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일반적인 미적분학 문제
limit as x approaches 0 of e^x
lim
x
→
0
(
e
x
)
derivative y= 1/(sqrt(x^2+1))
derivative
y
=
1
√
x
2
+
1
integral of-2/(sqrt(9-9x^2))
∫
−
2
√
9
−
9
x
2
dx
integral of 1/((x^2+2x+5)^3)
∫
1
(
x
2
+
2
x
+
5
)
3
dx
derivative sec(tan(x))
derivative
sec
(
tan
(
x
)
)
derivative of (6x^2+2x+2/(sqrt(x)))
d
dx
(
6
x
2
+
2
x
+
2
√
x
)
xy^'+3y=((2e^{4x}))/(x^2)
xy
′
+
3
y
=
(
2
e
4
x
)
x
2
integral of 1/(x^2+3^2)
∫
1
x
2
+
3
2
dx
tangent y=x^3-3x+2,(3,20)
tangent
y
=
x
3
−
3
x
+
2
,
(
3
,
2
0
)
derivative y= 1/((4x^2+3)^5)
derivative
y
=
1
(
4
x
2
+
3
)
5
integral of (2x^3+5x^2-2x+7)
∫
(
2
x
3
+
5
x
2
−
2
x
+
7
)
dx
(\partial)/(\partial y)(xy+ln(x/y))
∂
∂
y
(
xy
+
ln
(
x
y
)
)
integral of sqrt(x^4)
∫
√
x
4
dx
integral of-x^{-2}
∫
−
x
−
2
dx
integral of 1/(8+5x)
∫
1
8
+
5
x
dx
derivative of sin(sqrt(x^2-1))
d
dx
(
sin
(
√
x
2
−
1
)
)
derivative x^{3/2}(x+ce^x)
derivative
x
3
2
(
x
+
ce
x
)
(\partial)/(\partial x)(e^{x/y}(1-x/y))
∂
∂
x
(
e
x
y
(
1
−
x
y
)
)
y^'=(x^2+y^2)/(2xy)
y
′
=
x
2
+
y
2
2
xy
derivative ln(289sin^2(x))
derivative
ln
(
2
8
9
sin
2
(
x
)
)
derivative f(x)=sin^3(2x-3)
derivative
f
(
x
)
=
sin
3
(
2
x
−
3
)
(\partial)/(\partial u(v))((e^v)/(u(v)+v^5))
∂
∂
u
(
v
)
(
e
v
u
(
v
)
+
v
5
)
derivative of x/(sqrt(x^2+4))
d
dx
(
x
√
x
2
+
4
)
limit as x approaches 25 of log_{5}(x)
lim
x
→
2
5
(
log
5
(
x
)
)
derivative of x^5ln(2x)
d
dx
(
x
5
ln
(
2
x
)
)
derivative f(x)=((x^2)/(x-1))^2
derivative
f
(
x
)
=
(
x
2
x
−
1
)
2
integral from 0 to 1 of 1
∫
0
1
1
dx
integral of e^{-4}
∫
e
−
4
normal f(x)=-x^3+4x^2-1,\at x=1
normal
f
(
x
)
=
−
x
3
+
4
x
2
−
1
,
at
x
=
1
derivative of e^{-3x+4}
d
dx
(
e
−
3
x
+
4
)
derivative f(x)=x^{23}+50x^{17}+223
derivative
f
(
x
)
=
x
2
3
+
5
0
x
1
7
+
2
2
3
integral from 1 to infinity of x^{-1/7}
∫
1
∞
x
−
1
7
dx
integral of x/((x^2+2)^2)
∫
x
(
x
2
+
2
)
2
dx
derivative of 0.01x^3-0.45x^2+2.43x+300
d
dx
(
0
.
0
1
x
3
−
0
.
4
5
x
2
+
2
.
4
3
x
+
3
0
0
)
integral from 1 to 2 of 2/x
∫
1
2
2
x
dx
integral of (-2)/x
∫
−
2
x
dx
derivative (15+5sqrt(5))/(12)a^3
derivative
1
5
+
5
√
5
1
2
a
3
(1+x^2)y^{''}=2x(y^')^2
(
1
+
x
2
)
y
′
′
=
2
x
(
y
′
)
2
y^'+(1.93)/(293+t)*y=2.7249
y
′
+
1
.
9
3
2
9
3
+
t
·
y
=
2
.
