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일반적인 미적분학 문제
derivative f(x)=8-x^2
derivative
f
(
x
)
=
8
−
x
2
integral of u^1
∫
u
1
du
y^{(1/2)}(dy)/(dx)+y^{(3/2)}=1,y(0)=9
y
(
1
2
)
dy
dx
+
y
(
3
2
)
=
1
,
y
(
0
)
=
9
f(x)=cos(x)-1
f
(
x
)
=
cos
(
x
)
−
1
derivative of e^{sqrt(2)x}
d
dx
(
e
√
2
x
)
integral of y/((y+2)(5y-1))
∫
y
(
y
+
2
)
(
5
y
−
1
)
dy
y^{''}+y^'=sin(t)
y
′
′
+
y
′
=
sin
(
t
)
integral of 1/((x*sqrt(x^2-16)))
∫
1
(
x
·
√
x
2
−
1
6
)
dx
y=e^{-x}cos(sqrt(x))
y
=
e
−
x
cos
(
√
x
)
integral of 1/(x^3-4x^2)
∫
1
x
3
−
4
x
2
dx
(\partial)/(\partial x)((9x)/(7y+8z))
∂
∂
x
(
9
x
7
y
+
8
z
)
(xdy)/(dx)+6y=x^3-x
xdy
dx
+
6
y
=
x
3
−
x
integral of 8xe^{2x}
∫
8
xe
2
x
dx
derivative 1/(m+ke^m)
derivative
1
m
+
ke
m
integral of (3x^3+9x^2+2x+6)/(x^4+x^2)
∫
3
x
3
+
9
x
2
+
2
x
+
6
x
4
+
x
2
dx
테일러 x*sec(x)
taylor
x
·
sec
(
x
)
integral of 1/(xsqrt(16x^2-9))
∫
1
x
√
1
6
x
2
−
9
dx
(\partial)/(\partial x)(7/(x^3))
∂
∂
x
(
7
x
3
)
derivative of (pix/2)
d
dx
(
π
x
2
)
integral of (sin^3(x)cos(x))
∫
(
sin
3
(
x
)
cos
(
x
)
)
dx
integral of e^{-(2r)/a}r^2
∫
e
−
2
r
a
r
2
dr
tangent f(x)=x^3,\at-5
tangent
f
(
x
)
=
x
3
,
at
−
5
integral of-xsin(nx)
∫
−
x
sin
(
nx
)
dx
derivative of 1/x ln(x)
d
dx
(
1
x
ln
(
x
)
)
y^{''}-6y^'+9y=3xe^{3x}
y
′
′
−
6
y
′
+
9
y
=
3
xe
3
x
integral of (cos(3x))
∫
(
cos
(
3
x
)
)
dx
(\partial)/(\partial x)(2x-x^2y+xy^2)
∂
∂
x
(
2
x
−
x
2
y
+
xy
2
)
integral of 5cos^2(x)sin(2x)
∫
5
cos
2
(
x
)
sin
(
2
x
)
dx
derivative of sin(9)
d
dx
(
sin
(
9
)
)
limit as x approaches 0 of e^{xsin(1/x)}
lim
x
→
0
(
e
x
sin
(
1
x
)
)
derivative y=3
derivative
y
=
3
integral of 1/(sqrt(1-y^2))
∫
1
√
1
−
y
2
dy
derivative f(x)=x^{4x}
derivative
f
(
x
)
=
x
4
x
derivative e^{-3x}+e^{2x}
derivative
e
−
3
x
+
e
2
x
integral of (8-128x)/(sqrt(49-64x^2))
∫
8
−
1
2
8
x
√
4
9
−
6
4
x
2
dx
(\partial)/(\partial x)(3x^3+4x^2y-3y^3)
∂
∂
x
(
3
x
3
+
4
x
2
y
−
3
y
3
)
limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x
lim
x
→
0
(
3
√
8
+
x
−
3
√
8
x
)
integral of (x+5)/(x^2+10x+26)
∫
x
+
5
x
2
+
1
0
x
+
2
6
dx
(dy)/(dt)=3t^2cos(t^3)
dy
dt
=
3
t
2
cos
(
t
3
)
derivative x^{-x}
derivative
x
−
x
derivative of 5x^2cos(xcot(x))
d
dx
(
5
x
2
cos
(
x
)
cot
(
x
)
)
laplace변환 3e^{-t}
laplacetransform
3
e
−
t
limit as s approaches 2/3 of 3s(2s-1)
lim
s
→
2
3
(
3
s
(
2
s
−
1
)
)
integral of 9/(64+4r^2)
∫
9
6
4
+
4
r
2
dr
derivative of 9x^3-7x
d
dx
(
9
x
3
−
7
x
)
derivative of (x^3+3^5)
d
dx
(
(
x
3
+
3
)
5
)
integral of 1/((x+4)sqrt(x^2+8x+12))
∫
1
(
x
+
4
)
√
x
2
+
8
x
+
1
2
dx
derivative of (x^4/2)
d
dx
(
x
4
2
)
integral from-1 to 4 of (x+3)
∫
−
1
4
(
x
+
3
)
dx
derivative of-7e^x
d
dx
(
−
7
e
x
)
d/(ds)(6/((s-2)^2+36))
d
ds
(
6
(
s
−
2
)
2
+
3
6
)
integral of 1/(x^5+x^4+2x^3+2x^2+x+1)
∫
