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일반적인 미적분학 문제
(\partial)/(\partial x)((x+y)^{1/2})
∂
∂
x
(
(
x
+
y
)
1
2
)
(\partial)/(\partial x)(4x^3+y^2)
∂
∂
x
(
4
x
3
+
y
2
)
integral of x^2(5^3+7^2-6x-3)
∫
x
2
(
5
3
+
7
2
−
6
x
−
3
)
dx
지역 x=-2,x=1,y=e^x,y=3-e^x
area
x
=
−
2
,
x
=
1
,
y
=
e
x
,
y
=
3
−
e
x
integral of (cot(x))[ln(sin(x))]
∫
(
cot
(
x
)
)
[
ln
(
sin
(
x
)
)
]
dx
integral of x^2+x+6
∫
x
2
+
x
+
6
dx
integral of (3x^2+5x)/((x-1)(x+1)^2)
∫
3
x
2
+
5
x
(
x
−
1
)
(
x
+
1
)
2
dx
(x+2y^2)dx+xydy=0
(
x
+
2
y
2
)
dx
+
xydy
=
0
x^2y^{''}-3xy^'+4y=x,y(1)=0,y^'(1)=0
x
2
y
′
′
−
3
xy
′
+
4
y
=
x
,
y
(
1
)
=
0
,
y
′
(
1
)
=
0
(dy)/(dx)= x/(sqrt(x^2+64))
dy
dx
=
x
√
x
2
+
6
4
sum from n=1 to infinity of n!(2x-1)^n
∑
n
=
1
∞
n
!
(
2
x
−
1
)
n
(dx)/(dt)=-8
dx
dt
=
−
8
integral of (x^4+5x^3-3)/x
∫
x
4
+
5
x
3
−
3
x
dx
integral of (6xy+4x)
∫
(
6
xy
+
4
x
)
dy
경사지 (-5,-8),(9,-8)
slope
(
−
5
,
−
8
)
,
(
9
,
−
8
)
limit as x approaches-9 of 5x-4
lim
x
→
−
9
(
5
x
−
4
)
inverse라플라스-(75)/(s^2+6s+25)
inverselaplace
−
7
5
s
2
+
6
s
+
2
5
(dy)/(dx)=((x^2+xy+y^2))/(x^2)
dy
dx
=
(
x
2
+
xy
+
y
2
)
x
2
limit as h approaches 0 of (h^2)/(3|h|)
lim
h
→
0
(
h
2
3
|
h
|
)
integral of 1/(sin(x)-1)
∫
1
sin
(
x
)
−
1
dx
derivative of ln(4x+9)
d
dx
(
ln
(
4
x
+
9
)
)
limit as x approaches-6 of (x^2-5)/(6-x)
lim
x
→
−
6
(
x
2
−
5
6
−
x
)
ty^'+y=t^2
ty
′
+
y
=
t
2
(dy)/(dx)= 1/(2x+y+1)
dy
dx
=
1
2
x
+
y
+
1
integral of 1/(2y)
∫
1
2
y
dy
integral from 0 to 8 of |sqrt(5x+6)-x|
∫
0
8
|
√
5
x
+
6
−
x
|
dx
derivative of sqrt(3x-7)
d
dx
(
√
3
x
−
7
)
limit as x approaches 0 of |7x|
lim
x
→
0
(
|
7
x
|
)
tangent y=x^2+8
tangent
y
=
x
2
+
8
(arctan(4x))^'
(
arctan
(
4
x
)
)
′
derivative 7x^2(x-4)^3
derivative
7
x
2
(
x
−
4
)
3
integral of (5x^2)/(sqrt(4x-x^2))
∫
5
x
2
√
4
x
−
x
2
dx
integral of 4/u
∫
4
u
du
sum from n=2 to infinity of e^{5-2n}
∑
n
=
2
∞
e
5
−
2
n
x^2y^'+y^2-xy=0
x
2
y
′
+
y
2
−
xy
=
0
integral of (sqrt(x-3))/(x+4)
∫
√
x
−
3
x
+
4
dx
integral of-16x
∫
−
1
6
xdx
integral of (x+1)^{10}(x+2)
∫
(
x
+
1
)
1
0
(
x
+
2
)
dx
derivative 1/(x-6)
derivative
1
x
−
6
지역 x, 1/x , 1/2
area
x
,
1
x
,
1
2
derivative y=ln(sec(x))
derivative
y
=
ln
(
sec
(
x
)
)
limit as x approaches 0 of (1/x)^{x^2}
lim
x
→
0
(
(
1
x
)
x
2
)
(\partial)/(\partial x)(((1+y))/(1+x))
∂
∂
x
(
(
1
+
y
)
1
+
x
)
limit as x approaches-1 of x^4-x^3+2x
lim
x
→
−
1
(
x
4
−
x
3
+
2
x
)
derivative of e^{-2x}(acos(x+bsin(x)))
d
dx
(
e
−
2
x
(
a
cos
(
x
)
+
b
sin
(
x
)
)
)
limit as x approaches 0+of 6/(sin(x))
lim
x
→
0
+
(
6
sin
(
x
)
)
integral of 1/(v^2+8v-9)
∫
1
v
2
+
8
v
−
9
dv
integral of-2/(x+1)
∫
−
2
x
+
1
dx
integral of sqrt(x)(3x-2)
∫
√
x
(
3
x
−
2
)
dx
(dy)/(dx)+xy=y
dy
dx
+
xy
=
y
integral from-1 to 9 of 9-x^2+8x
∫
−
1
9
9
−
x
