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일반적인 미적분학 문제
xyy^'=x^2+1
xyy
′
=
x
2
+
1
integral of 4xln(x)
∫
4
x
ln
(
x
)
dx
tangent x^2-xy+y^2=3,(1,2)
tangent
x
2
−
xy
+
y
2
=
3
,
(
1
,
2
)
derivative (4x^5+5)/(x^3)
derivative
4
x
5
+
5
x
3
y^'=xy^2
y
′
=
xy
2
derivative of e^xsin(xcos(x))
d
dx
(
e
x
sin
(
x
)
cos
(
x
)
)
derivative of 1/x+1/y
d
dx
(
1
x
+
1
y
)
y^{''}+(y^')^2=0
y
′
′
+
(
y
′
)
2
=
0
지역 7cos(7x),7-7cos(7x),[0, pi/7 ]
area
7
cos
(
7
x
)
,
7
−
7
cos
(
7
x
)
,
[
0
,
π
7
]
5ysqrt(x^2+1)(dy)/(dx)+4x=0
5
y
√
x
2
+
1
dy
dx
+
4
x
=
0
derivative of 1/((3x+1^2))
d
dx
(
1
(
3
x
+
1
)
2
)
derivative y=ln((x^2)/4)
derivative
y
=
ln
(
x
2
4
)
derivative of (2x^3-2/(3x+4))
d
dx
(
2
x
3
−
2
3
x
+
4
)
limit as x approaches-8 of (x^2-3)/(8-x)
lim
x
→
−
8
(
x
2
−
3
8
−
x
)
f^'(x)=(3x^5-2)^{20}
f
′
(
x
)
=
(
3
x
5
−
2
)
2
0
integral of 8/(1-cos(2x))
∫
8
1
−
cos
(
2
x
)
dx
integral of (sin(2x))/4
∫
sin
(
2
x
)
4
dx
integral of 1/(x^{4/3)}
∫
1
x
4
3
dx
(\partial)/(\partial y)(x^2-y^3-x^2y+y)
∂
∂
y
(
x
2
−
y
3
−
x
2
y
+
y
)
integral from 1 to R of (ln(4x))/(x^2)
∫
1
R
ln
(
4
x
)
x
2
dx
integral of e/pi
∫
e
π
dx
(\partial)/(\partial x)(x^2e^{sqrt(4xy)})
∂
∂
x
(
x
2
e
√
4
xy
)
derivative (e^x)/(x^n)
derivative
e
x
x
n
derivative In(x^2)
derivative
In
(
x
2
)
derivative of (90/(6+9e^{-0.025x)})
d
dx
(
9
0
6
+
9
e
−
0
.
0
2
5
x
)
(dy)/(dt)=(1-ty^2)/(2t^2y)
dy
dt
=
1
−
ty
2
2
t
2
y
integral of 2cos(t)
∫
2
cos
(
t
)
dt
limit as x approaches 2 of (x+1)/(x-2)
lim
x
→
2
(
x
+
1
x
−
2
)
integral of ((7-x))/(x^2-4x+4)
∫
(
7
−
x
)
x
2
−
4
x
+
4
dx
tangent y=3x+6cos(x),(0,6)
tangent
y
=
3
x
+
6
cos
(
x
)
,
(
0
,
6
)
integral of 1/(2-x^{1/5)}
∫
1
2
−
x
1
5
dx
f(x)=(x+xe^x)/(x^2-5)
f
(
x
)
=
x
+
xe
x
x
2
−
5
derivative of \sqrt[3]{1+tan(x^2})
d
dx
(
3
√
1
+
tan
(
x
2
)
)
derivative x(3-x)^3
derivative
x
(
3
−
x
)
3
derivative f(x)=x^2cos(1/x)
derivative
f
(
x
)
=
x
2
cos
(
1
x
)
derivative y=(sqrt(x)+1)/(sqrt(x)-1)
derivative
y
=
√
x
+
1
√
x
−
1
sum from n=2 to infinity of 1/(nln(n))
∑
n
=
2
∞
1
n
ln
(
n
)
limit as x approaches 0 of (4cos(x)-4)/x
lim
x
→
0
(
4
cos
(
x
)
−
4
x
)
(\partial)/(\partial x)(6xyz)
∂
∂
x
(
6
xyz
)
derivative of-,x
d
dx
(
−
,
x
)
경사지 (-8,-9),(-5,-3)
slope
(
−
8
,
−
9
)
,
(
−
5
,
−
3
)
integral of ln(x)y
∫
ln
(
x
)
ydx
integral of xe^{7x^2}
∫
xe
7
x
2
dx
derivative of xsqrt(81-x^2)
d
dx
(
x
√
8
1
−
x
2
)
derivative of arctan^2((x+y/(1-xy)))
d
dx
(
arctan
2
(
x
+
y
1
−
xy
)
)
integral of (x^2e^{-x}+sin(2x))
∫
(
x
2
e
−
x
+
sin
(
2
x
)
)
dx
integral from 1 to 4 of (ln(x))/(x^2)
∫
1
4
ln
(
x
)
x
2
dx
limit as x approaches 0 of cos(3/x)
lim
x
→
0
(
cos
(
3
x
)
)
limit as x approaches 0 of x^{7sin(x)}
lim
x
→
0
(
x
7
sin
(
x
)
)
integral of (x^2-x+1)/(x^2+x)
∫
x
2
−
x
+
1
x
2
+
x
dx
inverse라플라스 (1/s)/(s^2+2s+3)
inverselaplace
1
s
s
2
+
2
s
+
3
