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일반적인 미적분학 문제
derivative of-sqrt(3)sin(x+cos(x))
d
dx
(
−
√
3
sin
(
x
)
+
cos
(
x
)
)
derivative y=3^{-x^2}
derivative
y
=
3
−
x
2
integral of e^{0.2y}
∫
e
0
.
2
y
dy
integral of (8x^3+13x)/((x^2+2)^2)
∫
8
x
3
+
1
3
x
(
x
2
+
2
)
2
dx
integral from 2 to infinity of 1/(x^2)
∫
2
∞
1
x
2
dx
integral from 1 to 3 of (3x^2-2x+1)
∫
1
3
(
3
x
2
−
2
x
+
1
)
dx
integral of 16sin^2(θ)
∫
1
6
sin
2
(
θ
)
d
θ
derivative f(x)= A/(x^{14)}+Be^x
derivative
f
(
x
)
=
A
x
1
4
+
Be
x
derivative y=2+sqrt(x-7)
derivative
y
=
2
+
√
x
−
7
limit as x approaches infinity of e^{1/x ln(2^x+3^x+5^x)}
lim
x
→
∞
(
e
1
x
ln
(
2
x
+
3
x
+
5
x
)
)
derivative of cos^2(1-2x)
d
dx
(
cos
2
(
1
−
2
x
)
)
xy+y^'=166x
xy
+
y
′
=
1
6
6
x
(2xy+2y^2)dx+(x^2+4xy)dy=0,y(1)=1
(
2
xy
+
2
y
2
)
dx
+
(
x
2
+
4
xy
)
dy
=
0
,
y
(
1
)
=
1
integral of 1/(x^2)+1
∫
1
x
2
+
1
dx
sum from n=2 to infinity of 3/(5^n)
∑
n
=
2
∞
3
5
n
derivative of-x^4-4/3 x^3+4x^2
d
dx
(
−
x
4
−
4
3
x
3
+
4
x
2
)
integral of (sin(x)+2cos(x))
∫
(
sin
(
x
)
+
2
cos
(
x
)
)
dx
derivative of x^t
d
dx
(
x
t
)
integral from 0 to 4 of (2t+4)^{-1/2}
∫
0
4
(
2
t
+
4
)
−
1
2
dt
y^'+2y=y^2
y
′
+
2
y
=
y
2
integral of-2ln(3/2 x)-cos(3x)
∫
−
2
ln
(
3
2
x
)
−
cos
(
3
x
)
dx
integral of (xe^x)/(sqrt(1+e^x))
∫
xe
x
√
1
+
e
x
dx
integral of 7e^{-t}
∫
7
e
−
t
dt
derivative of (1-2e^x/(1-2cos(x)))
d
dx
(
1
−
2
e
x
1
−
2
cos
(
x
)
)
(x+1)y^'=x^2-y
(
x
+
1
)
y
′
=
x
2
−
y
integral of 9/(x^2+1)
∫
9
x
2
+
1
dx
(x/(1-x))^'
(
x
1
−
x
)
′
y^{''}-8y^'+20y=200x^2-52xe^x
y
′
′
−
8
y
′
+
2
0
y
=
2
0
0
x
2
−
5
2
xe
x
(\partial)/(\partial x)(7x+6y+7xy)
∂
∂
x
(
7
x
+
6
y
+
7
xy
)
integral of cos(sqrt(7x))
∫
cos
(
√
7
x
)
dx
지역 x^2-4x+1,3x-5,1,4
area
x
2
−
4
x
+
1
,
3
x
−
5
,
1
,
4
integral of (2y-x)/(-(y+xy))
∫
2
y
−
x
−
(
y
+
xy
)
dx
integral of 5ln(x^2+5)
∫
5
ln
(
x
2
+
5
)
dx
tangent f(x)=(1+2x)^{12},\at x=0
tangent
f
(
x
)
=
(
1
+
2
x
)
1
2
,
at
x
=
0
4y^{''}+4y^'+17y=0
4
y
′
′
+
4
y
′
+
1
7
y
=
0
2y^'+y=3t
2
y
′
+
y
=
3
t
(\partial)/(\partial x)(10x+5y)
∂
∂
x
(
1
0
x
+
5
y
)
sum from n=1 to infinity}cos(e^{-n of)
∑
n
=
1
∞
cos
(
e
−
n
)
integral of x^{(-3)/2}
∫
x
−
3
2
dx
integral of 2x-8
∫
2
x
−
8
dx
d/(dθ)(3sin(θ))
d
d
θ
(
3
sin
(
θ
)
)
지역 y=2x^2,(3,18)
area
y
=
2
x
2
,
(
3
,
1
8
)
integral of x/(sqrt(1-16x^4))
∫
x
√
1
−
1
6
x
4
dx
derivative x/((2x+2*sqrt(x+3)))
derivative
x
(
2
x
+
2
·
√
x
+
3
)
integral from 0 to 5 of 1/(x^{16/17)}
∫
0
5
1
x
1
6
1
7
dx
d/(dθ)(5sin(θ))
d
d
θ
(
5
sin
(
θ
)
)
limit as x approaches 0 of 1/4 (4)^4
lim
x
→
0
(
1
4
(
4
)
4
)
integral of tan(3t)
∫
tan
(
3
t
)
dt
y^{'''}+y^{''}=x
y
′
′
′
+
y
′
′
=
x
integral of 3/(3+e^x)
∫
3
3
+
e
x
dx
y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2
