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일반적인 미적분학 문제
경사지 (2,3),(1,3)
slope
(
2
,
3
)
,
(
1
,
3
)
sum from n=6 to infinity of n^2-16
∑
n
=
6
∞
n
2
−
1
6
지역 2x+y=4,y=x,y=0
area
2
x
+
y
=
4
,
y
=
x
,
y
=
0
integral of 7e^{4x+e^{4x}}
∫
7
e
4
x
+
e
4
x
dx
d/(ds)(((s-3)(s-5))/((s+1)(s+2)))
d
ds
(
(
s
−
3
)
(
s
−
5
)
(
s
+
1
)
(
s
+
2
)
)
d/(dt)(3-2t)
d
dt
(
3
−
2
t
)
derivative (1-x^2+x^4)/(x^2*sqrt(x))
derivative
1
−
x
2
+
x
4
x
2
·
√
x
limit as x approaches 0 of 0/0
lim
x
→
0
(
0
0
)
derivative f(t)=(4t^2-8t+7)^{3/2}
derivative
f
(
t
)
=
(
4
t
2
−
8
t
+
7
)
3
2
integral of (2x^2+x-1)/(2x^3+x^2-5x+2)
∫
2
x
2
+
x
−
1
2
x
3
+
x
2
−
5
x
+
2
dx
integral of (x-1)/(x^2-4)
∫
x
−
1
x
2
−
4
dx
integral of 9/(x^2-16)
∫
9
x
2
−
1
6
dx
limit as x approaches 2-of x^3
lim
x
→
2
−
(
x
3
)
integral of 3/(5+3x)
∫
3
5
+
3
x
dx
y^{''}+36y=0,y(0)=1,y^'(0)=0
y
′
′
+
3
6
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
derivative f(x)=4x
derivative
f
(
x
)
=
4
x
derivative of (x^3/(x^3+1))
d
dx
(
x
3
x
3
+
1
)
limit as x approaches 0 of 4x^2-2x+3
lim
x
→
0
(
4
x
2
−
2
x
+
3
)
integral of x/(10^x)
∫
x
1
0
x
dx
지역 10-7x,x^2-20,0
area
1
0
−
7
x
,
x
2
−
2
0
,
0
derivative of x^6{f}(x)
d
dx
(
x
6
f
(
x
)
)
f(u)=ln(u)
f
(
u
)
=
ln
(
u
)
integral from 0 to 1 of (-12e^x)
∫
0
1
(
−
1
2
e
x
)
dx
limit as x approaches infinity of (-1)/x
lim
x
→
∞
(
−
1
x
)
derivative of x^9{f}(x)
d
dx
(
x
9
f
(
x
)
)
derivative of ce^{x/6}
d
dx
(
ce
x
6
)
integral of 4x^2-sin(x)+C
∫
4
x
2
−
sin
(
x
)
+
Cdx
integral of 1/(x^3)+x
∫
1
x
3
+
xdx
derivative (x-3)/2
derivative
x
−
3
2
(\partial)/(\partial x)(x^3yz^2+7yz)
∂
∂
x
(
x
3
yz
2
+
7
yz
)
derivative of x^2e^{x+3}
d
dx
(
x
2
e
x
+
3
)
y^{''}-2y^'+y=1
y
′
′
−
2
y
′
+
y
=
1
(dy)/(dx)=(x^2+y^2)/(yx)
dy
dx
=
x
2
+
y
2
yx
derivative ln(x+9)
derivative
ln
(
x
+
9
)
limit as t approaches 0 of e^{-3t}
lim
t
→
0
(
e
−
3
t
)
inverse라플라스 3/(s^2-4)
inverselaplace
3
s
2
−
4
derivative of ax^2e^{4x}
d
dx
(
ax
2
e
4
x
)
지역 y=x,y=(6.75x)/(x^2+1)
area
y
=
x
,
y
=
6
.
7
5
x
x
2
+
1
derivative f(x)=(x+2)e^{-x}
derivative
f
(
x
)
=
(
x
+
2
)
e
−
x
integral of x/(sqrt(27+x^2))
∫
x
√
2
7
+
x
2
dx
d/(dt)(2te^t)
d
dt
(
2
te
t
)
derivative of x(x+1^2)
d
dx
(
x
(
x
+
1
)
2
)
derivative (3x-1)^2(x^2+1)^2
derivative
(
3
x
−
1
)
2
(
x
2
+
1
)
2
y^'-y=9t
y
′
−
y
=
9
t
integral of sec^6(3y)tan^2(3y)
∫
sec
6
(
3
y
)
tan
2
(
3
y
)
dy
(\partial)/(\partial x)((2x)(3z))
∂
∂
x
(
(
2
x
)
(
3
z
)
)
(dy)/(dx)=6y
dy
dx
=
6
y
integral of (cos(x))^2-(sin(x))^2
∫
(
cos
(
x
)
)
2
−
(
sin
(
x
)
)
2
dx
derivative of (2x-1/(x^2))
d
dx
(
2
x
−
1
x
2
)
integral of 8x+9
∫
8
x
+
9
dx
integral of e^θcos(2θ)
∫
e
θ
cos
(
2
θ
)
d
θ
(d^2)/(dx^2)((1+1/x)^3)
d
2
dx
2
(
(
1
+
1
x
)
3
)
tangent f(x)=x^2+2,(-3,11)
tangent
f
(
x
)
=
x
2
+
2
,
(
−
3
,
1
1
)
(\partial)/(\partial x)(xe^y+ye^z+ze^x)
∂
∂
x
(
xe
y
+
ye
z
+
ze
