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일반적인 미적분학 문제
limit as x approaches 0+of (x^2)/6-4/x
lim
x
→
0
+
(
x
2
6
−
4
x
)
(\partial)/(\partial y)(e^{2x}cos(2y))
∂
∂
y
(
e
2
x
cos
(
2
y
)
)
y^'=e^{x-2y}
y
′
=
e
x
−
2
y
지역 x=-2,x=3,y=2x^2+6,y=0
area
x
=
−
2
,
x
=
3
,
y
=
2
x
2
+
6
,
y
=
0
limit as x approaches 0+of (x^2+1)/x
lim
x
→
0
+
(
x
2
+
1
x
)
limit as x approaches 2 of 1/(x^2-9)
lim
x
→
2
(
1
x
2
−
9
)
y^{''}+15y=0
y
′
′
+
1
5
y
=
0
derivative of {f}(x(x)^{{g}(x)})
d
dx
(
f
(
x
)
(
x
)
g
(
x
)
)
derivative of ((x+1(2x-5))/(2x+3))
d
dx
(
(
x
+
1
)
(
2
x
−
5
)
2
x
+
3
)
(\partial)/(\partial y)(sin(3x+2y))
∂
∂
y
(
sin
(
3
x
+
2
y
)
)
derivative ye^y
derivative
ye
y
integral of xcos(n)pix
∫
x
cos
(
n
)
π
xdx
integral of (x^2,left(sin(x)))
∫
(
x
2
,
left
(
sin
(
x
)
)
)
dx
limit as z approaches-2 of (z^2-9)/(z-3)
lim
z
→
−
2
(
z
2
−
9
z
−
3
)
integral of (6-x^2)^{3/2}
∫
(
6
−
x
2
)
3
2
dx
sum from n=0 to infinity of 1/(2-e^n)
∑
n
=
0
∞
1
2
−
e
n
derivative (x^2)/(x^2)
derivative
x
2
x
2
integral of 2csc^2(x)
∫
2
csc
2
(
x
)
dx
integral of sinh^{15}(x)
∫
sinh
1
5
(
x
)
dx
tangent f(x)=x^2+4,\at x=3
tangent
f
(
x
)
=
x
2
+
4
,
at
x
=
3
integral of x(2x+3)^{99}
∫
x
(
2
x
+
3
)
9
9
dx
tangent x^2-7x
tangent
x
2
−
7
x
integral from 0 to 8 of xsqrt(1+x)
∫
0
8
x
√
1
+
x
dx
derivative 1/(6x-1)
derivative
1
6
x
−
1
integral of-6/pi x
∫
−
6
π
xdx
limit as x approaches 0 of (3x)^{x^2}
lim
x
→
0
(
(
3
x
)
x
2
)
tangent f(x)2x+10y-9=0
tangent
f
(
x
)
2
x
+
1
0
y
−
9
=
0
integral of cos(-6x)
∫
cos
(
−
6
x
)
dx
derivative y=(-13)/(\sqrt[4]{x)}
derivative
y
=
−
1
3
4
√
x
derivative g(x)=x^2(1-3x)
derivative
g
(
x
)
=
x
2
(
1
−
3
x
)
integral of bx*sin((pix)/(2a))
∫
bx
·
sin
(
π
x
2
a
)
dx
(\partial)/(\partial y)(5x^2-2xy+3y^3)
∂
∂
y
(
5
x
2
−
2
xy
+
3
y
3
)
경사지 (5.8)(3.9)
slope
(
5
.
8
)
(
3
.
9
)
y^{''}-y= 1/(e^x+e^{-x)}
y
′
′
−
y
=
1
e
x
+
e
−
x
(\partial)/(\partial x)(cos(xy))
∂
∂
x
(
cos
(
xy
)
)
derivative of (tan(x)/(1+cos(x)))
d
dx
(
tan
(
x
)
1
+
cos
(
x
)
)
integral from 2 to 3 of (36)/(sqrt(3-x))
∫
2
3
3
6
√
3
−
x
dx
sum from n=1 to infinity of 1/(3n)
∑
n
=
1
∞
1
3
n
limit as x approaches-5+of 8
lim
x
→
−
5
+
(
8
)
tangent 5x^3-4x^2+7x-8,\at x=1
tangent
5
x
3
−
4
x
2
+
7
x
−
8
,
at
x
=
1
integral from 0 to 1 of (4x+2)e^{2x}
∫
0
1
(
4
x
+
2
)
e
2
x
dx
integral of 19tan^2(xse)c^3x
∫
1
9
tan
2
(
xse
)
c
3
xdx
derivative f(x)=(3x)/(x^2-1)
derivative
f
(
x
)
=
3
x
x
2
−
1
integral from 0 to 5 of pi((y^2)/3)^2
∫
0
5
π
(
y
2
3
)
2
dy
integral of (8x-12)(4x^2-12x)
∫
(
8
x
−
1
2
)
(
4
x
2
−
1
2
x
)
dx
derivative 7sin(x)
derivative
7
sin
(
x
)
derivative y=ln(sqrt((x+1)/(x-1)))
derivative
y
=
ln
(
√
x
+
1
x
−
1
)
(dy)/(dt)=2ty^2+3y^2
dy
dt
=
2
ty
2
+
3
y
2
limit as x approaches+0+of (7x)^x
lim
x
→
+
0
+
(
(
7
x
)
x
)
integral from-infinity to infinity of xe^{x^2}
∫
−
∞
∞
xe
x
2
dx
(dy)/(dx)=-k(y-a)
dy
dx
=
−
k
(
y
−
a
)
