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統計
人気の高い微分積分問題
limit as x approaches infinity of 2-x
lim
x
→
∞
(
2
−
x
)
derivative f(x)=x^2e^{1/x}
derivative
f
(
x
)
=
x
2
e
1
x
integral of t^3e^{sin(t^4)}cos(t^4)
∫
t
3
e
sin
(
t
4
)
cos
(
t
4
)
dt
sum from n=0 to infinity of 0.9^{2n}
∑
n
=
0
∞
0
.
9
2
n
cos^2(x)sin(x)y^'+cos^3(x)y=1
cos
2
(
x
)
sin
(
x
)
y
′
+
cos
3
(
x
)
y
=
1
2t(dy)/(dt)=8y
2
t
dy
dt
=
8
y
(\partial)/(\partial x)(xe^{6y})
∂
∂
x
(
xe
6
y
)
(\partial}{\partial x}(\frac{x^{3/2})/3)
∂
∂
x
(
x
3
2
3
)
(\partial)/(\partial y)(2x^2y+3xy^3)
∂
∂
y
(
2
x
2
y
+
3
xy
3
)
integral from 0 to 8 of x^3sqrt(x^2+64)
∫
0
8
x
3
√
x
2
+
6
4
dx
(\partial)/(\partial x)(e^{-20})
∂
∂
x
(
e
−
2
0
)
derivative of 2x^6-9x^5+15x^4-10x^3+3x-1
d
dx
(
2
x
6
−
9
x
5
+
1
5
x
4
−
1
0
x
3
+
3
x
−
1
)
derivative of (x^2+x-12/(x-4))
d
dx
(
x
2
+
x
−
1
2
x
−
4
)
limit as x approaches 0 of (2x^2+x)/x
lim
x
→
0
(
2
x
2
+
x
x
)
derivative y=(x^2)/(5-8x)
derivative
y
=
x
2
5
−
8
x
derivative of x/(4+x^2)
d
dx
(
x
4
+
x
2
)
limit as x approaches 0 of x^3*sin(1/x)
lim
x
→
0
(
x
3
·
sin
(
1
x
)
)
limit as x approaches 0 of (1-2x)^{5/x}
lim
x
→
0
(
(
1
−
2
x
)
5
x
)
integral of cot^2(θ)
∫
cot
2
(
θ
)
d
θ
y^'+y/(120)=3
y
′
+
y
1
2
0
=
3
integral of x^4(y-2)
∫
x
4
(
y
−
2
)
derivative y=(4x^2+6x+8)/(sqrt(x))
derivative
y
=
4
x
2
+
6
x
+
8
√
x
x^2(dy)/(dx)-2xy=5y^4,y(1)= 1/3
x
2
dy
dx
−
2
xy
=
5
y
4
,
y
(
1
)
=
1
3
integral of ((sec(x)+cos(x))/(2cos(x)))
∫
(
sec
(
x
)
+
cos
(
x
)
2
cos
(
x
)
)
dx
derivative of (2x+9^2)
d
dx
(
(
2
x
+
9
)
2
)
derivative y=3+log_{2}(x)
derivative
y
=
3
+
log
2
(
x
)
dy=x^2dx
dy
=
x
2
dx
derivative of (2x+5/(2x-5))
d
dx
(
2
x
+
5
2
x
−
5
)
(\partial)/(\partial x)(sqrt(26-x^2-y^2))
∂
∂
x
(
√
2
6
−
x
2
−
y
2
)
derivative of sec(sqrt(x^2-1))
d
dx
(
sec
(
√
x
2
−
1
)
)
laplace変換する (t-1)^4
laplacetransform
(
t
−
1
)
4
derivative of (2x^4+5/(4-4x))
d
dx
(
2
x
4
+
5
4
−
4
x
)
(\partial)/(\partial x)(sqrt(25-x^2))
∂
∂
x
(
√
2
5
−
x
2
)
(dy)/(dx)+1/(x+8)y=x^{-2}
dy
dx
+
1
x
+
8
y
=
x
−
2
derivative (x^2-2x)/((x-1)^2)
derivative
x
2
−
2
x
(
x
−
1
)
2
tangent f(x)=x^4+9e^x,(0,9)
tangent
f
(
x
)
=
x
4
+
9
e
x
,
(
0
,
9
)
e^xydy=(e^{-y}+e^{-2x-y})dx
e
x
ydy
=
(
e
−
y
+
e
−
2
x
−
y
)
dx
sum from n=0 to infinity of (n+1)/(n!)
∑
n
=
0
∞
n
+
1
n
!
