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人気の高い微分積分問題
derivative y=arcsin(x+1)
derivative
y
=
arcsin
(
x
+
1
)
integral of 2/3 x^{3/2}-9sin(x)
∫
2
3
x
3
2
−
9
sin
(
x
)
dx
(\partial)/(\partial x)(7xsin(y-z))
∂
∂
x
(
7
x
sin
(
y
−
z
)
)
limit as x approaches 8 of (sqrt(7+\sqrt[3]{x)}-3)/(x-8)
lim
x
→
8
(
√
7
+
3
√
x
−
3
x
−
8
)
integral of 3x^2-2y^2
∫
3
x
2
−
2
y
2
dx
integral of x/(1-2x)
∫
x
1
−
2
x
dx
limit as x approaches 1 of sqrt(3+f(x))
lim
x
→
1
(
√
3
+
f
(
x
)
)
integral of t^2e^{-4t}
∫
t
2
e
−
4
t
dt
derivative of (4x/(7x-2))
d
dx
(
4
x
7
x
−
2
)
inverselaplace 1/((2s+1)s)
inverselaplace
1
(
2
s
+
1
)
s
integral of x^2ln(9x)
∫
x
2
ln
(
9
x
)
dx
derivative of (tan^2(x)/(tan(x^2)))
d
dx
(
tan
2
(
x
)
tan
(
x
2
)
)
sqrt(x)(dy)/(dx)=e^{7y+sqrt(x)}
√
x
dy
dx
=
e
7
y
+
√
x
sum from n=1 to infinity of 5(-1/6)^{5n}
∑
n
=
1
∞
5
(
−
1
6
)
5
n
derivative f(x)=(2x^2-x-1)/(2x+2)
derivative
f
(
x
)
=
2
x
2
−
x
−
1
2
x
+
2
limit as x approaches 0+of x^{20x}
lim
x
→
0
+
(
x
2
0
x
)
derivative of 7x^4cot(x)
d
dx
(
7
x
4
cot
(
x
)
)
xydx-(1+x^2)dy=0
xydx
−
(
1
+
x
2
)
dy
=
0
x''
x
′
′
(dy)/(dx)+3y=40
dy
dx
+
3
y
=
4
0
derivative of sqrt(x)(2x+4)
d
dx
(
√
x
(
2
x
+
4
)
)
limit as x approaches 7 of (x+6)/(x+1)
lim
x
→
7
(
x
+
6
x
+
1
)
tangent (x^3+2x)^3,\at x=4
tangent
(
x
3
+
2
x
)
3
,
at
x
=
4
integral from 0 to 2 of x^6
∫
0
2
x
6
dx
integral of xcos(4pi)x^2
∫
x
cos
(
4
π
)
x
2
dx
derivative of (x^2+x+2/(2x))
d
dx
(
x
2
+
x
+
2
2
x
)
面積 y=2x^2,y=2x+6
area
y
=
2
x
2
,
y
=
2
x
+
6
derivative ln(x)
derivative
ln
(
x
)
derivative of (e^x-e^{-x}/5)
d
dx
(
e
x
−
e
−
x
5
)
(xdy)/(dx)=y+sqrt(x^2-y^2)
xdy
dx
=
y
+
√
x
2
−
y
2
integral from-1/4 to 1/4 of 1/(1-x^2)
∫
−
1
4
1
4
1
1
−
x
2
dx
laplacetransform-9t^2
laplacetransform
−
9
t
2
integral of (3x)/(1+x^2)
∫
3
x
1
+
x
2
dx
integral of (-2sqrt(x))
∫
(
−
2
√
x
)
dx
(\partial)/(\partial x)(x+y^3)
∂
∂
x
(
x
+
y
3
)
(\partial)/(\partial x)(2yx-3y+y^2)
∂
∂
x
(
2
yx
−
3
y
+
y
2
)
ye^{xy}dx+xe^{xy}dy=0
ye
xy
dx
+
xe
xy
dy
=
0
derivative of a/(bx^2)
d
dx
(
a
bx
2
)
derivative 2x
derivative
2
x
inverselaplace ((s-10))/((s^2-2s-3))
inverselaplace
(
s
−
1
0
)
(
s
2
−
2
s
−
3
)
implicit (dy)/(dx),x^6-5xy^3=9xy
implicit
dy
dx
,
x
6
−
5
xy
3
=
9
xy
limit as x approaches 0 of arctan(1/x)
lim
x
→
0
(
arctan
(
1
x
)
)
integral of (x^2+2)/(x^3(x+1)^3)
∫
x
2
+
2
x
3
(
x
+
1
)
3
dx
面積 1/((sqrt(1-7x))),-6<x<0
area
1
(
√
1
−
7
x
)
,
−
6
<
x
<
0
(\partial)/(\partial x)(4x^{-x^2-y^2-z^2})
∂
∂
x
(
4
x
−
x
2
−
y
2
−
z
2
)
integral of 7.9t-16.6
∫
7
.
9
t
−
1
6
.
