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人気の高い微分積分問題
(\partial)/(\partial x)(1/2 (x^2+10y^2))
∂
∂
x
(
1
2
(
x
2
+
1
0
y
2
)
)
f(x)=x-cos(x)
f
(
x
)
=
x
−
cos
(
x
)
integral from 0 to 6 of 2.3^tsin(t/2)
∫
0
6
2
.
3
t
sin
(
t
2
)
dt
integral of ((2x+4))/(x^2+4x+5)
∫
(
2
x
+
4
)
x
2
+
4
x
+
5
dx
integral of (x^2+2x+3)/(x^3+3x^2+9x+1)
∫
x
2
+
2
x
+
3
x
3
+
3
x
2
+
9
x
+
1
dx
integral of 1/(2x^2+x)
∫
1
2
x
2
+
x
dx
面積 sin(x),-sin(x),[0,4]
area
sin
(
x
)
,
−
sin
(
x
)
,
[
0
,
4
]
integral of (10x^3-5x^2+4x)/(x^2)
∫
1
0
x
3
−
5
x
2
+
4
x
x
2
dx
derivative of tanh(2x-3)
d
dx
(
tanh
(
2
x
−
3
)
)
tangent f(x)=x^2+x,(1,2)
tangent
f
(
x
)
=
x
2
+
x
,
(
1
,
2
)
勾配intercept (-1,-4),(0,2)
slopeintercept
(
−
1
,
−
4
)
,
(
0
,
2
)
面積-x^2+3x+1,-x-1,[0,4]
area
−
x
2
+
3
x
+
1
,
−
x
−
1
,
[
0
,
4
]
integral of (-3)/x
∫
−
3
x
dx
integral of (4t-3)/(t+1)
∫
4
t
−
3
t
+
1
dt
tangent f(x)=x^4+5x^2-x,(1,5)
tangent
f
(
x
)
=
x
4
+
5
x
2
−
x
,
(
1
,
5
)
integral of (4x+3)/(x^2+4)
∫
4
x
+
3
x
2
+
4
dx
(x^4-x+y)dx-xdy=0
(
x
4
−
x
+
y
)
dx
−
xdy
=
0
derivative ln(xsqrt(x^2+1))
derivative
ln
(
x
√
x
2
+
1
)
tangent f(x)=6x-6x
tangent
f
(
x
)
=
6
x
−
6
x
integral from 1 to 2 of xe^{x^2}
∫
1
2
xe
x
2
dx
(dy)/(dx)=(4y)
dy
dx
=
(
4
y
)
derivative of (3x^2+4(2x-3))
d
dx
(
(
3
x
2
+
4
)
(
2
x
−
3
)
)
integral of 5/x+e^x
∫
5
x
+
e
x
dx
tangent y=5+5x^2-2x^3
tangent
y
=
5
+
5
x
2
−
2
x
3
integral of (x-5)^2e^x
∫
(
x
−
5
)
2
e
x
dx
limit as x approaches 8+of 1/((x-8)^2)
lim
x
→
8
+
(
1
(
x
−
8
)
2
)
y^'+3y=3
y
′
+
3
y
=
3
derivative 5x+3sqrt(x)
derivative
5
x
+
3
√
x
inverseラプラス (12s)/((132s+30s^2))
inverselaplace
1
2
s
(
1
3
2
s
+
3
0
s
2
)
面積 y=2x,y=4x^2
area
y
=
2
x
,
y
=
4
x
2
integral of x^2-x^4
∫
x
2
−
x
4
dx
derivative of sin^2(xcos^2(x))
d
dx
(
sin
2
(
x
)
cos
2
(
x
)
)
derivative of (2x^2+4x-3/(x-5))
d
dx
(
2
x
2
+
4
x
−
3
x
−
5
)
derivative e^{-9x}
derivative
e
−
9
x
derivative of sec^2(6x)
d
dx
(
sec
2
(
6
x
)
)
derivative of c_{1}e^x+c_{2}e^{2x}
d
dx
(
c
1
e
x
+
c
2
e
2
x
)
(dx}{dt}=t^5-\frac{2x)/t
dx
dt
=
t
5
−
2
x
t
integral from 0 to pi/6 of xsin(x+y)
∫
0
π
6
x
sin
(
x
+
y
)
dx
derivative of ln(1+10x)
d
dx
(
ln
(
1
+
1
0
x
)
)
integral of 1/(sqrt(x+1)+\sqrt[4]{x+1)}
∫
1
√
x
+
1
+
4
√
x
+
1
dx
limit as x approaches 4+of 2x
lim
x
→
4
+
(
2
x
)
limit as x approaches 0+of cot(x)
lim
x
→
0
+
(
cot
(
x
)
)
integral from 0 to 2 of (2x+5)
∫
0
2
(
2
x
+
5
)
dx
(0^2e^{0+3})^'
(
0
2
e
0
+
3
)
′
derivative of (x^5/(2-x^4))
d
dx
(
x
5
2
−
x
4
)
3y^{''}-30y^'+72y=6sin(4x)
3
y
′
′
−
3
0
y
′
+
7
2
y
=
6
sin
(
4
x
)
integral of (3x^2+6)/((x^2-2x+2)^2)
∫
3
x
2
+
6
(
x
2
−
2
x
+
2
)
2
dx
derivative of sin(x^3+3xy)
d
dx
(
sin
(
x
3
)
+
3
xy
)
tangent f(x)= x/(x+3),\at x=1
tangent
f
(
x
)
=
x
x
+
3
,
at
x
=
1
derivative f(x)=e^{6x}cos(9x)
derivative
f
(
x
)
=
e
6
x
cos
(
9
x
)
derivative of ln(2+x^2)
d
dx
(
