=e^{y-x},y(0)=0
y
′
=
e
y
−
x
,
y
(
0
)
=
0
derivative of cx^{-8}
d
dx
(
cx
−
8
)
derivative sqrt(x^2)
derivative
√
x
2
(\partial)/(\partial x)(e^{xyz^6})
∂
∂
x
(
e
xyz
6
)
(\partial)/(\partial x)(|x+y|-2)
∂
∂
x
(
|
x
+
y
|
−
2
)
integral of (-3x^{-2.5}-7x^{-1})
∫
(
−
3
x
−
2
.
5
−
7
x
−
1
)
dx
d/(da)((sin(a)+cos(a))/(sec(a)+csc(a)))
d
da
(
sin
(
a
)
+
cos
(
a
)
sec
(
a
)
+
csc
(
a
)
)
derivative of 10sin(2x)
d
dx
(
1
0
sin
(
2
x
)
)
integral of-e^{x^2}x
∫
−
e
x
2
xdx
derivative of x^{log_{6}(x})
d
dx
(
x
log
6
(
x
)
)
integral of-6cos(x)
∫
−
6
cos
(
x
)
dx
integral of 11ln(x^2-x+2)
∫
1
1
ln
(
x
2
−
x
+
2
)
dx
derivative ((e^x+e^{-x}))/2
derivative
(
e
x
+
e
−
x
)
2
y^'-2ty=4t^3
y
′
−
2
ty
=
4
t
3
integral from 4 to 5 of xsqrt(25-x^2)
∫
4
5
x
√
2
5
−
x
2
dx
integral of (e^{-y})
∫
(
e
−
y
)
dy
derivative ((x-8))/(9x^2e^x)
derivative
(
x
−
8
)
9
x
2
e
x
x^'=(1-x)*0.03-((0.03x))/((e^3-1))
x
′
=
(
1
−
x
)
·
0
.
0
3
−
(
0
.
0
3
x
)
(
e
3
−
1
)
y^'-(2y)/x =-x^2y^2
y
′
−
2
y
x
=
−
x
2
y
2
integral of (ax)/(x^4+b^4)
∫
ax
x
4
+
b
4
dx
limit as x approaches 0 of (-1)/(5x)
lim
x
→
0
(
−
1
5
x
)
f(x)=sec^2(2x)
f
(
x
)
=
sec
2
(
2
x
)
limit as x approaches-2 of 2x+sqrt(2+x)
lim
x
→
−
2
(
2
x
+
√
2
+
x
)
(\partial)/(\partial x)(e^{xyz^7})
∂
∂
x
(
e
xyz
7
)
derivative of x^2+sin(x)
d
dx
(
x
2
+
sin
(
x
)
)
xy^2(dy)/(dx)=y^3-x^3
xy
2
dy
dx
=
y
3
−
x
3
derivative 36x^2-48x
derivative
3
6
x
2
−
4
8
x
derivative ln(x)+1
derivative
ln
(
x
)
+
1
((sin(x))^2)^'
(
(
sin
(
x
)
)
2
)
′
inverse拉普拉斯 4(1/(s^3))
inverselaplace
4
(
1
s
3
)
sum from n=0 to infinity of (n^2)/(5n)
∑
n
=
0
∞
n
2
5
n
derivative 6x^4
derivative
6
x
4
(\partial)/(\partial u)(warctan(uv))
∂
∂
u
(
w
arctan
(
uv
)
)
integral of sinh(t)
∫
sinh
(
t
)
dt
integral of (x^4)/(1-x)
∫
x
4
1
−
x
dx
(\partial)/(\partial x)(y-z)
∂
∂
x
(
y
−
z
)
d/(du)(e^u)
d
du
(
e
u
)
laplace变换 5t-pi/3
laplacetransform
5
t
−
π
3
derivative of (x-9/(8x^2e^x))
d
dx
(
x
−
9
8
x
2
e
x
)
(dy)/(dx)=4x(x-2)
dy
dx
=
4
x
(
x
−
2
)
sum from n=1 to infinity of-1/(sqrt(n))
∑
n
=
1
∞
−
1
√
n
integral of e^{3x^2}
∫
e
3
x
2
dx
(\partial)/(\partial θ)(rsin(θ))
∂
∂
θ
(
r
sin
(
θ
)
)
integral of 2/(x^3+x^2+x+1)
∫
2
x
3
+
x
2
+
x
+
1
dx
integral of 7x^3e^{5x}
∫
7
x
3
e
5
x
dx
泰勒 (1+x)^2
taylor
(
1
+
x
)
2
x((dy)/(dx))-y=x^2
x
(
dy
dx
)
−
y
=
x
2
sum from n=0 to infinity of (2^n)/(5^n)
∑
n
=
0
∞
2
n
5
n
limit as x approaches infinity-of 1/x
lim
x
→
∞
−
(
1
x
)
xy^'=xe^{-2x}-(2x+1)y
xy
′
=
xe
−
2
x
−
(
2
x
+
1
)
y
limit as x approaches 8-of 4x
lim
x
→
8
−
(
4
x
)
derivative of c_{2}-3c_{1}-3c_{2}x
d
dx
(
c
2
−
3
c
1
−
3
c
2
x
)
integral of 8/(1+x^2)
∫
8
1
+
x
2
dx
(\partial)/(\partial x)(5x^4+y^7)
∂
∂
x
(
5
x
4
+
y
7
)
y(dy)/(dx)+25x=0
y
dy
dx
+
2
5
x
=
0
limit as x approaches 4 of sqrt(4x+48)
lim
x
→
4
(
√
4
x
+
4
8
)
(\partial)/(\partial x)(-3x(-9-x-2y))
∂
∂
x
(
−
3
x
(
−
9
−
x
−
2
y
)
)
(dy)/(dt)t=y+6t^2sin(t)
dy
dt
t
=
y
+
6
t
2
sin
(
t
)
laplace变换 0.2t
laplacetransform
0
.
2
t
integral of xsqrt(x^2-4)
∫
x
√
x
2
−
4
dx
(dy)/(dx)-7y=xe^{2x}
dy
dx
−
7
y
=
xe
2
x
derivative of (4x+3/(5e^x))
d
dx
(
4
x
+
3
5
e
x
)
derivative of ln(x^2-2x+1)
d
dx
(
ln
(
x
2
−
2
x
+
1
)
)
limit as x approaches-19 of 13+x
lim
x
→
−
1
9
(
1
3
+
x
)
integral of (x^2)/(sqrt(25-x^2))
∫
x
2
√
2
5
−
x
2
dx
derivative of x^y+y^x
d
dx
(
x
y
+
y
x
)
tangent f(x)=x^3-3x+2,\at x=3
tangent
f
(
x
)
=
x
3
−
3
x
+
2
,
at
x
=
3
sum from n=1 to infinity of 7(1/10)^n
∑
n
=
1
∞
7
(
1
1
0
)
n
derivative of sin(sqrt(1-x))
d
dx
(
sin
(
√
1
−
x
)
)
inverse拉普拉斯 1/((s+5)^2)
inverselaplace
1
(
s
+
5
)
2
derivative of (2x^5+3x^4-x^3+2/(x^2))
d
dx
(
2
x
5
+
3
x
4
−
x
3
+
2
x
2
)
integral from 0 to 3 of 2x-1
∫
0
3
2
x
−
1
dx
integral of 3/2 x^{1/2}
∫
3
2
x
1
2
dx
1
..
550
551
552
553
554
..
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