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幾何学
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統計
人気の高い微分積分問題
sum from n=0 to infinity of 7(-1/8)^n
∑
n
=
0
∞
7
(
−
1
8
)
n
xy^'+4y=2x^3
xy
′
+
4
y
=
2
x
3
tangent y=sqrt(7x+2),(2,4)
tangent
y
=
√
7
x
+
2
,
(
2
,
4
)
integral of e^{-16x}
∫
e
−
1
6
x
dx
derivative of 1-e^{-x}sin(y)
d
dx
(
1
−
e
−
x
sin
(
y
)
)
derivative of sqrt(x/(x^2+5))
d
dx
(
√
x
x
2
+
5
)
(\partial)/(\partial x)(1/(sqrt(x)))
∂
∂
x
(
1
√
x
)
integral of-e^{4x}+4x^5
∫
−
e
4
x
+
4
x
5
dx
tangent f(x)=sqrt(x),\at x=36
tangent
f
(
x
)
=
√
x
,
at
x
=
3
6
derivative f(x)=4x^3+9
derivative
f
(
x
)
=
4
x
3
+
9
(-x^{-2})^'
(
−
x
−
2
)
′
(x^2+2x-1)y^'-(x+1)y=x-1
(
x
2
+
2
x
−
1
)
y
′
−
(
x
+
1
)
y
=
x
−
1
integral of t^2(t^3-4)^2
∫
t
2
(
t
3
−
4
)
2
dt
勾配 (x-2)^4+e^{x-2}+(x-2*z)^2
slope
(
x
−
2
)
4
+
e
x
−
2
+
(
x
−
2
·
z
)
2
(dy)/(dx)=x+7y
dy
dx
=
x
+
7
y
integral of 27x^{26}
∫
2
7
x
2
6
dx
inverselaplace (-5s)/((s^2+1)^2)
inverselaplace
−
5
s
(
s
2
+
1
)
2
limit as x approaches 1 of 3/(x-1)
lim
x
→
1
(
3
x
−
1
)
(\partial)/(\partial x)(sqrt(8-x^2))
∂
∂
x
(
√
8
−
x
2
)
integral from 1 to 100 of (21)/(x^3)
∫
1
1
0
0
2
1
x
3
dx
derivative ln(x+sqrt(x^2-7))
derivative
ln
(
x
+
√
x
2
−
7
)
2y^{''}-6y^'+5y=0
2
y
′
′
−
6
y
′
+
5
y
=
0
integral of cot(15x)
∫
cot
(
1
5
x
)
dx
(\partial)/(\partial s)(sqrt(s^2+t^2))
∂
∂
s
(
√
s
2
+
t
2
)
sum from n=0 to infinity of nsin(n*pi)
∑
n
=
0
∞
n
sin
(
n
·
π
)
inverselaplace (s+1)/((s(s^2+s+1)))
inverselaplace
s
+
1
(
s
(
s
2
+
s
+
1
)
)
(\partial)/(\partial x)(e^{cos(x)})
∂
∂
x
(
e
cos
(
x
)
)
derivative of (8x+9(9x-10))
d
dx
(
(
8
x
+
9
)
(
9
x
−
1
0
)
)
integral of x^2-4x+4
∫
x
2
−
4
x
+
4
dx
(dy)/(dx)=(cos(12x))/(e^{12y)}
dy
dx
=
cos
(
1
2
x
)
e
1
2
y
integral from 1 to 2 of (15)/(x^3+5x)
∫
1
2
1
5
x
3
+
5
x
dx
簡約 xL(x)-x
simplify
xL
(
x
)
−
x
y^{''}-y^'-6y=0,y(0)=0,y^'(0)=4
y
′
′
−
y
′
−
6
y
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
4
limit as x approaches 2 of-6
lim
x
→
2
(
−
6
)
integral of 1/(9x^2-18x+72)
∫
1
9
x
2
−
1
8
x
+
7
2
dx
integral of-4ln(2x+1)
∫
−
4
ln
(
2
x
+
1
)
dx
簡約 (y^{-1}+y^{-2})(2y^{-3}-6y^{-4})
simplify
(
y
−
1
+
y
−
2
)
(
2
y
−
3
−
6
y
−
4
)
limit as x approaches infinity of 1/(x*log_{e)(x)}
lim
x
→
∞
(
1
x
·
log
e
(
x
)
)
limit as x approaches 2-of (x-2)/(x-2)
lim
x
→
2
−
(
x
−
2
x
−
2
)
limit as x approaches infinity of 1+a/x
lim
x
→
∞
(
1
+
a
x
)
integral of 3/((5v-1)^4)
∫
3
(
5
v
−
1
)
4
dv
derivative of cos(x-x)
d
dx
(
cos
(
x
)
−
x
)
tangent (x-5)^2+(y-3)^2=18,(8,6)
tangent
(
x
−
5
)
2
+
(
y
−
3
)
2
=
1
8
,
(
8
,
6
)
integral from 0 to 4 of pi(3x)^2
∫
0
4
π
(
3
x
)
2
dx
derivative f(x)=cos(tan(x))
derivative
f
(
x
)
=
cos
(
tan
(
x
)
)
y^{''}+ay^'+by=t+e^{3t}
y
′
′
+
ay
′
+
by
=
t
+
e
3
t
limit as x approaches-1 of ln(x+1)
lim
x
→
−
1
(
ln
(
x
+
1
)
)
(\partial)/(\partial x)(1/2 (x^2+4y^2))
∂
∂
x
(
1
2
(
x
2
+
4
y
2
)
)
(\partial)/(\partial x)(1/(sqrt(2x)))
∂
∂
x
(
1
√
2
x
)
2xy(dy)/(dx)=y^2-x^2+1
2
xy
dy
dx
=
y
2
−
x
2
+
1
tangent 100x^2+400x+5000,0.5
tangent
1
0
0
x
2
+
4
0
0
x
+
5
0
0
0
,
0
.
