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常见 微积分 问题
integral from 2 to 5 of (4-2x)
∫
2
5
(
4
−
2
x
)
dx
derivative of ln(5x^2+6)
d
dx
(
ln
(
5
x
2
+
6
)
)
derivative 9x^3-x^2y+y^3-3
derivative
9
x
3
−
x
2
y
+
y
3
−
3
(\partial)/(\partial y)(xy^2-2x)
∂
∂
y
(
xy
2
−
2
x
)
integral of (x+1)^2e^{1-x}
∫
(
x
+
1
)
2
e
1
−
x
dx
derivative f(x)=(x+3)^4(7-x)^5
derivative
f
(
x
)
=
(
x
+
3
)
4
(
7
−
x
)
5
(\partial)/(\partial y)(xy+z)
∂
∂
y
(
xy
+
z
)
derivative of 1/((2x+3^3))
d
dx
(
1
(
2
x
+
3
)
3
)
derivative y=x^2ln(7x)
derivative
y
=
x
2
ln
(
7
x
)
limit as a approaches infinity of a^2
lim
a
→
∞
(
a
2
)
integral from 1 to 6 of 6/x
∫
1
6
6
x
dx
derivative of (e^{sin(x})/(2+cos(pi)x))
d
dx
(
e
sin
(
x
)
2
+
cos
(
π
)
x
)
implicit (dy)/(dx),y^4=x^5
implicit
dy
dx
,
y
4
=
x
5
integral of t^2e^{4t}
∫
t
2
e
4
t
dt
integral of 9xe^{6x}
∫
9
xe
6
x
dx
derivative of (x^2+x^x)
d
dx
(
(
x
2
+
x
)
x
)
limit as x approaches infinity of e^{px}(acos(q(x)x)+bsin(q(x)x))
lim
x
→
∞
(
e
px
(
a
cos
(
q
(
x
)
x
)
+
b
sin
(
q
(
x
)
x
)
)
)
(dy)/(dx)=4+e^{y-4x+5}
dy
dx
=
4
+
e
y
−
4
x
+
5
integral of x^2*e^{3x}
∫
x
2
·
e
3
x
dx
derivative of \sqrt[4]{3x^2-5x+2}
d
dx
(
4
√
3
x
2
−
5
x
+
2
)
y^{''}+2y^'+y=4e^{-t},y(0)=2,y^'(0)=-1
y
′
′
+
2
y
′
+
y
=
4
e
−
t
,
y
(
0
)
=
2
,
y
′
(
0
)
=
−
1
x^'=x^2+1
x
′
=
x
2
+
1
y^{''}+6y^'-5y=0
y
′
′
+
6
y
′
−
5
y
=
0
derivative of e^{5-2x}
d
dx
(
e
5
−
2
x
)
limit as x approaches-infinity of-8x
lim
x
→
−
∞
(
−
8
x
)
斜率intercept (-2,3),(2,7)
slopeintercept
(
−
2
,
3
)
,
(
2
,
7
)
derivative f(x)=18^r
derivative
f
(
x
)
=
1
8
r
integral from 0 to 4 of pi(4-y)
∫
0
4
π
(
4
−
y
)
dy
(\partial)/(\partial y)(x^4+y^4-4xy+1)
∂
∂
y
(
x
4
+
y
4
−
4
xy
+
1
)
integral of x^3+x
∫
x
3
+
xdx
(dy)/(dx)=6x^2e^{-y}
dy
dx
=
6
x
2
e
−
y
integral of (y^3+1.8y^2-2.4y)
∫
(
y
3
+
1
.
8
y
2
−
2
.
4
y
)
dy
limit as x approaches-2 of (3x-1)/x
lim
x
→
−
2
(
3
x
−
1
x
)
(\partial)/(\partial x)((4x)/(sqrt(x^2+2)))
∂
∂
x
(
4
x
√
x
2
+
2
)
斜率 (0,4),(1,1)
slope
(
0
,
4
)
,
(
1
,
1
)
泰勒 e^{-x},4,0.25
taylor
e
−
x
,
4
,
0
.