x
)
y(1+x^2)y^'-x(1+y^2)=0
y
(
1
+
x
2
)
y
′
−
x
(
1
+
y
2
)
=
0
derivative y=12
derivative
y
=
1
2
limit as x approaches 0 of 2x-7
lim
x
→
0
(
2
x
−
7
)
(\partial)/(\partial x)(3-x^4+2x^2-y^2)
∂
∂
x
(
3
−
x
4
+
2
x
2
−
y
2
)
integral from-pi/6 to 0 of 2sec^3(x)
∫
−
π
6
0
2
sec
3
(
x
)
dx
(\partial)/(\partial y)(x^ay^bz^c)
∂
∂
y
(
x
a
y
b
z
c
)
derivative f(x)= 3/(x^2+3)
derivative
f
(
x
)
=
3
x
2
+
3
테일러 (e^x-e^{-x})/2
taylor
e
x
−
e
−
x
2
derivative of ln(e^{3x^2}*4^{5x})
d
dx
(
ln
(
e
3
x
2
·
4
5
x
)
)
(\partial)/(\partial x)((1+xy)^{3/2})
∂
∂
x
(
(
1
+
xy
)
3
2
)
limit as x approaches infinity of e^{-4x}cos(4x)
lim
x
→
∞
(
e
−
4
x
cos
(
4
x
)
)
integral from 0 to 10 of x-5
∫
0
1
0
x
−
5
dx
(\partial)/(\partial x)(-x+345sqrt(x+10000))
∂
∂
x
(
−
x
+
3
4
5
√
x
+
1
0
0
0
0
)
(\partial)/(\partial y)(ye^{x/y})
∂
∂
y
(
ye
x
y
)
(\partial)/(\partial x)(2yarctan(x))
∂
∂
x
(
2
y
arctan
(
x
)
)
y^{''}+10y^'+61y=0
y
′
′
+
1
0
y
′
+
6
1
y
=
0
derivative of (x+2x^2/(1+x^2))
d
dx
(
x
+
2
x
2
1
+
x
2
)
limit as x approaches 4-of 3/(sqrt(x)-2)
lim
x
→
4
−
(
3
√
x
−
2
)
integral of (sqrt(x)+1/(5sqrt(x)))
∫
(
√
x
+
1
5
√
x
)
dx
지역 y= 1/(12x^2),y=x,y= x/(18)
area
y
=
1
1
2
x
2
,
y
=
x
,
y
=
x
1
8
integral of (3x^5-6x^2+2x-5)/(x^3)
∫
3
x
5
−
6
x
2
+
2
x
−
5
x
3
dx
sum from n=0 to infinity of e^{4n}
∑
n
=
0
∞
e
4
n
integral from 2 to-1 of 3^x
∫
2
−
1
3
x
dx
sum from n=2 to infinity of 1/(n^{3/2)}
∑
n
=
2
∞
1
n
3
2
integral of ((x^2))/(((x-1)(x^2+2x+1)))
∫
(
x
2
)
(
(
x
−
1
)
(
x
2
+
2
x
+
1
)
)
dx
derivative of 1/(cos(sqrt(x)))
d
dx
(
1
cos
(
√
x
)
)
inverse라플라스 (s+1)/((s+2)(s+3))
inverselaplace
s
+
1
(
s
+
2
)
(
s
+
3
)
limit as x approaches 0+of ln(7/(x^2))
lim
x
→
0
+
(
ln
(
7
x
2
)
)
sum from n=1 to infinity of (3/8)^{1-n}
∑
n
=
1
∞
(
3
8
)
1
−
n
limit as x approaches 1 of e^{6x^4-6x}
lim
x
→
1
(
e
6
x
4
−
6
x
)
f^'(x)=2^x
f
′
(
x
)
=
2
x
integral of (x^{2/3})
∫
(
x
2
3
)
dx
limit as x approaches 0 of ln(x)x
lim
x
→
0
(
ln
(
x
)
x
)
(\partial)/(\partial x)(x^2y^3+6xyz-2yz)
∂
∂
x
(
x
2
y
3
+
6
xyz
−
2
yz
)
integral of 1/(1+sin^2(x))
∫
1
1
+
sin
2
(
x
)
dx
(\partial)/(\partial x)(7xe^{x^2}+y^2)
∂
∂
x
(
7
xe
x
2
+
y
2
)
integral of (23)/((x^2-1)^2)
∫
2
3
(
x
2
−
1
)
2
dx
sum from n=1 to infinity of (n-1)/(5n-1)
∑
n
=
1
∞
n
−
1
5
n
−
1
(x^2+2y^')y^{''}+2xy^'=0
(
x
2
+
2
y
′
)
y
′
′
+
2
xy
′
=
0
derivative of (3+8x/(5-6x))
d
dx
(
3
+
8
x
5
−
6
x
)
integral of (4/(sqrt(x)))
∫
(
4
√
x
)
dx
limit as x approaches 1+of (ln(x))^{x-1}
lim
x
→
1
+
(
(
ln
(
x
)
)
x
−
1
)
derivative of 8x^3-108x^2+480x
d
dx
(
8
x
3
−
1
0
8
x
2
+
4
8
0
x
)
limit as x approaches 0 of (0.5)^x
lim
x
→
0
(
(
0
.
5
)
x
)
y'=y^2
y
′
=
y
2
integral of (x(x-1))/(sqrt(1-x)\sqrt{2-x)}
∫
x
(
x
−
1
)
√
1
−
x
√
2
−
x
dx
1
..
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1200
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