5
integral of e^{y(1-x)}
∫
e
y
(
1
−
x
)
dx
derivative of y=7x^2cos(x)cot(x)
d
dx
y
=
7
x
2
cos
(
x
)
cot
(
x
)
(dy)/(dx)+e^xy=-9e^x
dy
dx
+
e
x
y
=
−
9
e
x
integral of ((2x^3+3x))/(x^4+3x^2+7)
∫
(
2
x
3
+
3
x
)
x
4
+
3
x
2
+
7
dx
(\partial)/(\partial x)(4xcos(4xy))
∂
∂
x
(
4
x
cos
(
4
xy
)
)
limit as x approaches 2+of-1/(x^2-4)
lim
x
→
2
+
(
−
1
x
2
−
4
)
integral of (tan(θ)sec(θ))
∫
(
tan
(
θ
)
sec
(
θ
)
)
d
θ
integral of e^{2x-7}
∫
e
2
x
−
7
dx
derivative of 4arcsin(x^3)
d
dx
(
4
arcsin
(
x
3
)
)
derivative 2/(\sqrt[3]{x^2)}
derivative
2
3
√
x
2
derivative of (4csc(x)/(5^x))
d
dx
(
4
csc
(
x
)
5
x
)
limit as x approaches infinity of n/(n!)
lim
x
→
∞
(
n
n
!
)
derivative ln(49sin^2(x))
derivative
ln
(
4
9
sin
2
(
x
)
)
(\partial)/(\partial v)(v^2)
∂
∂
v
(
v
2
)
f(x)=(25)/x
f
(
x
)
=
2
5
x
integral of 5sin(sqrt(x))
∫
5
sin
(
√
x
)
dx
derivative of sqrt(x^2+y)
d
dx
(
√
x
2
+
y
)
d/(dy)(t/(2y^4))
d
dy
(
t
2
y
4
)
integral of 1/(sqrt(64x^2+1))
∫
1
√
6
4
x
2
+
1
dx
6x^2((dy)/(dx))=((dy)/(dx))+9xe^{-y}
6
x
2
(
dy
dx
)
=
(
dy
dx
)
+
9
xe
−
y
integral of 8x^{-3}
∫
8
x
−
3
dx
integral from 0 to 2 of e^{-x}
∫
0
2
e
−
x
dx
integral of sqrt(3+x^2)
∫
√
3
+
x
2
dx
integral of (3x^2-9x+2)
∫
(
3
x
2
−
9
x
+
2
)
dx
integral of sqrt((1+cos(x))/(1-cos(x)))
∫
√
1
+
cos
(
x
)
1
−
cos
(
x
)
dx
derivative of arcsin(5x)
d
dx
(
arcsin
(
5
x
)
)
derivative 3/5 x^{5/3}-3/4 x^{1/3}+9
derivative
3
5
x
5
3
−
3
4
x
1
3
+
9
limit as x approaches-2+of (1-x)/(x^3+8)
lim
x
→
−
2
+
(
1
−
x
x
3
+
8
)
limit as x approaches 1-of 2/(x-1)
lim
x
→
1
−
(
2
x
−
1
)
(\partial)/(\partial x)((3x^2+y)e^{xy^2})
∂
∂
x
(
(
3
x
2
+
y
)
e
xy
2
)
laplacetransform (e^{2t}-e^t+t)^2
laplacetransform
(
e
2
t
−
e
t
+
t
)
2
derivative 2x^2-7x-195
derivative
2
x
2
−
7
x
−
1
9
5
integral of-cos((pit)/4)
∫
−
cos
(
π
t
4
)
dt
limit as x approaches-2 of-x^2+6x-8
lim
x
→
−
2
(
−
x
2
+
6
x
−
8
)
integral of aarctan(bx)
∫
a
arctan
(
bx
)
dx
limit as x approaches 1 of x^2+4
lim
x
→
1
(
x
2
+
4
)
tangent y=-0.02x^2-0.6x+90
tangent
y
=
−
0
.
0
2
x
2
−
0
.
6
x
+
9
0
derivative of 1/((x^2+1^3))
d
dx
(
1
(
x
2
+
1
)
3
)
integral of (e^{3x})/(e^{3x)+9}
∫
e
3
x
e
3
x
+
9
dx
integral from 0 to 1 of pi(6-3/2 x)^2
∫
0
1
π
(
6
−
3
2
x
)
2
dx
inverselaplace 2/(s^2+s)
inverselaplace
2
s
2
+
s
y^{''}+9y=3cos(2x)+3
y
′
′
+
9
y
=
3
cos
(
2
x
)
+
3
integral of sqrt(9-x^2)(-2x)
∫
√
9
−
x
2
(
−
2
x
)
dx
derivative of (x-2^2(x+1))
d
dx
(
(
x
−
2
)
2
(
x
+
1
)
)
(\partial)/(\partial y)(x^2+y^2-9)
∂
∂
y
(
x
2
+
y
2
−
9
)
derivative f(x)=6x^2+x-3
derivative
f
(
x
)
=
6
x
2
+
x
−
3
laplacetransform t/2
laplacetransform
t
2
面積 y=sqrt(x),x=9,y=0
area
y
=
√
x
,
x
=
9
,
y
=
0
3y^{''}+5y^'+2y=0
3
y
′
′
+
5
y
′
+
2
y
=
0
1
..
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330
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332
333
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