2
5
(\partial)/(\partial x)(xz+xyz)
∂
∂
x
(
xz
+
xyz
)
derivative (x^2+1/5)sqrt(1+5x^2)
derivative
(
x
2
+
1
5
)
√
1
+
5
x
2
integral of 5x+7
∫
5
x
+
7
dx
f(x)=sqrt(5x+1)
f
(
x
)
=
√
5
x
+
1
integral of sec^4(3x)tan^3(3x)
∫
sec
4
(
3
x
)
tan
3
(
3
x
)
dx
derivative of 2e^x+3x^2+x^{3/2}+5
d
dx
(
2
e
x
+
3
x
2
+
x
3
2
+
5
)
limit as x approaches 0 of (5x+1)/x
lim
x
→
0
(
5
x
+
1
x
)
inverse拉普拉斯 (2s+5)/(s^2-s-6)
inverselaplace
2
s
+
5
s
2
−
s
−
6
limit as x approaches 0 of (1+3/(x^5))^x
lim
x
→
0
(
(
1
+
3
x
5
)
x
)
derivative of 6e^{-x}
d
dx
(
6
e
−
x
)
面积 y=5x,y= 1/7 x,y=50-x^2
area
y
=
5
x
,
y
=
1
7
x
,
y
=
5
0
−
x
2
d/(dθ)(sin(θ)+tan(θ))
d
d
θ
(
sin
(
θ
)
+
tan
(
θ
)
)
integral of 1/(sqrt(x^2-2x-8))
∫
1
√
x
2
−
2
x
−
8
dx
(\partial)/(\partial x)(3ln(sqrt(x^2+y^2)))
∂
∂
x
(
3
ln
(
√
x
2
+
y
2
)
)
integral of (x^3)/(x-1)
∫
x
3
x
−
1
dx
(8-6y+e^{-3x})dx-2dy=0
(
8
−
6
y
+
e
−
3
x
)
dx
−
2
dy
=
0
integral of (x/((x-2)(x-3)))
∫
(
x
(
x
−
2
)
(
x
−
3
)
)
dx
derivative f(x)=e^xx^{-n}
derivative
f
(
x
)
=
e
x
x
−
n
derivative of (3x-x^3+1^4)
d
dx
(
(
3
x
−
x
3
+
1
)
4
)
d/(dt)(ssin(t))
d
dt
(
s
sin
(
t
)
)
integral from 0 to 500 of 6(700y-y^2)
∫
0
5
0
0
6
(
7
0
0
y
−
y
2
)
dy
integral of (40-2/(sec(θ)))
∫
(
4
0
−
2
sec
(
θ
)
)
d
θ
f(y)=e^{2y}
f
(
y
)
=
e
2
y
integral from-2 to 1 of-x^2-x+2
∫
−
2
1
−
x
2
−
x
+
2
dx
(5+x^8)(dy}{dx}=\frac{x^7)/y
(
5
+
x
8
)
dy
dx
=
x
7
y
derivative of (8-3x/(x^2-6x+8))
d
dx
(
8
−
3
x
x
2
−
6
x
+
8
)
limit as x approaches 0 of (-7+x)/(x^2)
lim
x
→
0
(
−
7
+
x
x
2
)
limit as x approaches 2 of 3
lim
x
→
2
(
3
)
integral from 0 to 1 of 2pi(x+1)x^2
∫
0
1
2
π
(
x
+
1
)
x
2
dx
laplace变换 te^{2t}cos(3t)
laplacetransform
te
2
t
cos
(
3
t
)
9y^'-9tan(x)y=(20)/(cos(x))
9
y
′
−
9
tan
(
x
)
y
=
2
0
cos
(
x
)
(\partial)/(\partial x)(2x-e^{x+y})
∂
∂
x
(
2
x
−
e
x
+
y
)
sum from n=0 to infinity of (100)/n
∑
n
=
0
∞
1
0
0
n
integral of x^{-2}(3x^4+4x^2-5)
∫
x
−
2
(
3
x
4
+
4
x
2
−
5
)
dx
斜率 x^2+y^2=23
slope
x
2
+
y
2
=
2
3
(dx)/(dt)=8+4sin(t/4)-x/(100)
dx
dt
=
8
+
4
sin
(
t
4
)
−
x
1
0
0
tangent f(x)= 4/(sqrt(x)),\at x= 1/4
tangent
f
(
x
)
=
4
√
x
,
at
x
=
1
4
integral from 1 to 4 of-3sqrt(t)ln(t)
∫
1
4
−
3
√
t
ln
(
t
)
dt
integral from 0 to 5 of 2pix(1/(x+4))
∫
0
5
2
π
x
(
1
x
+
4
)
dx
inverse拉普拉斯-1.621s-0.462945095
inverselaplace
−
1
.