1
x
5
+
x
4
+
2
x
3
+
2
x
2
+
x
+
1
dx
laplace변환 2cos(t-pi/6)
laplacetransform
2
cos
(
t
−
π
6
)
integral from 0 to infinity of e^{-y}
∫
0
∞
e
−
y
dy
integral of 7x+8y^2
∫
7
x
+
8
y
2
dx
integral of 1/((x-5)^2(x+3))
∫
1
(
x
−
5
)
2
(
x
+
3
)
dx
x(dy)/(dx)+y=4x+1
x
dy
dx
+
y
=
4
x
+
1
tangent f(x)= 3/x ,\at x=3
tangent
f
(
x
)
=
3
x
,
at
x
=
3
derivative of (3x-3/(2sqrt(x)))
d
dx
(
3
x
−
3
2
√
x
)
(dy)/(dx)= 3/(1+x)
dy
dx
=
3
1
+
x
f(x)=3cos(2x)
f
(
x
)
=
3
cos
(
2
x
)
(\partial)/(\partial x)(sin(x)-cos(y))
∂
∂
x
(
sin
(
x
)
−
cos
(
y
)
)
derivative of arctanh(sqrt(x))
d
dx
(
arctanh
(
√
x
)
)
테일러 1/(sqrt(3-2x)),1
taylor
1
√
3
−
2
x
,
1
sum from k=0 to infinity of x^k
∑
k
=
0
∞
x
k
derivative f(x)=x^2-3x
derivative
f
(
x
)
=
x
2
−
3
x
inverse라플라스 1/(s+2)
inverselaplace
1
s
+
2
tangent 1/(3+2x)
tangent
1
3
+
2
x
테일러 1/(sqrt(1-x)),0
taylor
1
√
1
−
x
,
0
limit as x approaches 0+of ln^2(x)
lim
x
→
0
+
(
ln
2
(
x
)
)
limit as x approaches 2 of (x+6)/(x^2)
lim
x
→
2
(
x
+
6
x
2
)
limit as x approaches 0.9 of x^2+3x+2
lim
x
→
0
.
9
(
x
2
+
3
x
+
2
)
(\partial)/(\partial x)(-aksin(kx-wt))
∂
∂
x
(
−
ak
sin
(
kx
−
wt
)
)
derivative f(x)=e^{-2.5x^2}
derivative
f
(
x
)
=
e
−
2
.
5
x
2
sum from n=1 to infinity}(-1)^{n-1 of (7/(9^n-1))
∑
n
=
1
∞
(
−
1
)
n
−
1
(
7
9
n
−
1
)
derivative of (x^4+9/(x^2))
d
dx
(
x
4
+
9
x
2
)
derivative sin(e^x)
derivative
sin
(
e
x
)
derivative of \sqrt[3]{8/x}
d
dx
(
3
√
8
x
)
integral from 0 to 3 of 1/(sqrt(x^2+9))
∫
0
3
1
√
x
2
+
9
dx
xy^'+2y=3
xy
′
+
2
y
=
3
derivative of x/(x^2+6)
d
dx
(
x
x
2
+
6
)
laplace변환 (8t)/(24)-t^5
laplacetransform
8
t
2
4
−
t
5
(\partial)/(\partial x)(sin^2(x-5y))
∂
∂
x
(
sin
2
(
x
−
5
y
)
)
d/(dh)((pih^2)/3 (3sqrt(6)-h))
d
dh
(
π
h
2
3
(
3
√
6
−
h
)
)
x^3y^'+2x^2y=-2cos(3x)y^{-1/2}
x
3
y
′
+
2
x
2
y
=
−
2
cos
(
3
x
)
y
−
1
2
integral of (sin(x))/(1-2cos(x))
∫
sin
(
x
)
1
−
2
cos
(
x
)
dx
integral of e^xcos(9x)
∫
e
x
cos
(
9
x
)
dx
(\partial)/(\partial x)(5x^4+y^8)
∂
∂
x
(
5
x
4
+
y
8
)
derivative of ((3x+512/(x+1))^{2/3})
d
dx
(
(
3
x
+
5
1
2
x
+
1
)
2
3
)
yy^'= x/(x^2+1),y(0)=-2
yy
′
=
x
x
2
+
1
,
y
(
0
)
=
−
2
(dy)/(dx)-y/(3x)+x/(3y)=0
dy
dx
−
y
3
x
+
x
3
y
=
0
integral of xsin^2(6x)
∫
x
sin
2
(
6
x
)
dx
derivative of 4x^3-46x^2+120x
d
dx
(
4
x
3
−
4
6
x
2
+
1
2
0
x
)
integral of 1/x
∫
1
x
dx
integral of sin(5x)cos(x)
∫
sin
(
5
x
)
cos
(
x
)
dx
integral of (x^3-x^2+2x-6)/x
∫
x
3
−
x
2
+
2
x
−
6
x
dx
지역 4x+7,2x+29,6,16
area
4
x
+
7
,
2
x
+
2
9
,
6
,
1
6
limit as x approaches-4 of (1-x)^3
lim
x
→
−
4
(
(
1
−
x
)
3
)
sum from n=1 to infinity of (x+5)^n
∑
n
=
1
∞
(
x
+
5
)
n
derivative y=(x^4+1)^4
derivative
y
=
(
x
4
+
1
)
4
1
..
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1210
..
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