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일반적인 미적분학 문제
derivative of e^x*sin(y)
d
dx
(
e
x
·
sin
(
y
)
)
maclaurin x/((1+x^2)^2)
maclaurin
x
(
1
+
x
2
)
2
f(x)=2xe^{x^2}
f
(
x
)
=
2
xe
x
2
sum from n=0 to infinity}(1-10^{42 of)^n
∑
n
=
0
∞
(
1
−
1
0
4
2
)
n
derivative of ln(xsin(x))
d
dx
(
ln
(
x
)
sin
(
x
)
)
(d^2y)/(dx^2)=3e^{-x},y(0)=1,y^'(0)=4
d
2
y
dx
2
=
3
e
−
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
4
integral of 1 1/(x^2)
∫
1
1
x
2
dx
derivative (((x+3))/(x-1))^2
derivative
(
(
x
+
3
)
x
−
1
)
2
y^'-2x=4x^3,y(0)=1
y
′
−
2
x
=
4
x
3
,
y
(
0
)
=
1
derivative 7xln((16x)/(16x+1))
derivative
7
x
ln
(
1
6
x
1
6
x
+
1
)
(dy)/(dx)=2x+3y
dy
dx
=
2
x
+
3
y
integral of x*e^{2*x}
∫
x
·
e
2
·
x
dx
integral of 1/(3(x+1))
∫
1
3
(
x
+
1
)
dx
integral of sqrt(x)cos(x)
∫
√
x
cos
(
x
)
dx
derivative of 4x-10
d
dx
(
4
x
−
1
0
)
tangent (8x)/(x^2+1),\at x=0
tangent
8
x
x
2
+
1
,
at
x
=
0
integral of (2x-4)e^{2x-4}
∫
(
2
x
−
4
)
e
2
x
−
4
dx
integral from 0 to 3 of (xsqrt(14-x^2))
∫
0
3
(
x
√
1
4
−
x
2
)
dx
(\partial)/(\partial θ)(ρsin(φ)sin(θ))
∂
∂
θ
(
ρ
sin
(
φ
)
sin
(
θ
)
)
integral of (e^{2x})/(e^x+5)
∫
e
2
x
e
x
+
5
dx
(\partial)/(\partial x)(y(-3-x))
∂
∂
x
(
y
(
−
3
−
x
)
)
integral of cos(x)\sqrt[7]{5+sin(x)}
∫
cos
(
x
)
7
√
5
+
sin
(
x
)
dx
(\partial)/(\partial x)(xy-x^2y)
∂
∂
x
(
xy
−
x
2
y
)
(\partial)/(\partial x)(2xz^3e^{y^2})
∂
∂
x
(
2
xz
3
e
y
2
)
integral of 1/(sqrt(1+z^2))
∫
1
√
1
+
z
2
dz
derivative f(x)=4(4e^x-25)^7
derivative
f
(
x
)
=
4
(
4
e
x
−
2
5
)
7
tangent y=15-x^2,(1,14)
tangent
y
=
1
5
−
x
2
,
(
1
,
1
4
)
integral of x^5(2-5x^3)^{2/3}
∫
x
5
(
2
−
5
x
3
)
2
3
dx
y^{''}+1=0
y
′
′
+
1
=
0
d/(dy)(\sqrt[3]{y})
d
dy
(
3
√
y
)
integral of (12y^2)/(4y^3+1)
∫
1
2
y
2
4
y
3
+
1
dy
(\partial)/(\partial x)(sin(8x-3y))
∂
∂
x
(
sin
(
8
x
−
3
y
)
)
integral of (3x^2+4x+2)/(2(y-1))
∫
3
x
2
+
4
x
+
2
2
(
y
−
1
)
sum from n=0 to infinity of e^{-3/(n^2)}
∑
n
=
0
∞
e
−
3
n
2
sum from n=0 to infinity of (1+k/n)^n
∑
n
=
0
∞
(
1
+
k
n
)
n
integral from 0.5 to 1 of 3/8 (2-x)^2
∫
0
.
5
1
3
8
(
2
−
x
)
2
dx
integral from 4 to 5 of (tsqrt(t-4))
∫
4
5
(
t
√
t
−
4
)
dt
integral of 1/(ln(t))
∫
1
ln
(
t
)
dt
integral of 15+0.55x
∫
1
5
+
0
.
5
5
xdx
integral of x^{-5/2}
∫
x
−
5
2
dx
inverse라플라스 (2-3s)/(s^2-3)
inverselaplace
2
−
3
s
s
2
−
3
지역 y=(|x-2|)^3,y=8-4x
area
y
=
(
|
x
−
2
|
)
3
,
y
=
8
−
4
x
limit as x approaches 0 of ((2^x-1))/x
lim
x
→
0
(
(
2
x
−
1
)
x
)
integral of 1/(y^2-y^3)
∫
1
y
2
−
y
3
dy
derivative of 2x+(100/x)
d
dx
(
2
x
+
1
0
0
x
)
integral of x^3((2x^2+1)/x)
∫
x
3
(
2
x
2
+
1
x
)
dx
derivative x/(x+3)
derivative
x
x
+
3
integral from 0 to 2 of 5^{-x}
∫
0
2
5
−
x
dx
xy^'+15y=0
xy
′
+
1
5
y
=
0
derivative of sin(3x^3)
d
dx
(
sin
(
3
x
3
)
)
integral of (2x-13)/(x^2-13x+50)
∫
2
x
−
1
3
x
2
−
1
3
x
+
5
0
dx
y^'+0.564y^2=0
y
′
+
0
.