y
′
′
+
y
′
−
3
0
y
=
0
,
y
(
0
)
=
2
,
y
′
(
0
)
=
−
2
(2x+1)^'
(
2
x
+
1
)
′
y^'=(y+2x)^2,y(0)=sqrt(3)
y
′
=
(
y
+
2
x
)
2
,
y
(
0
)
=
√
3
테일러 4x^4+3x^3+2x^2+x+11
taylor
4
x
4
+
3
x
3
+
2
x
2
+
x
+
1
1
derivative of (-1/x)
d
dx
(
−
1
x
)
(d^2)/(dx^2)((x^2)/(2+x))
d
2
dx
2
(
x
2
2
+
x
)
(dy)/(dx)-3*y=e^{2*x}
dy
dx
−
3
·
y
=
e
2
·
x
derivative of 460(1+x/(x^2+80))
d
dx
(
4
6
0
(
1
+
x
x
2
+
8
0
)
)
integral of (5x-2)/((x-2)^2)
∫
5
x
−
2
(
x
−
2
)
2
dx
integral of (-3x^2)/(sqrt(4x-x^2))
∫
−
3
x
2
√
4
x
−
x
2
dx
derivative of 1/27 (9x^2+6^{3/2})
d
dx
(
1
2
7
(
9
x
2
+
6
)
3
2
)
y^'+9y=t+e^{-5t}
y
′
+
9
y
=
t
+
e
−
5
t
(x-y)dx+xdy=0
(
x
−
y
)
dx
+
xdy
=
0
derivative of-4sec(x+2csc(x))
d
dx
(
−
4
sec
(
x
)
+
2
csc
(
x
)
)
지역 (4x)/(x^2+1),(2x)/(25)
area
4
x
x
2
+
1
,
2
x
2
5
integral from 0 to infinity of x^2e^{-x/2}
∫
0
∞
x
2
e
−
x
2
dx
limit as x approaches 0+of sqrt(xe^{sin(pi/x))}
lim
x
→
0
+
(
√
xe
sin
(
π
x
)
)
테일러 sin(x)pi
taylor
sin
(
x
)
π
integral of (6ln^2(x))/x
∫
6
ln
2
(
x
)
x
dx
integral of (-4x)/((1-2x^2)^2)
∫
−
4
x
(
1
−
2
x
2
)
2
dx
테일러 ln((1+x)/(1-x)),0
taylor
ln
(
1
+
x
1
−
x
)
,
0
y^'+xy^2=0
y
′
+
xy
2
=
0
limit as x approaches 0 of sqrt(x+a)
lim
x
→
0
(
√
x
+
a
)
limit as x approaches 3.1 of (5x)/(6-2x)
lim
x
→
3
.
1
(
5
x
6
−
2
x
)
(\partial)/(\partial y)(3x^2y^4+3)
∂
∂
y
(
3
x
2
y
4
+
3
)
integral of x/(x^4-16)
∫
x
x
4
−
1
6
dx
integral of sin(\sqrt[3]{x})
∫
sin
(
3
√
x
)
dx
integral from 0 to 5 of 25-x^2
∫
0
5
2
5
−
x
2
dx
limit as h approaches 0 of x^2+2x+h-4
lim
h
→
0
(
x
2
+
2
x
+
h
−
4
)
limit as x approaches 0 of |x^2|
lim
x
→
0
(
|
x
2
|
)
(\partial)/(\partial x)(x^3sin(y))
∂
∂
x
(
x
3
sin
(
y
)
)
integral of 1/(x^2)x
∫
1
x
2
xdx
derivative of (2x+3y^{10})
d
dx
(
(
2
x
+
3
y
)
1
0
)
integral of 2cos^3(6x)
∫
2
cos
3
(
6
x
)
dx
integral of 1/(z^3sqrt(z^2-49))
∫
1
z
3
√
z
2
−
4
9
dz
derivative of (x+4^{2/3})
d
dx
(
(
x
+
4
)
2
3
)
integral of 1/(-y^2+y+20)
∫
1
−
y
2
+
y
+
2
0
dy
limit as x approaches 2 of (-1)/0
lim
x
→
2
(
−
1
0
)
tangent y=(1+5x)^{10},(0,1)
tangent
y
=
(
1
+
5
x
)
1
0
,
(
0
,
1
)
derivative of-(2x/((3+x^2)^2))
d
dx
(
−
2
x
(
3
+
x
2
)
2
)
integral of ((2x+y+z)/((x+y)(x+z)))
∫
(
2
x
+
y
+
z
(
x
+
y
)
(
x
+
z
)
)
dx
테일러 x^4cos(x^3)
taylor
x
4
cos
(
x
3
)
(\partial)/(\partial x)(4cos(x^2+y^2))
∂
∂
x
(
4
cos
(
x
2
+
y
2
)
)
laplace변환 e^tcos(6t)
laplacetransform
e
t
cos
(
6
t
)
tangent 5-x^2
tangent
5
−
x
2
derivative f(x)=ln(sqrt(x^2+3))
derivative
f
(
x
)
=
ln
(
√
x
2
+
3
)
derivative y=(x+1)(sqrt(x)+2)
derivative
y
=
(
x
+
1
)
(
√
x
+
2
)
integral of cos(200tn)
∫
cos
(
2
0
0
tn
)
dt
integral of sin(20x)cos(17x)
∫
sin
(
2
0
x
)
cos
(
1
7
x
)
dx
x^2y^'=y^2+5xy+4x^2
x
2
y
′
=
y
2
+
5
xy
+
4
x
2
1
..
1385
1386
1387
1388
1389
..
2459