d/(dθ)(3+3sin(θ))
d
d
θ
(
3
+
3
sin
(
θ
)
)
laplace変換する 0
laplacetransform
0
laplace変換する t+2
laplacetransform
t
+
2
integral of-(26)/(x^{27)}
∫
−
2
6
x
2
7
dx
limit as x approaches infinity of 2^2
lim
x
→
∞
(
2
2
)
integral of e^{x/4}
∫
e
x
4
dx
y^'-2y=e^{3x}
y
′
−
2
y
=
e
3
x
limit as n approaches 1 of ((-1/5)^n)/n
lim
n
→
1
(
(
−
1
5
)
n
n
)
(dy)/(dx)= y/(xln(x))
dy
dx
=
y
x
ln
(
x
)
integral of 3/(2sqrt(x))
∫
3
2
√
x
dx
integral of 1/(2^n)
∫
1
2
n
limit as x approaches 2+of 2/((x-2)^2)
lim
x
→
2
+
(
2
(
x
−
2
)
2
)
integral from 2 to 4 of 25
∫
2
4
2
5
dx
(\partial)/(\partial x)(e^{(7xy)}ln(6y))
∂
∂
x
(
e
(
7
xy
)
ln
(
6
y
)
)
integral of (2x^2-1)
∫
(
2
x
2
−
1
)
dx
integral of 2cos(x)+7
∫
2
cos
(
x
)
+
7
dx
derivative of ax^2+by(x^2+c)
d
dx
(
ax
2
+
by
(
x
)
2
+
c
)
integral from 0 to y of integral from 0 to x of (x^2+y^2)^{3/2}
∫
0
y
∫
0
x
(
x
2
+
y
2
)
3
2
dydx
面積 3x, 3/4 x,70-x^2
area
3
x
,
3
4
x
,
7
0
−
x
2
q^{''}+20q^'+500q=12
q
′
′
+
2
0
q
′
+
5
0
0
q
=
1
2
limit as x approaches 1 of 3x^2-2x+1
lim
x
→
1
(
3
x
2
−
2
x
+
1
)
integral of cos^2(3x)sin^2(3x)
∫
cos
2
(
3
x
)
sin
2
(
3
x
)
dx
limit as x approaches 0 of xsin(5/x)
lim
x
→
0
(
x
sin
(
5
x
)
)
y^'=((y+y^2))/(x^2)
y
′
=
(
y
+
y
2
)
x
2
derivative of x^{3/4}y^3
d
dx
(
x
3
4
y
3
)
integral from 0 to 3 of |3x-1|
∫
0
3
|
3
x
−
1
|
dx
(\partial)/(\partial x)(x^2+xy+3y)
∂
∂
x
(
x
2
+
xy
+
3
y
)
integral of (z+1)e^{2z}
∫
(
z
+
1
)
e
2
z
dz
integral of cos^5(x)sin^3(x)
∫
cos
5
(
x
)
sin
3
(
x
)
dx
integral of x(x^2-3)^3
∫
x
(
x
2
−
3
)
3
dx
integral of 1/(sqrt(16-9x^2))
∫
1
√
1
6
−
9
x
2
dx
(\partial)/(\partial x)(a^{-x})
∂
∂
x
(
a
−
x
)
integral from 0 to pi of 8sin(x/2)
∫
0
π
8
sin
(
x
2
)
dx
y^{''}-6y^'+8y=-2cos(4t)
y
′
′
−
6
y
′
+
8
y
=
−
2
cos
(
4
t
)
integral from 0 to 2 of 8t
∫
0
2
8
tdt
derivative of x/(\sqrt[3]{x^2+4})
d
dx
(
x
3
√
x
2
+
4
)
derivative f(t)=t
derivative
f
(
t
)
=
t
derivative of-(2x/((x^2-4)^2))
d
dx
(
−
2
x
(
x
2
−
4
)
2
)
integral of (12)/(x^2+1)
∫
1
2
x
2
+
1
dx
テイラー (1-x)^{1/5}
taylor
(
1
−
x
)
1
5
derivative of (sqrt(x)/(1+x))
d
dx
(
√
x
1
+
x
)
integral of (7(sin(2x))/(sin(x)))
∫
(
7
sin
(
2
x
)
sin
(
x
)
)
dx
integral from-5 to 5 of 1/2 (25^2-x^4)
∫
−
5
5
1
2
(
2
5
2
−
x
4
)
dx
integral of x/(1-x^2+sqrt(1-x^2))
∫
x
1
−
x
2
+
√
1
−
x
2
dx
integral of (3x^2+14x)(x^3+7x^2+1)
∫
(
3
x
2
+
1
4
x
)
(
x
3
+
7
x
2
+
1
)
dx
derivative g(t)=sqrt(1/(t^2-2))
derivative
g
(
t
)
=
√
1
t
2
−
2
tangent sqrt((5x^2-3x+2))^7
tangent
√
(
5
x
2
−
3
x
+
2
)
7
integral from 1 to 9 of (x-1)
∫
1
9
(
x
−
1
)
dx
(dy)/(dt)=(t^2)/(y+t^3y)
dy
dt
=
t
2
y
+
t
3
y
(\partial)/(\partial x)(ln(7x))
∂
∂
x
(
ln
(
7
x
)
)
x^{''}+3x^'=0,x(0)=0,x^'(0)=-3
x
′
′
+
3
x
′
=
0
,
x
(
0
)
=
0
,
x
′
(
0
)
=
−
3
derivative e^{x^e}
derivative
e
x
e
limit as x approaches 6-of sqrt(x-6)
lim
x
→
6
−
(
√
x
−
6
)
y^'=18x^2e^{-y}
y
′
=
1
8
x
2
e
−
y
tangent f(x)=x^2+3,\at x=2
tangent
f
(
x
)
=
x
2
+
3
,
at
x
=
2
derivative f(x)=ln(x^3+2x^2+2x)
derivative
f
(
x
)
=
ln
(
x
3
+
2
x
2
+
2
x
)
integral of 1/(x(x^2-1))
∫
1
x
(
x
2
−
1
)
dx
integral of ((2x+1))/(x^2-2x+5)
∫
(
2
x
+
1
)
x
2
−
2
x
+
5
dx
limit as x approaches pi/4 of tan^2(x)
lim
x
→
π
4
(
tan
2
(
x
)
)
integral of 9tan(x)
∫
9
tan
(
x
)
dx
limit as x approaches-1 of (x+2)/(x+1)
lim
x
→
−
1
(
x
+
2
x
+
1
)
integral of (5x+2)/(\sqrt[3]{6x+3)}
∫
5
x
+
2
3
√
6
x
+
3
dx
1
..
330
331
332
333
334
..
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