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일반적인 미적분학 문제
tangent f(x)=x^3-3x+2\at (2.4)
tangent
f
(
x
)
=
x
3
−
3
x
+
2
at
(
2
.
4
)
지역 x=sqrt(y),x= y/2
area
x
=
√
y
,
x
=
y
2
limit as x approaches infinity of 2x^2-3
lim
x
→
∞
(
2
x
2
−
3
)
지역 x^2-4,x=-4,x=3,y=0
area
x
2
−
4
,
x
=
−
4
,
x
=
3
,
y
=
0
integral from 0 to 1 of (3x^2-4x+1)
∫
0
1
(
3
x
2
−
4
x
+
1
)
dx
y^{''}+1/4 y=0
y
′
′
+
1
4
y
=
0
limit as x approaches-4 of 3
lim
x
→
−
4
(
3
)
limit as x approaches infinity of 1/(log_{2)(x)}
lim
x
→
∞
(
1
log
2
(
x
)
)
integral from-1 to 0 of 1/(x^2)
∫
−
1
0
1
x
2
dx
inverse라플라스 (4se^{-4s})/(2s^2+50)
inverselaplace
4
se
−
4
s
2
s
2
+
5
0
inverse라플라스 (s+1)/(s^2+s+1)
inverselaplace
s
+
1
s
2
+
s
+
1
d/(dt)(ln(sec(t)+tan(t)))
d
dt
(
ln
(
sec
(
t
)
+
tan
(
t
)
)
)
y^'=y(2x-5)
y
′
=
y
(
2
x
−
5
)
integral of 24(1-x)^5
∫
2
4
(
1
−
x
)
5
dx
derivative of A(2xe^{2x}+e^{2x}*2x^2)
d
dx
(
A
(
2
xe
2
x
+
e
2
x
·
2
x
2
)
)
derivative f(x)=x(3x^4-sqrt(x))
derivative
f
(
x
)
=
x
(
3
x
4
−
√
x
)
derivative 10log_{10}(x)
derivative
1
0
log
1
0
(
x
)
limit as x approaches 9 of 6/9
lim
x
→
9
(
6
9
)
(\partial)/(\partial x)(x^2+4y^2+3z^2)
∂
∂
x
(
x
2
+
4
y
2
+
3
z
2
)
normal y=4x^2,(-1,4)
normal
y
=
4
x
2
,
(
−
1
,
4
)
xy^'-2y=2x^2+2x+1
xy
′
−
2
y
=
2
x
2
+
2
x
+
1
경사지 (-2,0),(0,1)
slope
(
−
2
,
0
)
,
(
0
,
1
)
y^'+3/(t^2)y=0
y
′
+
3
t
2
y
=
0
laplace변환 sin(6(t-(3pi)/6))
laplacetransform
sin
(
6
(
t
−
3
π
6
)
)
derivative of x(e^{-x})
d
dx
(
x
(
e
−
x
)
)
(\partial)/(\partial x)((xy)/(e^{x^2+y^2)})
∂
∂
x
(
xy
e
x
2
+
y
2
)
derivative ln(arctan(2x^3))
derivative
ln
(
arctan
(
2
x
3
)
)
integral of 3/x+2e^x
∫
3
x
+
2
e
x
dx
derivative of 3x-x^2
d
dx
(
3
x
−
x
2
)
derivative of (4-x^2/(4+x^2))
d
dx
(
4
−
x
2
4
+
x
2
)
integral of (x+1/(x^4sqrt(x)))
∫
(
x
+
1
x
4
√
x
)
dx
integral of sec^8(x)
∫
sec
8
(
x
)
dx
(\partial)/(\partial x)(40xy*e^{5x^2-2y})
∂
∂
x
(
4
0
xy
·
e
5
x
2
−
2
y
)
integral of 1/4 x^3
∫
1
4
x
3
dx
integral of ((sqrt(x)-x^3e^x+x^2)/(x^3))
∫
(
√
x
−
x
3
e
x
+
x
2
x
3
)
dx
y^'=sqrt((1-y^2)/(e^x))
y
′
=
√
1
−
y
2
e
x
sum from n=0 to infinity of p^n
∑
n
=
0
∞
p
n
limit as x approaches 3 of 6x
lim
x
→
3
(
6
x
)
integral of q/(pi(-0.125x+0.03125)^2)
∫
q
π
(
−
0
.
1
2
5
x
+
0
.
0
3
1
2
5
)
2
dx
integral of 1/(2-2x)
∫
1
2
−
2
x
dx
d/(dt)(t/(10)sin(5t))
d
dt
(
t
1
0
sin
(
5
t
)
)
derivative of sqrt(x^2-4x)
d
dx
(
√
x
2
−
4
x
)
(1+x^2)dy+(xy+x^3+x)dx=0
(
1
+
x
2
)
dy
+
(
xy
+
x
3
+
x
)
dx
=
0
(dy)/(dx)=((6x-2xy^3))/(y^2)
dy
dx
=
(
6
x
−
2
xy
3
)
y
2
tangent 2x^2+3x-2
tangent
2
x
2
+
3
x
−
2
derivative f(t)=(6t+38)/(t+9)
derivative
f
(
t
)
=
6
t
+
3
8
t
+
9
integral from 1 to 6 of (x^2+1)/(7x-x^2)
∫
1
6
x
2
+
1
7
x
−
x
2
dx
derivative of sqrt(pix)
d
dx
(
√
π
x
)
(dy)/(dx)+4/x y=-3x
dy
dx
+
4
x
y
=
−
3
x
inverse라플라스 1/((s^2+2s+1))
inverselaplace
1
(
s
2
+
2
s
+
1
)
derivative of (e^x/((1-e^x)^2))
d
dx
(
e
x
(
1
−
e
x
)
2
)
laplace변환 f(t)=-2
laplacetransform
f
(
t
)
=
−
2
limit as x approaches 0 of 0/(x^6)
lim
x
→
0
(
0
x
6
)
derivative y=x^2+2x
derivative
y
=
x
2
+
2
x
limit as x approaches 0 of xln(x^2)
lim
x
→
0
(
x
ln
(
x
2
)
)
limit as x approaches infinity of e^{ax}
lim
x
→
∞
(
e
ax
)
derivative of ln(x^2+7)
d
dx
(
ln
(
x
2
+
7
)
)
(x^{-1})^'
(
x
−
1
)
′
derivative (x-1)^2(x-1.05)^2
derivative
(
x
−
1
)
2
(
x
−
1
.