ln
(
2
+
x
2
)
)
integral of cos(5x)
∫
cos
(
5
x
)
dx
integral of sqrt(9-x^2)
∫
√
9
−
x
2
dx
laplace変換する g(t)=sin(2t)sin(t)
laplacetransform
g
(
t
)
=
sin
(
2
t
)
sin
(
t
)
derivative of tan(ln(ax+b))
d
dx
(
tan
(
ln
(
ax
+
b
)
)
)
derivative of x^3-1/(x^2)
d
dx
(
x
3
−
1
x
2
)
limit as x approaches-infinity of xe^x-1
lim
x
→
−
∞
(
xe
x
−
1
)
derivative (x^3)/(5-x^2)
derivative
x
3
5
−
x
2
derivative of 1/3 x^3+7x^2+50x
d
dx
(
1
3
x
3
+
7
x
2
+
5
0
x
)
integral of (y^4)/(sqrt(y^2-9))
∫
y
4
√
y
2
−
9
dy
integral of (1+sin(x))
∫
(
1
+
sin
(
x
)
)
dx
(\partial)/(\partial x)(2x^2-3y^2-2x)
∂
∂
x
(
2
x
2
−
3
y
2
−
2
x
)
(\partial)/(\partial x)(y^2+1)
∂
∂
x
(
y
2
+
1
)
integral of tan(x/(sqrt(2)))
∫
tan
(
x
√
2
)
dx
d/(dt)(tcos(6t))
d
dt
(
t
cos
(
6
t
)
)
(\partial)/(\partial x)(e^{2x^3-3y})
∂
∂
x
(
e
2
x
3
−
3
y
)
integral of (x^2-8x-1)/((x-1)^2(x^2+1))
∫
x
2
−
8
x
−
1
(
x
−
1
)
2
(
x
2
+
1
)
dx
derivative of 2x+8
d
dx
(
2
x
+
8
)
derivative of [arctan(3x]^2)
d
dx
(
[
arctan
(
3
x
)
]
2
)
derivative 1680(2x+5)^4
derivative
1
6
8
0
(
2
x
+
5
)
4
y^{''}+y=5e^{-8x}
y
′
′
+
y
=
5
e
−
8
x
integral of 0.007e^{-0.007x}
∫
0
.
0
0
7
e
−
0
.
0
0
7
x
dx
sum from n=1 to infinity of 2(2/3)^{n-1}
∑
n
=
1
∞
2
(
2
3
)
n
−
1
derivative of cos(xln(cos(x)))
d
dx
(
cos
(
x
)
ln
(
cos
(
x
)
)
)
(dy)/(dt)=2y+2t^2-10/3 t
dy
dt
=
2
y
+
2
t
2
−
1
0
3
t
integral of 2z
∫
2
zdz
マクローリン x^5sin(x)
maclaurin
x
5
sin
(
x
)
derivative of (sin(x)/(cos^2(x)))
d
dx
(
sin
(
x
)
cos
2
(
x
)
)
derivative of 4-x^{2/3}
d
dx
(
4
−
x
2
3
)
derivative of x^{4/3}-5
d
dx
(
x
4
3
−
5
)
integral from-1 to 3 of (1+4x)
∫
−
1
3
(
1
+
4
x
)
dx
derivative f(x)=arctan(cos(x))
derivative
f
(
x
)
=
arctan
(
cos
(
x
)
)
derivative of 3x^3+5x
d
dx
(
3
x
3
+
5
x
)
derivative of sqrt(x)(2-x^2)
d
dx
(
√
x
(
2
−
x
)
2
)
(\partial)/(\partial x)(xe^{-3z+2y})
∂
∂
x
(
xe
−
3
z
+
2
y
)
derivative arccos(3x^2)
derivative
arccos
(
3
x
2
)
derivative of e^{1-cos(x})
d
dx
(
e
1
−
cos
(
x
)
)
derivative of xe^2
d
dx
(
xe
2
)
derivative 4x(2x-3)^7
derivative
4
x
(
2
x
−
3
)
7
(\partial)/(\partial x)(x^4sin(2x))
∂
∂
x
(
x
4
sin
(
2
x
)
)
laplace変換する e^{-(t-1)}
laplacetransform
e
−
(
t
−
1
)
derivative of x-ln(sec(x+tan(x)))
d
dx
(
x
−
ln
(
sec
(
x
)
+
tan
(
x
)
)
)
derivative (-2x^3+x^2-2x-1)x^3
derivative
(
−
2
x
3
+
x
2
−
2
x
−
1
)
x
3
derivative of 2e^{5x}
d
dx
(
2
e
5
x
)
integral of 2xy+2x
∫
2
xy
+
2
xdx
limit as t approaches 0 of (1-e^{-2t})/t
lim
t
→
0
(
1
−
e
−
2
t
t
)
f(t)=sin^2(t)
f
(
t
)
=
sin
2
(
t
)
limit as x approaches 3 of (x^2+x)/(x+3)
lim
x
→
3
(
x
2
+
x
x
+
3
)
integral of (13)/(x^2-1)
∫
1
3
x
2
−
1
dx
limit as x approaches 0 of xe^{-x}
lim
x
→
0
(
xe
−
x
)
1
..
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1097
1098
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1100
..
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