6
dt
derivative of 1/((1-2x^{3/2)})
d
dx
(
1
(
1
−
2
x
)
3
2
)
(\partial)/(\partial x)(x^{2/3}+y^{2/3})
∂
∂
x
(
x
2
3
+
y
2
3
)
integral of 1/(sqrt(64+x^2))
∫
1
√
6
4
+
x
2
dx
f(x)=xcos(x)
f
(
x
)
=
x
cos
(
x
)
derivative of ln(x+2x)
d
dx
(
ln
(
x
)
+
2
x
)
テイラー 1/(1+x^2),0
taylor
1
1
+
x
2
,
0
integral from 0 to 1 of (1-x^7)^2
∫
0
1
(
1
−
x
7
)
2
dx
derivative x^3-2x^2-4x+6
derivative
x
3
−
2
x
2
−
4
x
+
6
y^{''}-2y^'=x+2e^x,y(0)=18,y^'(0)= 31/4
y
′
′
−
2
y
′
=
x
+
2
e
x
,
y
(
0
)
=
1
8
,
y
′
(
0
)
=
3
1
4
derivative of 2cos(x+3sin(x))
d
dx
(
2
cos
(
x
)
+
3
sin
(
x
)
)
inverselaplace (s+3)/(s^2+2s+2)
inverselaplace
s
+
3
s
2
+
2
s
+
2
tangent 5x^2+8x-8
tangent
5
x
2
+
8
x
−
8
d/(du)(sqrt(u))
d
du
(
√
u
)
derivative of (6x-1(5x-2)^{-1})
d
dx
(
(
6
x
−
1
)
(
5
x
−
2
)
−
1
)
derivative of 2(x-1^2)
d
dx
(
2
(
x
−
1
)
2
)
y^{''}+4y^'+5y=-10x+3e^{-x}
y
′
′
+
4
y
′
+
5
y
=
−
1
0
x
+
3
e
−
x
limit as x approaches 3 of sqrt(x-2)
lim
x
→
3
(
√
x
−
2
)
integral of (sec^2(x))/x
∫
sec
2
(
x
)
x
dx
derivative f(x)=(x+5)/(x-5)
derivative
f
(
x
)
=
x
+
5
x
−
5
limit as x approaches-2 of x^2-4/(x+2)
lim
x
→
−
2
(
x
2
−
4
x
+
2
)
面積 y=cos(x),y=0.5,0<= x<= pi
area
y
=
cos
(
x
)
,
y
=
0
.
5
,
0
≤
x
≤
π
1296y^{''}+1368y^'+361y=0
1
2
9
6
y
′
′
+
1
3
6
8
y
′
+
3
6
1
y
=
0
x(dy)/(dx)=y+(x^2-2)^2
x
dy
dx
=
y
+
(
x
2
−
2
)
2
integral of sin^2(pix)cos^5(pix)
∫
sin
2
(
π
x
)
cos
5
(
π
x
)
dx
derivative \sqrt[3]{6+2x+x^3}
derivative
3
√
6
+
2
x
+
x
3
derivative of csc^2(1-2x)
d
dx
(
csc
2
(
1
−
2
x
)
)
limit as x approaches-1 of 3x^4-6x+1
lim
x
→
−
1
(
3
x
4
−
6
x
+
1
)
integral of 3x^2+2x
∫
3
x
2
+
2
xdx
limit as x approaches 2 of x^3-5x
lim
x
→
2
(
x
3
−
5
x
)
limit as x approaches-6+of sqrt(x+6)
lim
x
→
−
6
+
(
√
x
+
6
)
derivative of 3\sqrt[3]{x^2}-2x
d
dx
(
3
3
√
x
2
−
2
x
)
integral of 1/(sqrt(cos(x)+cos^2(x)))
∫
1
√
cos
(
x
)
+
cos
2
(
x
)
dx
(\partial)/(\partial z)(ln(1+xy)-z)
∂
∂
z
(
ln
(
1
+
xy
)
−
z
)
derivative f(x)=sqrt(x+8)
derivative
f
(
x
)
=
√
x
+
8
integral of tln(1+t)
∫
t
ln
(
1
+
t
)
dt
integral from-8 to 0 of (y/8+sqrt(y+9))
∫
−
8
0
(
y
8
+
√
y
+
9
)
dy
limit as x approaches infinity of x+9
lim
x
→
∞
(
x
+
9
)
integral of 1/(x^2+3x+3)
∫
1
x
2
+
3
x
+
3
dx
y''(x)-3y'(x)+2y= 1/(1+e^{-x)}
y
′
′
(
x
)
−
3
y
′
(
x
)
+
2
y
=
1
1
+
e
−
x
limit as x approaches 0 of-arcsin(x)
lim
x
→
0
(
−
arcsin
(
x
)
)
derivative of 5e^x+2/(\sqrt[3]{x})
d
dx
(
5
e
x
+
2
3
√
x
)
integral from 0 to 1 of 9cos((pit)/2)
∫
0
1
9
cos
(
π
t
2
)
dt
integral of 1/(sqrt(x^2+36))
∫
1
√
x
2
+
3
6
dx
derivative ln(3)
derivative
ln
(
3
)
derivative of ln(1/(1-x))
d
dx
(
ln
(
1
1
−
x
)
)
面積 y=4x^2,y=x^2+6
area
y
=
4
x
2
,
y
=
x
2
+
6
limit as x approaches 7 of x+2
lim
x
→
7
(
x
+
2
)
integral of xe^xln(x-1)
∫
xe
x
ln
(
x
−
1
)
dx
integral of (sin^5(ln(x)))/x
∫
sin
5
(
ln
(
x
)
)
x
dx
limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)
lim
x
→
0
(
√
5
+
x
−
√
5
2
x
)
derivative f(t)=e^{7tsin(2t)}
derivative
f
(
t
)
=
e
7
t
sin
(
2
t
)
tangent f(x)=x(27x^{-2}+2),\at x=-3
tangent
f
(
x
)
=
x
(
2
7
x
−
2
+
2
)
,
at
x
=
−
3
(\partial)/(\partial x)((x-1)/(x+1))
∂
∂
x
(
x
−
1
x
+
1
)
integral from 0 to infinity of 1/(e^x-1)
∫
0
∞
1
e
x
−
1
dx
1
2
3
4
5
6
7
..
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