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人気の高い微分積分問題
y^{''}-2y^'-3y=9
y
′
′
−
2
y
′
−
3
y
=
9
面積 5,x^2+1
area
5
,
x
2
+
1
integral of (x^6-x^4+x^2)/(x^3)
∫
x
6
−
x
4
+
x
2
x
3
dx
integral from 1/2 to 1 of (x^{-3}-10)
∫
1
2
1
(
x
−
3
−
1
0
)
dx
derivative of 5sin(x+6cos(x))
d
dx
(
5
sin
(
x
)
+
6
cos
(
x
)
)
limit as x approaches 2 of 100
lim
x
→
2
(
1
0
0
)
(dy)/(dx)=(y^2-1)/(x^2-1),y(3)=3
dy
dx
=
y
2
−
1
x
2
−
1
,
y
(
3
)
=
3
derivative of 1-x/2
d
dx
(
1
−
x
2
)
y^{''}-5y^'+4y=0,y(0)=6,y(1)=3
y
′
′
−
5
y
′
+
4
y
=
0
,
y
(
0
)
=
6
,
y
(
1
)
=
3
sum from n=0 to infinity of (2^n)/n x^n
∑
n
=
0
∞
2
n
n
x
n
integral of sin(2x)sec(x)
∫
sin
(
2
x
)
sec
(
x
)
dx
derivative y=x^{10cos(x)}
derivative
y
=
x
1
0
cos
(
x
)
tangent y=4tan(x),\at x= pi/6
tangent
y
=
4
tan
(
x
)
,
at
x
=
π
6
integral from 1 to 3 of (x^2+1)^3x
∫
1
3
(
x
2
+
1
)
3
xdx
integral from 2 to 4 of 1/((x-4)(x-1))
∫
2
4
1
(
x
−
4
)
(
x
−
1
)
dx
integral from 9 to 16 of 1/(2-sqrt(x))
∫
9
1
6
1
2
−
√
x
dx
(\partial)/(\partial y)(sin(y)+y,x)
∂
∂
y
(
sin
(
y
)
+
y
,
x
)
integral from 0 to 2 of te^t
∫
0
2
te
t
dt
面積 sin^2(x),sin^3(x),0,pi
area
sin
2
(
x
)
,
sin
3
(
x
)
,
0
,
π
integral of 3sin(x)+2-3e^x
∫
3
sin
(
x
)
+
2
−
3
e
x
dx
面積 f(x)=4x(1-x),g(x)=4x-4
area
f
(
x
)
=
4
x
(
1
−
x
)
,
g
(
x
)
=
4
x
−
4
derivative of (6x^3-5x^2-2x/(4x-3x^2))
d
dx
(
6
x
3
−
5
x
2
−
2
x
4
x
−
3
x
2
)
derivative of 5x+(100/x)
d
dx
(
5
x
+
1
0
0
x
)
limit as x approaches 2 of (x+2)/(x-2)
lim
x
→
2
(
x
+
2
x
−
2
)
derivative of 5/3
d
dx
(
5
3
)
derivative of (x^6/(12)ln(x)-(x^6)/(72))
d
dx
(
x
6
1
2
ln
(
x
)
−
x
6
7
2
)
derivative of e^{-5x}-5e^{-5x}x
d
dx
(
e
−
5
x
−
5
e
−
5
x
x
)
derivative of x*e^{-2x}
d
dx
(
x
·
e
−
2
x
)
d/(d{x)}(({x})/((|{y)|-|{z}|)})
d
d
x
(
x
(
|
y
|
−
|
z
|
)
)
integral of (x^4+x^2+1)/(x-1)
∫
x
4
+
x
2
+
1
x
−
1
dx
derivative of sin(x-3cos(x))
d
dx
(
sin
(
x
)
−
3
cos
(
x
)
)
integral of (12)/(1+t^2)
∫
1
2
1
+
t
2
dt
laplace変換する-5sin(4t)
laplacetransform
−
5
sin
(
4
t
)
derivative of ((x-2(x^2-x+1))/(sqrt(x)))
d
dx
(
(
x
−
2
)
(
x
2
−
x
+
1
)
√
x
)
inverseラプラス (s^3+5s^2+9s+7)/(s^2+3s+2)
inverselaplace
s
3
+
5
s
2
+
9
s
+
7
s
2
+
3
s
+
2
(\partial)/(\partial x)(ax^2)
∂
∂
x
(
ax
2
)
limit as x approaches-3 of (x^2-4)/(3-x)
lim
x
→
−
3
(
x
2
−
4
3
−
x
)
derivative (x-4)/(x+2)
derivative
x
−
4
x
+
2
integral of (2x+1)/((x-1)(x+4)^2)
∫
2
x
+
1
(
x
−
1
)
(
x
+
4
)
2
dx
integral of 1/(sqrt(x-1)-\sqrt{x)}
∫
1
√
x
−
1
−
√
x
dx
integral of (-2y)/x
∫
−
2
y
x
dx
limit as x approaches 5+of (-3)/(x^2-25)
lim
x
→
5
+
(
−
3
x
2
−
2
5
)
(1+x^2)y^'=x(1-y)
(
1
+
x
2
)
y
′
=
x
(
1
−
y
)
面積 1+4x-x^2,11-x-x^2,1-(2x)/3
area
1
+
4
x
−
x
2
,
1
1
−
x
−
x
2
,
1
−
2
x
3
面積 sqrt(x+1),2x-4,0,3
area
√
x
+
1
,
2
x
−
4
,
0
,
3
integral of (3x^5-2)/(4x-4x^5)
∫
3
x
5
−
2
4
x
−
4
x
5
dx
テイラー 3/x ,-1
taylor
3
x
,
−
1
sum from n=1 to infinity of cos(3n)
∑
n
=
1
∞
cos
(
3
n
)
derivative of 9sin(5x)
d
dx
(
9
sin
(
5
x
)
)
derivative g(t)=2log_{5}(t)
derivative
g
(
t
)
=
2
log
5
(
t
)
integral from 0 to 1 of 2/(sqrt(4-x^2))
∫
0
1
2
√
4
−
x
2
dx
integral of tan(2x)sec^2(x)
∫
tan
(
2
x
)
sec
2
(
x
)
dx
(\partial)/(\partial x)(x^{0.25}y^{0.25})
∂
∂
x
(
x
0
.