0
5
)
2
integral of x/(x^2-7x+12)
∫
x
x
2
−
7
x
+
1
2
dx
limit as x approaches 1/2 of-4x+2
lim
x
→
1
2
(
−
4
x
+
2
)
derivative of sqrt(3x-x^2)
d
dx
(
√
3
x
−
x
2
)
integral from 0 to pi/(26) of tan(13x)
∫
0
π
2
6
tan
(
1
3
x
)
dx
5x^2y^'=y^'+2xe^{-y}
5
x
2
y
′
=
y
′
+
2
xe
−
y
y^{''}+4y^'+13y=0,y(0)=7,y(0)=7,y^'(0)=7
y
′
′
+
4
y
′
+
1
3
y
=
0
,
y
(
0
)
=
7
,
y
(
0
)
=
7
,
y
′
(
0
)
=
7
(\partial)/(\partial x)(2y(y^2+e^{2x}))
∂
∂
x
(
2
y
(
y
2
+
e
2
x
)
)
integral from 0 to N of e^{(-st)}sin(2t)
∫
0
N
e
(
−
st
)
sin
(
2
t
)
dt
limit as h approaches 3 of (3(x+h)^3-3x^3)/h
lim
h
→
3
(
3
(
x
+
h
)
3
−
3
x
3
h
)
integral from-1 to 2 of (2x-7)/(x^3)
∫
−
1
2
2
x
−
7
x
3
dx
maclaurin 1/(1-x),3
maclaurin
1
1
−
x
,
3
integral from 0 to 1 of 2/(x-2)
∫
0
1
2
x
−
2
dx
derivative of 1/(1+2x)
d
dx
(
1
1
+
2
x
)
derivative of sqrt(9+5x)
d
dx
(
√
9
+
5
x
)
derivative of 2x^{-7\sqrt[3]{x}}
d
dx
(
2
x
−
7
3
√
x
)
sum from n=1 to infinity of n!2^nn^{-n}
∑
n
=
1
∞
n
!
2
n
n
−
n
derivative sqrt(1+4x^2)
derivative
√
1
+
4
x
2
laplace변환 5(t-4)
laplacetransform
5
(
t
−
4
)
integral of (x^2+sqrt(2+x))/(\sqrt[3]{2+x)}
∫
x
2
+
√
2
+
x
3
√
2
+
x
dx
derivative x^2*2
derivative
x
2
·
2
limit as x approaches infinity of-2e^{-x}+2
lim
x
→
∞
(
−
2
e
−
x
+
2
)
integral of 3xsqrt(y)
∫
3
x
√
y
dy
implicit (dy)/(dx),y=(sin(x))^{6x}
implicit
dy
dx
,
y
=
(
sin
(
x
)
)
6
x
(\partial)/(\partial x)(x^2+y^2-9)
∂
∂
x
(
x
2
+
y
2
−
9
)
integral of sec^2(2xta)n^62x
∫
sec
2
(
2
xta
)
n
6
2
xdx
derivative of 3/x+e^{2x}*2
d
dx
(
3
x
+
e
2
x
·
2
)
tangent f(x)=x^2-3,(2,1)
tangent
f
(
x
)
=
x
2
−
3
,
(
2
,
1
)
sum from n=0 to infinity of (n+1)/3
∑
n
=
0
∞
n
+
1
3
derivative f(x)=2sin(x)
derivative
f
(
x
)
=
2
sin
(
x
)
laplace변환 e^{-2t}(t^2+4t+5)
laplacetransform
e
−
2
t
(
t
2
+
4
t
+
5
)
integral from a to 2a of (a-(a^3)/(x^2))
∫
a
2
a
(
a
−
a
3
x
2
)
dx
derivative of 2/(sqrt(x^2+5))
d
dx
(
2
√
x
2
+
5
)
integral of cos(x)cos(sin(x))
∫
cos
(
x
)
cos
(
sin
(
x
)
)
dx
limit as x approaches+5-of 5/((x-5)^3)
lim
x
→
+
5
−
(
5
(
x
−
5
)
3
)
integral of ((3x+5)^3)/(10)
∫
(
3
x
+
5
)
3
1
0
dx
d/(du)(u^3-5u^2+7/(3u^2)+6)
d
du
(
u
3
−
5
u
2
+
7
3
u
2
+
6
)
(\partial)/(\partial x)(10990+1120x+873y)
∂
∂
x
(
1
0
9
9
0
+
1
1
2
0
x
+
8
7
3
y
)
tangent sqrt(5x+1)
tangent
√
5
x
+
1
integral of (4+3x)/(1+x^2)
∫
4
+
3
x
1
+
x
2
dx
integral of (e^{-2x})/(x^2)
∫
e
−
2
x
x
2
dx
integral from 0 to pi/3 of sec^4(x)
∫
0
π
3
sec
4
(
x
)
dx
1
..
1205
1206
1207
1208
1209
..
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