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일반적인 미적분학 문제
(\partial)/(\partial x)(x+3xy^2+x^2y)
∂
∂
x
(
x
+
3
xy
2
+
x
2
y
)
inverse라플라스 1/(s(s+1)^3)
inverselaplace
1
s
(
s
+
1
)
3
derivative (x^3)/(x-1)
derivative
x
3
x
−
1
integral from 0 to 1 of (21)/(x^5)
∫
0
1
2
1
x
5
dx
y^{''}+y^'+5y=0
y
′
′
+
y
′
+
5
y
=
0
integral from-1 to 1 of (x-1)
∫
−
1
1
(
x
−
1
)
dx
integral of-8xcos(3x)
∫
−
8
x
cos
(
3
x
)
dx
integral of e^{-θ}cos(9θ)
∫
e
−
θ
cos
(
9
θ
)
d
θ
maclaurin (4x^2)e^{-10x}
maclaurin
(
4
x
2
)
e
−
1
0
x
limit as x approaches pi/2 of (tan(x)-sec(x))/(cos(x))
lim
x
→
π
2
(
tan
(
x
)
−
sec
(
x
)
cos
(
x
)
)
limit as x approaches 0 of 7csc(x)-7/x
lim
x
→
0
(
7
csc
(
x
)
−
7
x
)
y^{''}-(4/x)y^'-(8/(x^2))y=0
y
′
′
−
(
4
x
)
y
′
−
(
8
x
2
)
y
=
0
integral of x(4-2x^2)
∫
x
(
4
−
2
x
2
)
dx
derivative y= 6/(x^4)-4/(x^2)-3/x
derivative
y
=
6
x
4
−
4
x
2
−
3
x
(\partial)/(\partial x)(x^2e^{y/x})
∂
∂
x
(
x
2
e
y
x
)
integral of 9x^2-4x+1
∫
9
x
2
−
4
x
+
1
dx
integral of pie^x
∫
π
e
x
dx
(\partial)/(\partial u)(sin(u)sin(v))
∂
∂
u
(
sin
(
u
)
sin
(
v
)
)
(d^2)/(dx^2)(8e^x)
d
2
dx
2
(
8
e
x
)
integral from 0 to 2 of xe^{-3x}
∫
0
2
xe
−
3
x
dx
integral of 1/(1-x^2)*ln((1+x)/(1-x))
∫
1
1
−
x
2
·
ln
(
1
+
x
1
−
x
)
dx
tangent f(x)=5x^2,\at x=1
tangent
f
(
x
)
=
5
x
2
,
at
x
=
1
(dy)/(dx)=4(y^2+1)
dy
dx
=
4
(
y
2
+
1
)
maclaurin 1/(4z-5)
maclaurin
1
4
z
−
5
tangent y=(x^2-35)^6,\at x=6
tangent
y
=
(
x
2
−
3
5
)
6
,
at
x
=
6
derivative f(x)= x/(x^2-2)
derivative
f
(
x
)
=
x
x
2
−
2
derivative 3x*y
derivative
3
x
·
y
derivative f(x)=2x^3
derivative
f
(
x
)
=
2
x
3
integral from 0 to pi/4 of 5tan^3(x)
∫
0
π
4
5
tan
3
(
x
)
dx
ty^'+2y=t^2-t+1,y(1)= 1/2
ty
′
+
2
y
=
t
2
−
t
+
1
,
y
(
1
)
=
1
2
tangent f(x)=(x^3+2)(3x^2-4x+2),(1,3)
tangent
f
(
x
)
=
(
x
3
+
2
)
(
3
x
2
−
4
x
+
2
)
,
(
1
,
3
)
integral of (3x^2+3x+1)/(x^3+2x^2+2x+1)
∫
3
x
2
+
3
x
+
1
x
3
+
2
x
2
+
2
x
+
1
dx
경사지 (1,2),(5,-3)
slope
(
1
,
2
)
,
(
5
,
−
3
)
tangent y= 1/(x+1)
tangent
y
=
1
x
+
1
integral of (7x^2)/(sqrt(x^2-4))
∫
7
x
2
√
x
2
−
4
dx
integral of x^2+xy^2+z
∫
x
2
+
xy
2
+
zdx
derivative 4/(x-5)
derivative
4
x
−
5
(\partial)/(\partial x)(x/(y+2z))
∂
∂
x
(
x
y
+
2
z
)
integral of e^{-y/2}
∫
e
−
y
2
dy
derivative sin(x)+5pix
derivative
sin
(
x
)
+
5
π
x
derivative 1/8 (e^{4x}+e^{-4x})
derivative
1
8
(
e
4
x
+
e
−
4
x
)
integral of xsqrt(4x^2+5)
∫
x
√
4
x
2
+
5
dx
integral from-pi to pi of xsin(nx)
∫
−
π
π
x
sin
(
nx
)
dx
derivative of (x+1/(sqrt({f)(x)+4)})
d
dx
(
x
+
1
√
f
(
x
)
+
4
)
integral of (1/(x^5)-x^5-1/4)
∫
(
1
x
5
−
x
5
−
1
4
)
dx
integral of 2ye^{-y^2}
∫
2
ye
−
y
2
dy
inverse라플라스 1/(s^2)e^{-s}
inverselaplace
1
s
2
e
−
s
limit as x approaches 2 of 2x+1
lim
x
→
2
(
2
x
+
1
)
(\partial)/(\partial y)(2^x+2^y)
∂
∂
y
(
2
x
+
2
y
)
limit as x approaches 2 of (x-3)/(x^2-9)
lim
x
→
2
(
x
−
3
x
2
−
9
)
d/(d{x)}((e^{{x}})/(e^{{x)}+e^{{y}}+e^{{z}}})
d
d
x
(
e
x
e
x
+
e
y
+
e
z
)
(dy)/(dx)=3x^7y-y,y(1)=-9
dy
dx
=
3
x
7
y
−
y
,
y
(
1
)
=
−
9
y^{''}+4y^'+4y=3e^{-2x}
y
′
′
+
4
y
′
+
4
y
=
3
e
−
2
x
integral of tan(ax)
∫
tan
(
ax
)
dx
derivative of e^{sec(x})
d
dx
(
e
sec
(
x
)
)
integral of (6x^3+4x^2-45x-33)/(x^2-9)
∫
6
x
3
+
4
x
2
−
4
5
x
−
3
3
x
2
−
9
dx
지역 sqrt(x+7),0.5(x+7)
area
√
x
+
7
,
0
.