2
5
y
0
.
2
5
)
integral of ((4x^{19}-5x^{-8})/(x^2))
∫
(
4
x
1
9
−
5
x
−
8
x
2
)
dx
(dy)/(dx)=((y^3)/(x^2))
dy
dx
=
(
y
3
x
2
)
integral of x(x^2+2)^6
∫
x
(
x
2
+
2
)
6
dx
integral of-(y^2)/2
∫
−
y
2
2
dy
derivative (2x^2)/(6x+5)
derivative
2
x
2
6
x
+
5
integral from 0 to ln(2) of e^{3x}
∫
0
ln
(
2
)
e
3
x
dx
derivative of x/(sqrt(y))
d
dx
(
x
√
y
)
integral of 4/(sqrt(x)(x+6))
∫
4
√
x
(
x
+
6
)
dx
y^'=(x^2+y^2)/(xy),y(1)=1
y
′
=
x
2
+
y
2
xy
,
y
(
1
)
=
1
sum from n=1 to infinity of 8(3/4)^n
∑
n
=
1
∞
8
(
3
4
)
n
(\partial)/(\partial x)(4x^2y^2)
∂
∂
x
(
4
x
2
y
2
)
勾配 (-2,1),(3,-9)
slope
(
−
2
,
1
)
,
(
3
,
−
9
)
integral of 1/((r^2+x^2)^{3/2)}
∫
1
(
r
2
+
x
2
)
3
2
dx
integral of xe^{1+x^2}
∫
xe
1
+
x
2
dx
integral of (x^3+x-1)/((x^2+2)^2)
∫
x
3
+
x
−
1
(
x
2
+
2
)
2
dx
integral of-csc^2((7x)/6)
∫
−
csc
2
(
7
x
6
)
dx
integral from 0 to 5 of (8t)/((t-6)^2)
∫
0
5
8
t
(
t
−
6
)
2
dt
integral of x^{2/5}
∫
x
2
5
dx
limit as x approaches-2 of e^{2x-x^2}
lim
x
→
−
2
(
e
2
x
−
x
2
)
derivative of-2x^{-2}
d
dx
(
−
2
x
−
2
)
tangent f(x)=(x-1)/(2-x),\at x=4
tangent
f
(
x
)
=
x
−
1
2
−
x
,
at
x
=
4
integral of (x^3-3sqrt(x)+x^{-5/4})
∫
(
x
3
−
3
√
x
+
x
−
5
4
)
dx
x^{''}+2.25x^'+0.14x=0,x^'(0)=1,x(0)=2
x
′
′
+
2
.
2
5
x
′
+
0
.
1
4
x
=
0
,
x
′
(
0
)
=
1
,
x
(
0
)
=
2
tangent f(x)=x^3-2x^2-3x,(1,-4)
tangent
f
(
x
)
=
x
3
−
2
x
2
−
3
x
,
(
1
,
−
4
)
(\partial)/(\partial x)(sqrt(xy)-z)
∂
∂
x
(
√
xy
−
z
)
f(x)=7x^2
f
(
x
)
=
7
x
2
勾配 (-5,2),(5,6)
slope
(
−
5
,
2
)
,
(
5
,
6
)
inverseラプラス t^{1/2}
inverselaplace
t
1
2
derivative of tan(y/x)
d
dx
(
tan
(
y
x
)
)
limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42)
lim
x
→
6
(
x
2
+
1
1
x
−
3
0
x
2
−
1
3
x
−
4
2
)
derivative csc^2(x)-1
derivative
csc
2
(
x
)
−
1
面積 y=sqrt(x),y=2-x,y=0
area
y
=
√
x
,
y
=
2
−
x
,
y
=
0
integral of tan(1)
∫
tan
(
1
)
dx
derivative (t+e^t)(2-sqrt(t))
derivative
(
t
+
e
t
)
(
2
−
√
t
)
derivative x^3y
derivative
x
3
y
derivative 2/(2x+1)
derivative
2
2
x
+
1
tangent sqrt(7x+1)
tangent
√
7
x
+
1
integral of e^{3x}sin(7x)
∫
e
3
x
sin
(
7
x
)
dx
integral of sin(8x)cos(3x)
∫
sin
(
8
x
)
cos
(
3
x
)
dx
integral from-1 to 4 of x+1
∫
−
1
4
x
+
1
dx
derivative 1/(xln(x))
derivative
1
x
ln
(
x
)
integral from 0 to pi of 17sin^2(4x)
∫
0
π
1
7
sin
2
(
4
x
)
dx
y^{'''}+4y^'=3x-1
y
′
′
′
+
4
y
′
=
3
x
−
1
integral of (x^3-3x+\sqrt[4]{x}-5)
∫
(
x
3
−
3
x
+
4
√
x
−
5
)
dx
tangent y= 1/(5+2x),(-1, 1/3)
tangent
y
=
1
5
+
2
x
,
(
−
1
,
1
3
)
x(dy)/(dx)=sqrt(x^2-y^2)+y
x
dy
dx
=
√
x
2
−
y
2
+
y
integral of-t
∫
−
tdt
1
..
876
877
878
879
880
..
2459