2
+
8
xdx
y^'=(5xsec(y/x)+y)/x
y
′
=
5
x
sec
(
y
x
)
+
y
x
laplace변환 3cos(t+pi/3)
laplacetransform
3
cos
(
t
+
π
3
)
단순화 (sqrt(x)+1/(\sqrt[3]{x)})^2
simplify
(
√
x
+
1
3
√
x
)
2
derivative of cot(7x)
d
dx
(
cot
(
7
x
)
)
integral of 1/(x^2)-1/(x^3)
∫
1
x
2
−
1
x
3
dx
limit as x approaches 0 of 1/(2x-1)
lim
x
→
0
(
1
2
x
−
1
)
d/(du)(x^2+x{y}(x,u)(x,u)^3)
d
du
(
x
2
+
x
y
(
x
,
u
)
(
x
,
u
)
3
)
limit as x approaches-1-of x-1
lim
x
→
−
1
−
(
x
−
1
)
integral of sqrt(t)ln(t)
∫
√
t
ln
(
t
)
dt
integral of x^{5/4}
∫
x
5
4
dx
t^2(d^2y)/(dt^2)+2t(dy)/(dt)-6y=0
t
2
d
2
y
dt
2
+
2
t
dy
dt
−
6
y
=
0
derivative of (4x^2+4x+4/(sqrt(x)))
d
dx
(
4
x
2
+
4
x
+
4
√
x
)
inverse라플라스 (4s+3)/(s^2+109s+990)
inverselaplace
4
s
+
3
s
2
+
1
0
9
s
+
9
9
0
tangent (x+2)^2+(y-3)^2=37,(-8,4)
tangent
(
x
+
2
)
2
+
(
y
−
3
)
2
=
3
7
,
(
−
8
,
4
)
integral of cos^2(u)sin^2(u)
∫
cos
2
(
u
)
sin
2
(
u
)
du
integral of (x+1)cos(2x^2+4x)
∫
(
x
+
1
)
cos
(
2
x
2
+
4
x
)
dx
derivative of 6x^5e^{6x}
d
dx
(
6
x
5
e
6
x
)
derivative of (1-2x/(6+x))
d
dx
(
1
−
2
x
6
+
x
)
integral of (x^3)/(2x^2-x-1)
∫
x
3
2
x
2
−
x
−
1
dx
tangent f(x)=4x-3sqrt(x)
tangent
f
(
x
)
=
4
x
−
3
√
x
derivative of ax^n
d
dx
(
ax
n
)
derivative of 1/(sqrt(x^4+1))
d
dx
(
1
√
x
4
+
1
)
integral of (8^x-sec^2(x))
∫
(
8
x
−
sec
2
(
x
)
)
dx
x^2y^{''}-2xy^'-40y=x^4
x
2
y
′
′
−
2
xy
′
−
4
0
y
=
x
4
integral of 1/(t^2sqrt(225-t^2))
∫
1
t
2
√
2
2
5
−
t
2
dt
limit as x approaches 1+of-6
lim
x
→
1
+
(
−
6
)
derivative (7x+8)^2
derivative
(
7
x
+
8
)
2
(\partial}{\partial x}(\frac{-y+sqrt(y^2+4x^2))/2)
∂
∂
x
(
−
y
+
√
y
2
+
4
x
2
2
)
derivative of 6-x
d
dx
(
6
−
x
)
sum from k=1 to infinity of (k!)/(2^k)
∑
k
=
1
∞
k
!
2
k
integral from-1 to 1 of x^3
∫
−
1
1
x
3
dx
derivative of cos(5sqrt(12-4x^3))
d
dx
(
cos
(
5
√
1
2
−
4
x
3
)
)
integral from 2 to 5 of (x-3)^2
∫
2
5
(
x
−
3
)
2
dx
(\partial)/(\partial z)(-5e^xcos(yz))
∂
∂
z
(
−
5
e
x
cos
(
yz
)
)
tangent y=3x+8cos(x),(0,8)
tangent
y
=
3
x
+
8
cos
(
x
)
,
(
0
,
8
)
limit as x approaches 3+of (x-1)/(3-x)
lim
x
→
3
+
(
x
−
1
3
−
x
)
integral of 15tan^2(x)sec^3(x)
∫
1
5
tan
2
(
x
)
sec
3
(
x
)
dx
derivative 2xe^{4x}
derivative
2
xe
4
x
d/(dθ)(4sin(2θ))
d
d
θ
(
4
sin
(
2
θ
)
)
integral of 2/(x^3sqrt(x^2-3))
∫
2
x
3
√
x
2
−
3
dx
derivative sqrt(2)x+sqrt(3x)
derivative
√
2
x
+
√
3
x
y^{''}-3y^'+2y=e^{3x}
y
′
′
−
3
y
′
+
2
y
=
e
3
x
inverse라플라스 s/(s^2+2s+5)
inverselaplace
s
s
2
+
2
s
+
5
limit as x approaches infinity of 1/x+5
lim
x
→
∞
(
1
x
+
5
)
integral from 0 to 1 of e^{4x}
∫
0
1
e
4
x
dx
integral of sin(9x)cos(7x)
∫
sin
(
9
x
)
cos
(
7
x
)
dx
integral of xcos^2(7x)
∫
x
cos
2
(
7
x
)
dx
(sin(5x))^'
(
sin
(
5
x
)
)
′
경사지 f(x)=sqrt(x)+1/(sqrt(x))
slope
f
(
x
)
=
√
x
+
1
√
x
1
..
1376
1377
1378
1379
1380
..
2459