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常见 微积分 问题
麦克劳林 10^x
maclaurin
1
0
x
(dy)/(dx)-5y=6e^{8x}
dy
dx
−
5
y
=
6
e
8
x
derivative of e^{1/(x^2}+1/(e^{x^2)})
d
dx
(
e
1
x
2
+
1
e
x
2
)
integral of sqrt((x^2)/4-4x+17)
∫
√
x
2
4
−
4
x
+
1
7
dx
derivative of in(x+3)
d
dx
(
in
(
x
+
3
)
)
((x^2+2y^2)dx)/(dy)=xy
(
x
2
+
2
y
2
)
dx
dy
=
xy
integral from 5 to 8 of y/(y^2-y-2)
∫
5
8
y
y
2
−
y
−
2
dy
面积 e^x,e^{5x},0,1
area
e
x
,
e
5
x
,
0
,
1
derivative f(x)=\sqrt[7]{x}-7e^x
derivative
f
(
x
)
=
7
√
x
−
7
e
x
derivative of 1-sin(2x)
d
dx
(
1
−
sin
(
2
x
)
)
(\partial)/(\partial x)(z^3ln(yx))
∂
∂
x
(
z
3
ln
(
yx
)
)
laplace变换 2*((t-1)^2)*1((t-1))
laplacetransform
2
·
(
(
t
−
1
)
2
)
·
1
(
(
t
−
1
)
)
(\partial)/(\partial x)((7x)/(3y))
∂
∂
x
(
7
x
3
y
)
normal f(x)= x/(2x-3),(1,-1)
normal
f
(
x
)
=
x
2
x
−
3
,
(
1
,
−
1
)
integral of (e^{-st})/(s^2)
∫
e
−
st
s
2
dt
derivative y=(100)/(x^4)
derivative
y
=
1
0
0
x
4
f(x)=14400+600x+x^2
f
(
x
)
=
1
4
4
0
0
+
6
0
0
x
+
x
2
(\partial)/(\partial x)(sin(2x)cos(y))
∂
∂
x
(
sin
(
2
x
)
cos
(
y
)
)
(dy)/(dx)=e^{6x}+8y
dy
dx
=
e
6
x
+
8
y
(dy)/(dx)=5x(x-4)
dy
dx
=
5
x
(
x
−
4
)
integral of (\sqrt[7]{x})
∫
(
7
√
x
)
dx
integral of 15x
∫
1
5
xdx
tangent g(x)=e^{x^5-6x},\at x=-1
tangent
g
(
x
)
=
e
x
5
−
6
x
,
at
x
=
−
1
derivative (2x^2+6x+8)/(sqrt(x))
derivative
2
x
2
+
6
x
+
8
√
x
integral of (sqrt(u))/2
∫
√
u
2
du
(\partial)/(\partial x)(x^2sin(y)cos(y))
∂
∂
x
(
x
2
sin
(
y
)
cos
(
y
)
)
d/(dv)(u^2-v^2)
d
dv
(
u
2
−
v
2
)
integral from 0 to 2 of 1/(x+2)
∫
0
2
1
x
+
2
dx
limit as x approaches 0 of ((cos(11x)-cos(6x)))/x
lim
x
→
0
(
(
cos
(
1
1
x
)
−
cos
(
6
x
)
)
x
)
derivative f(x)=x^3sin(x)
derivative
f
(
x
)
=
x
3
sin
(
x
)
derivative of (x^2-6x+1/((x^2-1)^2))
d
dx
(
x
2
−
6
x
+
1
(
x
2
−
1
)
2
)
integral of cos(x)(5+5sin^2(x))
∫
cos
(
x
)
(
5
+
5
sin
2
(
x
)
)
dx
integral from 0 to 1 of (\sqrt[3]{1+7x})
∫
0
1
(
3
√
1
+
7
x
)
dx
integral of x^2-9x+3
∫
x
2
−
9
x
+
3
dx
tangent f(x)=xsqrt(x),(9,27)
tangent
f
(
x
)
=
x
√
x
,
(
9
,
2
7
)
sum from n=1 to infinity of 9/(6+9^n)
∑
n
=
1
∞
9
6
+
9
n
limit as x approaches-3 of (x^2-5)/(3-x)
lim
x
→
−
3
(
x
2
−
5
3
−
x
)
integral of 1/(1-9x^2)
∫
1
1
−
9
x
2
dx
integral of 2cos(x^2)
∫
2
cos
(
x
2
)
dx
derivative of (2x^2+8x+8/(sqrt(x)))
d
dx
(
2
x
2
+
8
x
+
8
√
x
)
derivative f(x)=(2e^x-3x^5)
derivative
f
(
x
)
=
(
2
e
x
−
3
x
5
)
integral of 1/(4t^2-4t+5)
∫
1
4
t
2
−
4
t
+
5
dt
(\partial)/(\partial x)(-4y^3sin(4x))
∂
∂
x
(
−
4
y
3
sin
(
4
x
)
)
derivative of sin(x-csc(x))
d
dx
(
sin
(
x
)
−
csc
(
x
)
)
integral of (2x^2-3)^2
∫
(
2
x
2
−
3
)
2
dx
limit as x approaches 2 of sqrt(x/(x-2))
lim
x
→
2
(
√
x
x
−
2
)
limit as x approaches infinity of x^3
lim
x
→
∞
(
x
3
)
derivative cos(x)+isin(x)
derivative
cos
(
x
)
+
i
sin
(
x
)
integral of e^{2x}x
∫
e
2
x