6
2
1
s
−
0
.
4
6
2
9
4
5
0
9
5
(\partial)/(\partial φ)(ρsin(φ)cos(θ))
∂
∂
φ
(
ρ
sin
(
φ
)
cos
(
θ
)
)
y^{''}-4y^'+5y=2020e^{-t}
y
′
′
−
4
y
′
+
5
y
=
2
0
2
0
e
−
t
tangent \sqrt[5]{2x^3+8x}(2.2)
tangent
5
√
2
x
3
+
8
x
(
2
.
2
)
斜率 (-7.1)(-7.9)
slope
(
−
7
.
1
)
(
−
7
.
9
)
derivative (x-2)^5
derivative
(
x
−
2
)
5
limit as n approaches infinity of 5ne^{-n}
lim
n
→
∞
(
5
ne
−
n
)
derivative y=(1-e^x)^2
derivative
y
=
(
1
−
e
x
)
2
y^'=ry+k
y
′
=
ry
+
k
derivative of 1/((2-x^2))
d
dx
(
1
(
2
−
x
)
2
)
integral of (2x-4+6sqrt(x))/(sqrt(x))
∫
2
x
−
4
+
6
√
x
√
x
dx
derivative 4x^2-7x+5
derivative
4
x
2
−
7
x
+
5
sum from n=1 to infinity of 4/(2^n)
∑
n
=
1
∞
4
2
n
integral from 2 to-1 of x^2+1
∫
2
−
1
x
2
+
1
dx
integral of x/(sqrt(1+x^4))
∫
x
√
1
+
x
4
dx
derivative of 5xy^2
d
dx
(
5
xy
2
)
derivative ((x-13))/(((x^5)-(135)))
derivative
(
x
−
1
3
)
(
(
x
5
)
−
(
1
3
5
)
)
(dx)/(dt)=((e^t-e^{-t}))/(x+3)
dx
dt
=
(
e
t
−
e
−
t
)
x
+
3
integral of 1/(x^2-6x+5)
∫
1
x
2
−
6
x
+
5
dx
(\partial)/(\partial x)(2(x+v(x,t)t))
∂
∂
x
(
2
(
x
+
v
(
x
,
t
)
t
)
)
derivative (t-4)e^{3t}
derivative
(
t
−
4
)
e
3
t
derivative 7(x^2+3x)^6(2x+3)
derivative
7
(
x
2
+
3
x
)
6
(
2
x
+
3
)
derivative y= 3/(x^2)-4/(x^3)
derivative
y
=
3
x
2
−
4
x
3
integral of e^{x/(60)}
∫
e
x
6
0
dx
(d^2)/(dx^2)(sqrt(2ax-x^2))
d
2
dx
2
(
√
2
ax
−
x
2
)
1
..
1411
1412
1413
1414
1415
..
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