3yln(x)-xy^'=0
3
y
ln
(
x
)
−
xy
′
=
0
derivative of tan(x^2-4x^5)
d
dx
(
tan
(
x
2
−
4
x
5
)
)
derivative of 2x^{1/2}+6x^{1/3}-2x^{3/2}
d
dx
(
2
x
1
2
+
6
x
1
3
−
2
x
3
2
)
derivative (sin(5x))/x
derivative
sin
(
5
x
)
x
(y+x)y^'=x-y
(
y
+
x
)
y
′
=
x
−
y
(dy)/(dt)-2ty=-12t^2e^{t^2}
dy
dt
−
2
ty
=
−
1
2
t
2
e
t
2
integral of (x^4-x^2+2)/(x^2(x-1))
∫
x
4
−
x
2
+
2
x
2
(
x
−
1
)
dx
integral of (Inx)/(x^2)
∫
Inx
x
2
dx
d/(dv)(sqrt(uv))
d
dv
(
√
uv
)
derivative \sqrt[3]{6x^2+1}
derivative
3
√
6
x
2
+
1
테일러 1/(x+1),0
taylor
1
x
+
1
,
0
integral from 0 to 5 of 2pi(7-x)(25-x^2)
∫
0
5
2
π
(
7
−
x
)
(
2
5
−
x
2
)
dx
integral of (arccos(x))/(sqrt(1-x^2))
∫
arccos
(
x
)
√
1
−
x
2
dx
integral of-e^{2x}cos(2x)
∫
−
e
2
x
cos
(
2
x
)
dx
integral of ((1+e^{2x})^3)/(e^{-2x)}
∫
(
1
+
e
2
x
)
3
e
−
2
x
dx
derivative y=3^x+1
derivative
y
=
3
x
+
1
integral of (sin(x)-cos(2x))^2
∫
(
sin
(
x
)
−
cos
(
2
x
)
)
2
dx
integral of (7+7tan^2(θ))
∫
(
7
+
7
tan
2
(
θ
)
)
d
θ
derivative of (x^4-3x^3-6x^2-3x+2/x)
d
dx
(
x
4
−
3
x
3
−
6
x
2
−
3
x
+
2
x
)
tangent f(x)= x/((2x-1)^6),\at x=1
tangent
f
(
x
)
=
x
(
2
x
−
1
)
6
,
at
x
=
1
(dy)/(dx)+3y+5=0
dy
dx
+
3
y
+
5
=
0
laplace변환 cos(sqrt(2)x)
laplacetransform
cos
(
√
2
x
)
derivative of 1/(7x+1)
d
dx
(
1
7
x
+
1
)
derivative (48)/(-4x)
derivative
4
8
−
4
x
limit as x approaches 0+of x/(sqrt(x)-1)
lim
x
→
0
+
(
x
√
x
−
1
)
derivative f(x)=(x-7)(5x+1)
derivative
f
(
x
)
=
(
x
−
7
)
(
5
x
+
1
)
derivative e^{1/t}
derivative
e
1
t
integral of x/(sqrt(x+6))
∫
x
√
x
+
6
dx
derivative of e^x+2^{(-x}+2cos(x)-6)
d
dx
(
e
x
+
2
(
−
x
)
+
2
cos
(
x
)
−
6
)
(dy)/(dx)+8y=e^xy^{-6}
dy
dx
+
8
y
=
e
x
y
−
6
(2xdy)/(dx)+y=6x
2
xdy
dx
+
y
=
6
x
derivative of 4x^3-16x+5
d
dx
(
4
x
3
−
1
6
x
+
5
)
integral of 1/(1+x^2+y^2)
∫
1
1
+
x
2
+
y
2
dy
y^{''}+16y=2sin(4t)
y
′
′
+
1
6
y
=
2
sin
(
4
t
)
limit as x approaches-3 of-2
lim
x
→
−
3
(
−
2
)
limit as x approaches infinity of e^{1/x}sin(1/x)
lim
x
→
∞
(
e
1
x
sin
(
1
x
)
)
derivative y=((x^2+2)/(x^2-2))^8
derivative
y
=
(
x
2
+
2
x
2
−
2
)
8
integral of cot(ax)
∫
cot
(
ax
)
dx
integral of csc^2(x)cot^5(x)
∫
csc
2
(
x
)
cot
5
(
x
)
dx
integral of e^{1/50 x}
∫
e
1
5
0
x
dx
(dy)/(dx)=-5yx
dy
dx
=
−
5
yx
integral from 0 to 4 of sqrt(1+x)
∫
0
4
√
1
+
x
dx
integral of (-1)/(1-x)
∫
−
1
1
−
x
dx
integral from 1 to 3 of (-x^2+4x-3)
∫
1
3
(
−
x
2
+
4
x
−
3
)
dx
limit as x approaches (0) of (ln(x))/x
lim
x
→
(
0
)
(
ln
(
x
)
x
)
limit as x approaches-3 of 2x-3ax+6a
lim
x
→
−
3
(
2
x
−
3
ax
+
6
a
)
limit as x approaches 1+of (|x-1|)/(x-1)
lim
x
→
1
+
(
|
x
−
1
|
x
−
1
)
(\partial)/(\partial x)((-x)/(y^2+x^2))
∂
∂
x
(
−
x
y
2
+
x
2
)
integral of ((x^3-4))/(x^3+2x^2+2x)
∫
(
x
3
−
4
)
x
3
+
2
x
2
+
2
x
dx
1
..
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1400
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1402
1403
..
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