7
2
4
9
(\partial)/(\partial x)((7x-5y)/(7x+5y))
∂
∂
x
(
7
x
−
5
y
7
x
+
5
y
)
inverse라플라스 ((s+1))/(6s^2+7s+2)
inverselaplace
(
s
+
1
)
6
s
2
+
7
s
+
2
limit as x approaches 2 of 1+2xe^{3x}
lim
x
→
2
(
1
+
2
xe
3
x
)
limit as x approaches 0-of |sin(x)|^x
lim
x
→
0
−
(
|
sin
(
x
)
|
x
)
integral of 1/((x-2)^2)
∫
1
(
x
−
2
)
2
dx
integral of sqrt(3x^2)
∫
√
3
x
2
dx
f(t)=sqrt(t)
f
(
t
)
=
√
t
derivative sqrt(2)u
derivative
√
2
u
integral of 1/(7x+5)
∫
1
7
x
+
5
dx
y^{''}+9y=sec(3t)
y
′
′
+
9
y
=
sec
(
3
t
)
sum from n=0 to infinity of 2(4/5)^n
∑
n
=
0
∞
2
(
4
5
)
n
derivative of (x^3/(5-x^2))
d
dx
(
x
3
5
−
x
2
)
(x-1)^'
(
x
−
1
)
′
tangent 8xsin(x)
tangent
8
x
sin
(
x
)
테일러 sqrt((1+x^2))
taylor
√
(
1
+
x
2
)
integral from 0 to pi of 9sin^2(xco)s^4x
∫
0
π
9
sin
2
(
xco
)
s
4
xdx
derivative of e^{sin(5x})
d
dx
(
e
sin
(
5
x
)
)
(\partial)/(\partial x)(sqrt(tan(x)+y))
∂
∂
x
(
√
tan
(
x
)
+
y
)
integral of cos^4(2y)
∫
cos
4
(
2
y
)
dy
cos(3x)y^'+3(tan(3x))y=sec(3x)
cos
(
3
x
)
y
′
+
3
(
tan
(
3
x
)
)
y
=
sec
(
3
x
)
(\partial)/(\partial x)(e^{-2x}cos(2pit))
∂
∂
x
(
e
−
2
x
cos
(
2
π
t
)
)
y^'=((4-2x))/((3+2y))
y
′
=
(
4
−
2
x
)
(
3
+
2
y
)
tangent (3x)/(x^2-6)
tangent
3
x
x
2
−
6
derivative y=5+5x^2-2x^3
derivative
y
=
5
+
5
x
2
−
2
x
3
derivative of e^x(1+x)
d
dx
(
e
x
(
1
+
x
)
)
derivative f(x)=5x+6
derivative
f
(
x
)
=
5
x
+
6
derivative of (3x^3+4(x^4-4x))
d
dx
(
(
3
x
3
+
4
)
(
x
4
−
4
x
)
)
derivative y= 1/(y^2)
derivative
y
=
1
y
2
(\partial)/(\partial x)(rsin(θ))
∂
∂
x
(
r
sin
(
θ
)
)
integral from-6 to 6 of ((36-x^2))/2
∫
−
6
6
(
3
6
−
x
2
)
2
dx
integral of 7re^{r/4}
∫
7
re
r
4
dr
derivative of 1/((x-1^3))
d
dx
(
1
(
x
−
1
)
3
)
지역 f(x)=x^2-4,y=0,x=-4,x=3
area
f
(
x
)
=
x
2
−
4
,
y
=
0
,
x
=
−
4
,
x
=
3
tangent y=x^2-6,(4,10)
tangent
y
=
x
2
−
6
,
(
4
,
1
0
)
derivative of xx^{1/2}
d
dx
(
xx
1
2
)
tangent 5x^2+xy+5y^2=11,(1,1)
tangent
5
x
2
+
xy
+
5
y
2
=
1
1
,
(
1
,
1
)
integral of sqrt(-4+9s)
∫
√
−
4
+
9
s
ds
derivative of sin^5(x^2+1^7)
d
dx
(
sin
5
(
x
2
+
1
)
7
)
integral of 3x^2e^{4x}
∫
3
x
2
e
4
x
dx
integral of ((x+1))/(xsqrt(x-2))
∫
(
x
+
1
)
x
√
x
−
2
dx
(\partial)/(\partial x)(cos(x)-xcos(y)-y)
∂
∂
x
(
cos
(
x
)
−
x
cos
(
y
)
−
y
)
limit as x approaches-2-of sqrt(2-x)
lim
x
→
−
2
−
(
√
2
−
x
)
4x(dy)/(dx)=2xe^x-4y+6x^2
4
x
dy
dx
=
2
xe
x
−
4
y
+
6
x
2
limit as x approaches 0 of 7/x-(3/x)^2
lim
x
→
0
(
7
x
−
(
3
x
)
2
)
derivative of (x+ae^2x+b)
d
dx
(
(
x
+
a
)
e
2
x
+
b
)
integral of x^2sqrt(2+x^3)
∫
x
2
√
2
+
x
3
dx
derivative f(x)=(sqrt(10))/(x^7)
derivative
f
(
x
)
=
√
1
0
x
7
(\partial)/(\partial x)(4+2x-3y^2)
∂
∂
x
(
4
+
2
x
−
3
y
2
)
integral of 3*sqrt(x)
∫
3
·
√
x
dx
(\partial)/(\partial p)(sqrt(pq))
∂
∂
p
(
√
pq
)
(\partial)/(\partial x)(3+xln(xy-5))
∂
∂
x
(
3
+
x
ln
(
xy
−
5
)
)
(\partial)/(\partial x)(4x^3+4y^2x+4x)
∂
∂
x
(
4
x
3
+
4
y
2
x
+
4
x
)
integral of t/(t^4+2)
∫
t
t
4
+
2
dt
inverse라플라스 (-4s+8)/(s^2+6s+8)
inverselaplace
−
4
s
+
8
s
2
+
6
s
+
8
limit as x approaches infinity of 7-2x
lim
x
→
∞
(
7
−
2
x
)
(\partial)/(\partial t)(e^{-4t}cos(pix))
∂
∂
t
(
e
−
4
t
cos
(
π
x
)
)
(d^2)/(dx^2)((x^2-6x)/(x+1))
d
2
dx
2
(
x
2
−
6
x
x
+
1
)
limit as x approaches 1 of ((x^{5/2}-2x^{3/2}+x^{1/2}))/(x-1)
lim
x
→
1
(
(
x
5
2
−
2
x
3
2
+
x
1
2
)
x
−
1
)
derivative f(x)=(a-5x)(a+5x)
derivative
f
(
x
)
=
(
a
−
5
x
)
(
a
+
5
x
)
integral of 4sec^6(t)
∫
4
sec
6
(
t
)
dt
2y^{''}+19y^'-10y=0
2
y
′
′
+
1
9
y
′
−
1
0
y
=
0
1
..
1398
1399
1400
1401
1402
..
2459