5
(
x
+
7
)
integral from 1 to 3 of (4x-x^2)
∫
1
3
(
4
x
−
x
2
)
dx
integral of 1/(sqrt(x^2+2x+122))
∫
1
√
x
2
+
2
x
+
1
2
2
dx
최소공배수 (csc^2(x))/4 ,4sin^2(x)
lcm
csc
2
(
x
)
4
,
4
sin
2
(
x
)
integral of x^{5/2}
∫
x
5
2
dx
maclaurin ((e^x-e^{-x}))/2
maclaurin
(
e
x
−
e
−
x
)
2
tangent 4/(sqrt(x))
tangent
4
√
x
tangent y=sqrt(x),\at x=81
tangent
y
=
√
x
,
at
x
=
8
1
f^'(x)=xsqrt(7-x^2)
f
′
(
x
)
=
x
√
7
−
x
2
limit as x approaches 3 of 77
lim
x
→
3
(
7
7
)
integral of (e^5)/(e^x)
∫
e
5
e
x
dx
integral of ((cos(x)+sin(x)))/(sin(2x))
∫
(
cos
(
x
)
+
sin
(
x
)
)
sin
(
2
x
)
dx
derivative of Cxe^x
d
dx
(
Cxe
x
)
integral from 0 to 1 of 6
∫
0
1
6
(\partial)/(\partial x)(xz-5x^2y^3z^4)
∂
∂
x
(
xz
−
5
x
2
y
3
z
4
)
(\partial)/(\partial x)((3x-2y)/(x^2+3y))
∂
∂
x
(
3
x
−
2
y
x
2
+
3
y
)
integral of (cos(x))/(sin^2(x)-36)
∫
cos
(
x
)
sin
2
(
x
)
−
3
6
dx
y^{''}+2y^'+122y=0
y
′
′
+
2
y
′
+
1
2
2
y
=
0
(\partial)/(\partial x)(sin(-e^y))
∂
∂
x
(
sin
(
−
e
y
)
)
derivative of cos((3x/2))
d
dx
(
cos
(
3
x
2
)
)
derivative of sqrt(9x^2+9)
d
dx
(
√
9
x
2
+
9
)
integral of sec^4(5x)
∫
sec
4
(
5
x
)
dx
tangent f(x)=2^x,\at x=0
tangent
f
(
x
)
=
2
x
,
at
x
=
0
integral of 1/(sqrt(9+x^2))
∫
1
√
9
+
x
2
dx
derivative y=(-5)/(\sqrt[3]{x)}
derivative
y
=
−
5
3
√
x
tangent f(x)=2x^2-4x-5,\at x=2
tangent
f
(
x
)
=
2
x
2
−
4
x
−
5
,
at
x
=
2
integral of sin(e^x)e^x
∫
sin
(
e
x
)
e
x
dx
(dy)/(dx)=(3y^2+10x^2)/(xy)
dy
dx
=
3
y
2
+
1
0
x
2
xy
derivative of 7x-5
d
dx
(
7
x
−
5
)
integral from 0 to 4 of x^{3/2}
∫
0
4
x
3
2
dx
integral from 1 to 5 of 5/x-3/(x^2)
∫
1
5
5
x
−
3
x
2
dx
limit as x approaches-2 of-x^2+8x-7
lim
x
→
−
2
(
−
x
2
+
8
x
−
7
)
integral from c to x of g(x)
∫
c
x
g
(
x
)
dx
integral from 2 to 4 of (x^3-6x^2+8x)
∫
2
4
(
x
3
−
6
x
2
+
8
x
)
dx
integral from 0 to 1 of sqrt(x)
∫
0
1
√
x
dx
tangent y=x^2+3x
tangent
y
=
x
2
+
3
x
테일러 e^{3x},1
taylor
e
3
x
,
1
derivative arctan(1/x)
derivative
arctan
(
1
x
)
derivative f(x)=(x^3-x^2-1)/(x^2)
derivative
f
(
x
)
=
x
3
−
x
2
−
1
x
2
limit as x approaches-2 of 2+x
lim
x
→
−
2
(
2
+
x
)
limit as x approaches 0 of (x-1)/x
lim
x
→
0
(
x
−
1
x
)
integral of 4/(x^2-x-6)
∫
4
x
2
−
x
−
6
dx
integral of sqrt(2x+2)
∫
√
2
x
+
2
dx
derivative sqrt(6+\sqrt{5x)}
derivative
√
6
+
√
5
x
1
..
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