limit as x approaches+(-35) of 34+x
lim
x
→
+
(
−
3
5
)
(
3
4
+
x
)
integral from-infinity to 10 of re^{r/5}
∫
−
∞
1
0
re
r
5
dr
limit as x approaches infinity of 2^{+x}
lim
x
→
∞
(
2
+
x
)
integral of xln(sqrt(x))
∫
x
ln
(
√
x
)
dx
derivative of (2-x^2^{1/2})
d
dx
(
(
2
−
x
2
)
1
2
)
integral of (tan(x))^5
∫
(
tan
(
x
)
)
5
dx
derivative of ln(1+x^3)
d
dx
(
ln
(
1
+
x
3
)
)
tangent y=x^3-2x+1,(0,1)
tangent
y
=
x
3
−
2
x
+
1
,
(
0
,
1
)
integral of x/((x^2+1)^{3/2)}
∫
x
(
x
2
+
1
)
3
2
dx
integral from 1 to 2 of (15)/(x^3+4x)
∫
1
2
1
5
x
3
+
4
x
dx
sum from n=1 to infinity}n^{50 of e^{-n}
∑
n
=
1
∞
n
5
0
e
−
n
(\partial)/(\partial y)((x+4y+3z)^{3/2})
∂
∂
y
(
(
x
+
4
y
+
3
z
)
3
2
)
limit as x approaches-1 of |x+1|
lim
x
→
−
1
(
|
x
+
1
|
)
integral of (x-10)^2
∫
(
x
−
1
0
)
2
dx
limit as x approaches-8 of (2x)/(x+8)
lim
x
→
−
8
(
2
x
x
+
8
)
y^{''}-6y^'+9y=18x^2+6-12e^{3x}
y
′
′
−
6
y
′
+
9
y
=
1
8
x
2
+
6
−
1
2
e
3
x
derivative y=3x+7
derivative
y
=
3
x
+
7
derivative of (x^2-1/(x^4-1))
d
dx
(
x
2
−
1
x
4
−
1
)
derivative-0.05(t+1.1)^{2.2}+0.7t+0.9
derivative
−
0
.
0
5
(
t
+
1
.
1
)
2
.
2
+
0
.
7
t
+
0
.
9
integral of 1/((y-2)(y+2))
∫
1
(
y
−
2
)
(
y
+
2
)
dy
derivative of sqrt(x-\sqrt{x)}
d
dx
(
√
x
−
√
x
)
integral of e^x(3e^x+1)^{-3/2}
∫
e
x
(
3
e
x
+
1
)
−
3
2
dx
integral of zsqrt(z-6)
∫
z
√
z
−
6
dz
y^{''}+(2/x)=0
y
′
′
+
(
2
x
)
=
0
integral from 0 to 3 of x^2ln(x)
∫
0
3
x
2
ln
(
x
)
dx
derivative of (y^2/(b^2))
d
dx
(
y
2
b
2
)
derivative of 20cos(2x-30sin(2x))
d
dx
(
2
0
cos
(
2
x
)
−
3
0
sin
(
2
x
)
)
integral of 8sin(2x)
∫
8
sin
(
2
x
)
dx
(d^2x)/(dt^2)
d
2
x
dt
2
(\partial)/(\partial x)(xe^y-yz)
∂
∂
x
(
xe
y
−
yz
)
integral from 0 to pi/2 of (5cos^2(x))
∫
0
π
2
(
5
cos
2
(
x
)
)
dx
(\partial)/(\partial y)(e^{x+y}sin(x-y))
∂
∂
y
(
e
x
+
y
sin
(
x
−
y
)
)
y^{''}-4y^'+8y=0,y(0)=9,y(pi/4)=7
y
′
′
−
4
y
′
+
8
y
=
0
,
y
(
0
)
=
9
,
y
(
π
4
)
=
7
tangent sqrt(x)(4.2)
tangent
√
x
(
4
.
2
)
derivative of tan(x+c)
d
dx
(
tan
(
x
+
c
)
)
integral of ((x^3+20x^2+8))/(x+20)
∫
(
x
3
+
2
0
x
2
+
8
)
x
+
2
0
dx
integral of 7e^{x^2}
∫
7
e
x
2
dx
integral of x^1e^x
∫
x
1
e
x
dx
integral of (6x+4)
∫
(
6
x
+
4
)
dx
6y^{''}+3y^'=0
6
y
′
′
+
3
y
′
=
0
f(x)= 2/(3x^4)
f
(
x
)
=
2
3
x
4
integral of 1/(sin(x)*cos(x))
∫
1
sin
(
x
)
·
cos
(
x
)
dx
integral from 1 to infinity of 9e^{-3x}
∫
1
∞
9
e
−
3
x
dx
derivative y=5(x^2+2x)^3
derivative
y
=
5
(
x
2
+
2
x
)
3
derivative of-ln(2*2^{-x})
d
dx
(
−
ln
(
2
)
·
2
−
x
)
integral from 0 to 3 of xsqrt(x+1)
∫
0
3
x
√
x
+
1
dx
tangent f(x)=9x-8sqrt(x),\at x=1
tangent
f
(
x
)
=
9
x
−
8
√
x
,
at
x
=
1
d/(dt)(e^{4(e^t-1)})
d
dt
(
e
4
(
e
t
−
1
)
)
derivative of ((4x+asqrt(1+x))/(x^2-1))
d
dx
(
(
4
x
+
a
√
1
+
x
)
x
2
−
1
)
1
..
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1493
1494
1495
1496
..
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