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일반적인 미적분학 문제
경사지 (x^2+y^2)^2=4x^2y,(-1,1)
slope
(
x
2
+
y
2
)
2
=
4
x
2
y
,
(
−
1
,
1
)
limit as x approaches 0 of (x+2)/x
lim
x
→
0
(
x
+
2
x
)
integral of e^x(2x-2)
∫
e
x
(
2
x
−
2
)
dx
derivative of 5/(x+10)
d
dx
(
5
x
+
1
0
)
derivative f(x)=e^{9sqrt(x)}
derivative
f
(
x
)
=
e
9
√
x
derivative of e^{-x}*cos(x)
d
dx
(
e
−
x
·
cos
(
x
)
)
inverse라플라스 1/(s^2+s+2)
inverselaplace
1
s
2
+
s
+
2
sum from n=0 to infinity of ((7-8n))/(4+3n)
∑
n
=
0
∞
(
7
−
8
n
)
4
+
3
n
integral of-6/(x^2)
∫
−
6
x
2
dx
tangent sqrt(5x+1),\at x=7
tangent
√
5
x
+
1
,
at
x
=
7
derivative of (x/(x+1)^x)
d
dx
(
(
x
x
+
1
)
x
)
integral from 4 to 9 of (sqrt(x))
∫
4
9
(
√
x
)
dx
integral of 1/(sqrt(8-4x-4x^2))
∫
1
√
8
−
4
x
−
4
x
2
dx
y^'+2y=3e^t
y
′
+
2
y
=
3
e
t
integral from 0 to 2 of x/(x^2+4)
∫
0
2
x
x
2
+
4
dx
limit as x approaches-3-of 1/(x^2-9)
lim
x
→
−
3
−
(
1
x
2
−
9
)
integral of 1/(4sqrt(x)(6+\sqrt{x))}
∫
1
4
√
x
(
6
+
√
x
)
dx
derivative (2000t)/(4t+75)
derivative
2
0
0
0
t
4
t
+
7
5
(\partial)/(\partial x)(sqrt(x+2))
∂
∂
x
(
√
x
+
2
)
integral of (15e^{5z})/(e^{5z)+2}
∫
1
5
e
5
z
e
5
z
+
2
dz
(\partial)/(\partial t)(x^2ycos(z/t))
∂
∂
t
(
x
2
y
cos
(
z
t
)
)
integral of sec^5(x)tan(x)
∫
sec
5
(
x
)
tan
(
x
)
dx
derivative f(x)=-(13)/(x^6)
derivative
f
(
x
)
=
−
1
3
x
6
integral of 3/(tsqrt(t^2-1))
∫
3
t
√
t
2
−
1
dt
derivative e^{-x^2}
derivative
e
−
x
2
limit as x approaches+0 of x/(x-1)
lim
x
→
+
0
(
x
x
−
1
)
integral from 2 to 4 of (x(2x-3))/6
∫
2
4
x
(
2
x
−
3
)
6
dx
derivative f(x)=log_{10}(x^8+9)
derivative
f
(
x
)
=
log
1
0
(
x
8
+
9
)
derivative e^{sin(x)}
derivative
e
sin
(
x
)
d/(dy)((y^3-8)/(y^3+8))
d
dy
(
y
3
−
8
y
3
+
8
)
integral of e^x(x^2+2x)
∫
e
x
(
x
2
+
2
x
)
dx
(\partial)/(\partial x)(xc^2(1/(sqrt(1-\frac{v^2){c^2)}}-1))
∂
∂
x
(
xc
2
(
1
√
1
−
v
2
c
2
−
1
)
)
integral from 0 to 1 of t/((2-t)^2)
∫
0
1
t
(
2
−
t
)
2
dt
integral of 1/(xsqrt(144x^2-144))
∫
1
x
√
1
4
4
x
2
−
1
4
4
dx
tangent f(x)= 2/(x-4),\at x=6
tangent
f
(
x
)
=
2
x
−
4
,
at
x
=
6
integral of (6x^6+3x^5+5x-4)
∫
(
6
x
6
+
3
x
5
+
5
x
−
4
)
dx
(\partial)/(\partial x)(e^{ix}cos(iy))
∂
∂
x
(
e
ix
cos
(
iy
)
)
integral of ln(x)*1/x
∫
ln
(
x
)
·
1
x
dx
integral of (sqrt(1-x^2)-x)x
∫
(
√
1
−
x
2
−
x
)
xdx
integral of (x^4+x-16)/(x^2+4)
∫
x
4
+
x
−
1
6
x
2
+
4
dx
derivative ln(sqrt((a^2-z^2)/(a^2+z^2)))
derivative
ln
(
√
a
2
−
z
2
a
2
+
z
2
)
derivative y=3(4x^2+4)
derivative
y
=
3
(
4
x
2
+
4
)
(\partial)/(\partial x)(zsqrt(x+y))
∂
∂
x
(
z
√
x
+
y
)
(\partial)/(\partial x)(sqrt((x^2+y^2)))
∂
∂
x
(
√
(
x
2
+
y
2
)
)
derivative of (x^2-7x+13/(x-3))
d
dx
(
x
2
−
7
x
+
1
3
x
−
3
)
y^{''}-2y^'=4t
y
′
′
−
2
y
′
=
4
t
derivative of x/(10)
d
dx
(
x
1
0
)
limit as x approaches 10+of (x^3)/(x-10)
lim
x
→
1
0
+
(
x
3
x
−
1
0
)
integral of 1/(x(1+2ln(x)))
∫
1
x
(
1
+
2
ln
(
x
)
)
dx
limit as x approaches 0 of 2+3e^{1/x}
lim
x
→
0
(
2
+
3
e
1
x
)