5
6
4
y
2
=
0
(\partial)/(\partial x)(4xzsin(y))
∂
∂
x
(
4
xz
sin
(
y
)
)
sum from n=2 to infinity of 6/(n^2-1)
∑
n
=
2
∞
6
n
2
−
1
(\partial)/(\partial y)(cos(xy)+sin(yz))
∂
∂
y
(
cos
(
xy
)
+
sin
(
yz
)
)
integral of 7/(sqrt(x^3))
∫
7
√
x
3
dx
derivative of (2xln(x+x^2-1)/(x-1))
d
dx
(
2
x
ln
(
x
)
+
x
2
−
1
x
−
1
)
integral from 1 to e^3 of (ln^5(x^2))/x
∫
1
e
3
ln
5
(
x
2
)
x
dx
derivative 35cos(x)
derivative
3
5
cos
(
x
)
d/(dt)((1-t^2)/(1+t^2))
d
dt
(
1
−
t
2
1
+
t
2
)
limit as x approaches-1 of (x^2-2)/(1-x)
lim
x
→
−
1
(
x
2
−
2
1
−
x
)
y^'=4y^2
y
′
=
4
y
2
(\partial)/(\partial y)(600-4x+10x^2y)
∂
∂
y
(
6
0
0
−
4
x
+
1
0
x
2
y
)
integral of (4x+1)^{1/2}
∫
(
4
x
+
1
)
1
2
dx
integral from 1/2 to 2 of 2/x-1/2 x
∫
1
2
2
2
x
−
1
2
xdx
integral of (4-32x)/(sqrt(81-16x^2))
∫
4
−
3
2
x
√
8
1
−
1
6
x
2
dx
limit as x approaches 3 of (9+x)/(3-x)
lim
x
→
3
(
9
+
x
3
−
x
)
limit as x approaches infinity of 8x+5
lim
x
→
∞
(
8
x
+
5
)
derivative f(x)=-x^2-3x+4
derivative
f
(
x
)
=
−
x
2
−
3
x
+
4
y^'+x^2y=1
y
′
+
x
2
y
=
1
maclaurin (-sin(x)2x)/3
maclaurin
−
sin
(
x
)
2
x
3
derivative of 3x^9
d
dx
(
3
x
9
)
derivative of (ln(x)^{ln(x)})
d
dx
(
(
ln
(
x
)
)
ln
(
x
)
)
integral of 1/(12x^5)
∫
1
1
2
x
5
dx
limit as x approaches-infinity+of-5x^3
lim
x
→
−
∞
+
(
−
5
x
3
)
derivative of (x^6/(4-x^5))
d
dx
(
x
6
4
−
x
5
)
derivative of \sqrt[3]{x^8}
d
dx
(
3
√
x
8
)
integral of e^{2x}sqrt(1+e^{2x)}
∫
e
2
x
√
1
+
e
2
x
dx
(\partial)/(\partial x)((6y)/((x+y)^2))
∂
∂
x
(
6
y
(
x
+
y
)
2
)
limit as x approaches-infinity of 2-x
lim
x
→
−
∞
(
2
−
x
)
integral from 1 to 5 of x/(sqrt(2x+1))
∫
1
5
x
√
2
x
+
1
dx
integral of pi(2x-4)^2
∫
π
(
2
x
−
4
)
2
dx
derivative ln(x-1)+1
derivative
ln
(
x
−
1
)
+
1
(\partial)/(\partial z)(3xy)
∂
∂
z
(
3
xy
)
integral from 0 to 7 of 8x*\sqrt[3]{x+1}
∫
0
7
8
x
·
3
√
x
+
1
dx
derivative f(x)=ln(x+6)
derivative
f
(
x
)
=
ln
(
x
+
6
)
integral from 0 to 15 of 1000e^{-0.05t}
∫
0
1
5
1
0
0
0
e
−
0
.
0
5
t
dt
limit as x approaches 1 of 3-3sqrt(x)
lim
x
→
1
(
3
−
3
√
x
)
y^'+1/6 y=40
y
′
+
1
6
y
=
4
0
(\partial)/(\partial y)((x+y+z)^2)
∂
∂
y
(
(
x
+
y
+
z
)
2
)
integral of e^{-x}-e^{-3x}
∫
e
−
x
−
e
−
3
x
dx
tangent f(x)=5e^xcos(x),(0,5)
tangent
f
(
x
)
=
5
e
x
cos
(
x
)
,
(
0
,
5
)
integral from 0 to 2 of y^{7/2}
∫
0
2
y
7
2
dy
derivative of (5sqrt(x)/x)
d
dx
(
5
√
x
x
)
f(t)=te^{2t}
f
(
t
)
=
te
2
t
integral of-x^2-3x
∫
−
x
2
−
3
xdx
derivative f(x)=4x^{5/4}+10x^{3/2}+3x
derivative
f
(
x
)
=
4
x
5
4
+
1
0
x
3
2
+
3
x
integral of x^5sqrt(x^6-1)
∫
x
5
√
x
6
−
1
dx
지역 x^2+4x+3,y=-1,x=0,[-2,0]
area
x
2
+
4
x
+
3
,
y
=
−
1
,
x
=
0
,
[
−
2
,
0
]
sum from k=1 to infinity of (20)^k
∑
k
=
1
∞
(
2
0
)
k
1
..
1166
1167
1168
1169
1170
..
2459