xdx
integral of 9x^2-24x-36
∫
9
x
2
−
2
4
x
−
3
6
dx
derivative of cos(1-4x)
d
dx
(
cos
(
1
−
4
x
)
)
derivative f(x)=(3-(1/(x^2)))/(x+4)
derivative
f
(
x
)
=
3
−
(
1
x
2
)
x
+
4
integral of e^{-st}cos(t)
∫
e
−
st
cos
(
t
)
dt
ty^'=2
ty
′
=
2
derivative of sec^2(sqrt(x))
d
dx
(
sec
2
(
√
x
)
)
derivative of (sin(x)/(8xe^x))
d
dx
(
sin
(
x
)
8
xe
x
)
d/(dt)(t^5)
d
dt
(
t
5
)
limit as x approaches 0 of tan(x)ln(x)
lim
x
→
0
(
tan
(
x
)
ln
(
x
)
)
tangent 1/(x^5)
tangent
1
x
5
integral of (x+1)(2x^2+sqrt(x))
∫
(
x
+
1
)
(
2
x
2
+
√
x
)
dx
(d^2y)/(dx^2)+6(dy)/(dx)=0
d
2
y
dx
2
+
6
dy
dx
=
0
limit as x approaches-3 of (3-|x|)/(3+x)
lim
x
→
−
3
(
3
−
|
x
|
3
+
x
)
y^{''}+6y^'+34y=25e^{-3x}
y
′
′
+
6
y
′
+
3
4
y
=
2
5
e
−
3
x
derivative of 4x-5x^{5/6}
d
dx
(
4
x
−
5
x
5
6
)
derivative f(x)=xcos(x)+2tan(x)
derivative
f
(
x
)
=
x
cos
(
x
)
+
2
tan
(
x
)
integral of coth(x/3)
∫
coth
(
x
3
)
dx
derivative of a*e^x
d
dx
(
a
·
e
x
)
limit as x approaches-5-of 2/(x^2-25)
lim
x
→
−
5
−
(
2
x
2
−
2
5
)
sum from n=1 to infinity of (6n)/(8n+9)
∑
n
=
1
∞
6
n
8
n
+
9
integral of p^8ln(p)
∫
p
8
ln
(
p
)
dp
integral of cos^3(8x)sin^{-2}(8x)
∫
cos
3
(
8
x
)
sin
−
2
(
8
x
)
dx
y^'=((y^2+1))/(2y)
y
′
=
(
y
2
+
1
)
2
y
integral of (12x^2+x+2)/(x(x^2+1))
∫
1
2
x
2
+
x
+
2
x
(
x
2
+
1
)
dx
sum from n=1 to infinity of 3/(n+1)
∑
n
=
1
∞
3
n
+
1
derivative f(x)=sin(8x+4)
derivative
f
(
x
)
=
sin
(
8
x
+
4
)
integral of (48x^2)/((x-21)(x+7)^2)
∫
4
8
x
2
(
x
−
2
1
)
(
x
+
7
)
2
dx
derivative of 4x+4
d
dx
(
4
x
+
4
)
derivative of 1/(x(x+2^2))
d
dx
(
1
x
(
x
+
2
)
2
)
(tan(2x))^'
(
tan
(
2
x
)
)
′
((4x^3)/3+2x+cos(x)+1)^'
(
4
x
3
3
+
2
x
+
cos
(
x
)
+
1
)
′
integral of (sqrt(16-4x^2))
∫
(
√
1
6
−
4
x
2
)
dx
derivative of 2-sin(x)
d
dx
(
2
−
sin
(
x
)
)
(x^2-x)(dy)/(dx)=y-2xy
(
x
2
−
x
)
dy
dx
=
y
−
2
xy
integral from 0 to 2 of 7x^3sqrt(x^2+4)
∫
0
2
7
x
3
√
x
2
+
4
dx
derivative of (x^2+6x/(10-x^2))
d
dx
(
x
2
+
6
x
1
0
−
x
2
)
y^{''}-7y^'+10y=-sin(3t)
y
′
′
−
7
y
′
+
1
0
y
=
−
sin
(
3
t
)
面积 y=x^2+2x-11,y=3,[3,5]
area
y
=
x
2
+
2
x
−
1
1
,
y
=
3
,
[
3
,
5
]
(\partial)/(\partial x)(4xsin(7x^2y))
∂
∂
x
(
4
x
sin
(
7
x
2
y
)
)
tangent f(x)=3x^2-5x
tangent
f
(
x
)
=
3
x
2
−
5
x
tangent f(x)=-4/3 x^{-5/2},\at x=4
tangent
f
(
x
)
=
−
4
3
x
−
5
2
,
at
x
=
4
derivative of x(x-1(x-2))
d
dx
(
x
(
x
−
1
)
(
x
−
2
)
)
derivative y=\sqrt[7]{x}
derivative
y
=
7
√
x
面积-4x^2+9,x+7
area
−
4
x
2
+
9
,
x
+
7
y^'+5y=te^{(4t)}
y
′
+
5
y
=
te
(
4
t
)
(\partial)/(\partial x)(3x^2-4)
∂
∂
x
(
3
x
2
−
4
)
integral of 9/(9+e^x)
∫
9
9
+
e
x
dx
integral of (-1)/(2sqrt(16-x))
∫
−
1
2
√
1
6
−
x
dx
limit as x approaches infinity of ce^x
lim
x
→
∞
(
ce
x
)
derivative of 4x^2+8
d
dx
(
4
x
2
+
8
)
integral from 0 to pi of cos(x)-sin(x)
∫
0
π
cos
(
x
)
−
sin
(
x
)
dx
1
..
1375
1376
1377
1378
1379
..
2459