(\partial)/(\partial m)(m/v)
∂
∂
m
(
m
v
)
d/(d{x)}(3({x}^2)i+5({y}^3)j+{z}k)
d
d
x
(
3
(
x
2
)
i
+
5
(
y
3
)
j
+
z
k
)
limit as x approaches-5+of 3[x]+4
lim
x
→
−
5
+
(
3
[
x
]
+
4
)
(\partial)/(\partial z)(5ze^{xyz})
∂
∂
z
(
5
ze
xyz
)
integral of csc(a)ycot(a)y
∫
csc
(
a
)
y
cot
(
a
)
ydy
integral of 4/(x(x+2))
∫
4
x
(
x
+
2
)
dx
integral from 0 to 4 of 1/(16+x^2)
∫
0
4
1
1
6
+
x
2
dx
inverse라플라스 1/(2s^2+2)
inverselaplace
1
2
s
2
+
2
integral of (x+1)/(x+3)
∫
x
+
1
x
+
3
dx
(\partial)/(\partial y)(e^x*sin(y))
∂
∂
y
(
e
x
·
sin
(
y
)
)
integral of sin(t)1+cos(t)
∫
sin
(
t
)
1
+
cos
(
t
)
dt
tangent f(x)=(sqrt(x))/(x+5),\at x=4
tangent
f
(
x
)
=
√
x
x
+
5
,
at
x
=
4
경사지 (3,5),(-1,5)
slope
(
3
,
5
)
,
(
−
1
,
5
)
integral from 0 to 4 of xsqrt(x)
∫
0
4
x
√
x
dx
derivative of 4e^xsin(x)
d
dx
(
4
e
x
sin
(
x
)
)
derivative of 2-sqrt(y-x^2)
d
dx
(
2
−
√
y
−
x
2
)
integral of x^2*ln(2x)
∫
x
2
·
ln
(
2
x
)
dx
limit as x approaches 2 of (\sqrt[3]{x}-2)/(x-8)
lim
x
→
2
(
3
√
x
−
2
x
−
8
)
integral from 0 to 1 of 1/(x^{19/18)}
∫
0
1
1
x
1
9
1
8
dx
derivative of e^{x^2}+x^2
d
dx
(
e
x
2
+
x
2
)
integral of 1/(sqrt(-x^2-10x))
∫
1
√
−
x
2
−
1
0
x
dx
derivative y=ln(7x^2+9y^2)
derivative
y
=
ln
(
7
x
2
+
9
y
2
)
integral of ln(1+2x)
∫
ln
(
1
+
2
x
)
dx
integral of (2xy+x^2-1)
∫
(
2
xy
+
x
2
−
1
)
dy
maclaurin 9sin(4x)
maclaurin
9
sin
(
4
x
)
derivative sqrt(w)e^w
derivative
√
w
e
w
(\partial)/(\partial x)((x^{5/7})/(e^x))
∂
∂
x
(
x
5
7
e
x
)
limit as x approaches 0 of 2/(x^2+x)-2/x
lim
x
→
0
(
2
x
2
+
x
−
2
x
)
derivative (3t^2+4t-8)/(t^{3/2)}
derivative
3
t
2
+
4
t
−
8
t
3
2
limit as x approaches 0 of x^3-4x^2+9x-2
lim
x
→
0
(
x
3
−
4
x
2
+
9
x
−
2
)
integral of cos(2x)2x
∫
cos
(
2
x
)
d
2
xdx
y^{''}+25y=0,y(0)=4.6,y^'(0)=-1.2
y
′
′
+
2
5
y
=
0
,
y
(
0
)
=
4
.
6
,
y
′
(
0
)
=
−
1
.
2
integral of x^5cos(x
∫
x
5
cos
(
d
)
xdx
(\partial)/(\partial x)(e^{2xy})
∂
∂
x
(
e
2
xy
)
derivative of 4+8x-5x^2
d
dx
(
4
+
8
x
−
5
x
2
)
integral of 8e^{4y}
∫
8
e
4
y
dy
inverse라플라스 1/((s^2+3))
inverselaplace
1
(
s
2
+
3
)
지역 4-x^2,x
area
4
−
x
2
,
x
-2y^{''}+2y^'=0,y(1)=-2,y^'(-2)=3
−
2
y
′
′
+
2
y
′
=
0
,
y
(
1
)
=
−
2
,
y
′
(
−
2
)
=
3
limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)}
lim
x
→
0
(
x
√
3
+
x
−
√
3
)
integral of ((x-4))/(x^2-5x+6)
∫
(
x
−
4
)
x
2
−
5
x
+
6
dx
integral of x^4e^{1-x^5}
∫
x
4
e
1
−
x
5
dx
tangent 2x^3+3x^2-12x+1
tangent
2
x
3
+
3
x
2
−
1
2
x
+
1
d/(dy)(ye^{xy}cos(2x)-2e^{xy}sin(2x)+2x)
d
dy
(
ye
xy
cos
(
2
x
)
−
2
e
xy
sin
(
2
x
)
+
2
x
)
sum from n=1 to infinity of ((n!)^2)/1
∑
n
=
1
∞
(
n
!
)
2
1
limit as x approaches a of 3sqrt(x^2-6x)
lim
x
→
a
(
3
√
x
2
−
6
x
)
derivative of x^3-x^2-3x+10
d
dx
(
x
3
−
x
2
−
3
x
+
1
0
)
derivative y=arccot(x)
derivative
y
=
arccot
(
x
)
integral from 0 to 6 of (36)/(x^2+36)
∫
0
6
3
6
x
2
+
3
6
dx
derivative of (2^x/(ln(2)))
d
dx
(
2
x
ln
(
2
)
)
1
..
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