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일반적인 미적분학 문제
limit as x approaches infinity of 5^x+1
lim
x
→
∞
(
5
x
+
1
)
지역 x^2,6-x
area
x
2
,
6
−
x
테일러 1/(1-x^3)
taylor
1
1
−
x
3
laplace변환 e^{a*t}
laplacetransform
e
a
·
t
f(x)=sqrt(x)e^x
f
(
x
)
=
√
x
e
x
derivative f(x)=((x+1)/(x-3))^2
derivative
f
(
x
)
=
(
x
+
1
x
−
3
)
2
derivative of 2/(x^2+2)
d
dx
(
2
x
2
+
2
)
limit as x approaches 0 of (x^5-2)/(x^4)
lim
x
→
0
(
x
5
−
2
x
4
)
derivative ((e^x))/(5x^2)
derivative
(
e
x
)
5
x
2
inverse라플라스 1/(s(s+1)(s+5))
inverselaplace
1
s
(
s
+
1
)
(
s
+
5
)
laplace변환-3(t-1)
laplacetransform
−
3
(
t
−
1
)
y^'=sqrt(-4y+57)
y
′
=
√
−
4
y
+
5
7
e^xdx-ydy=0,y(0)=1
e
x
dx
−
ydy
=
0
,
y
(
0
)
=
1
integral from 1 to sqrt(3 of) 4/(x^2+1)
∫
1
√
3
4
x
2
+
1
dx
integral from-2 to 2 of 4(4-x^2)
∫
−
2
2
4
(
4
−
x
2
)
dx
(d^2)/(dx^2)(x/(x^2-9))
d
2
dx
2
(
x
x
2
−
9
)
integral of sec^2(7/3 x+4)
∫
sec
2
(
7
3
x
+
4
)
dx
integral of (2x-e^x)
∫
(
2
x
−
e
x
)
dx
limit as x approaches 0 of (sin(10x))/(11x)
lim
x
→
0
(
sin
(
1
0
x
)
1
1
x
)
(\partial)/(\partial y)(3xy+y^2)
∂
∂
y
(
3
xy
+
y
2
)
derivative y=e^x+x^2
derivative
y
=
e
x
+
x
2
integral of (5e^x)/(e^{2x)+2e^x+1}
∫
5
e
x
e
2
x
+
2
e
x
+
1
dx
경사지 (-4,0),(1,-5)
slope
(
−
4
,
0
)
,
(
1
,
−
5
)
derivative of sqrt(x^2+2y^2-4)
d
dx
(
√
x
2
+
2
y
2
−
4
)
(y-x)dx+4xdy=0
(
y
−
x
)
dx
+
4
xdy
=
0
integral of 1/(sqrt(2x-1))
∫
1
√
2
x
−
1
dx
동등성 ln|sin(x)|
parity
ln
|
sin
(
x
)
|
integral of x^4(2x^5-5)^4
∫
x
4
(
2
x
5
−
5
)
4
dx
derivative of x/(sqrt(x^2-1))
d
dx
(
x
√
x
2
−
1
)
integral of ln(2/x)
∫
ln
(
2
x
)
dx
derivative ((2x^3+4x^2-2x+3))/((x-3))
derivative
(
2
x
3
+
4
x
2
−
2
x
+
3
)
(
x
−
3
)
derivative f(x)=4x(x^2-9)
derivative
f
(
x
)
=
4
x
(
x
2
−
9
)
integral of sqrt(x)+3
∫
√
x
+
3
dx
(\partial)/(\partial x)(e^xy+5xy^2-x^2)
∂
∂
x
(
e
x
y
+
5
xy
2
−
x
2
)
sum from n=0 to infinity of 3/(n^4)
∑
n
=
0
∞
3
n
4
derivative of xcos(x-sin(x))
d
dx
(
x
cos
(
x
)
−
sin
(
x
)
)
integral of sin(t)cos(nt)
∫
sin
(
t
)
cos
(
nt
)
dt
y^{''}-3y^'=e^{3t}
y
′
′
−
3
y
′
=
e
3
t
sum from k=1 to infinity of (5+(-2)^k)/(4^{k+1)}
∑
k
=
1
∞
5
+
(
−
2
)
k
4
k
+
1
integral of (sin^7(12x))/(cos^4(12x))
∫
sin
7
(
1
2
x
)
cos
4
(
1
2
x
)
dx
tangent f(x)=ln((7(x+3))/x)
tangent
f
(
x
)
=
ln
(
7
(
x
+
3
)
x
)
integral of x^2e^{-x/3}
∫
x
2
e
−
x
3
dx
integral from 1 to 5 of 1/(sqrt(4x+5))
∫
1
5
1
√
4
x
+
5
dx
y^{''}-2y=0
y
′
′
−
2
y
=
0
limit as x approaches-4 of 5x+1
lim
x
→
−
4
(
5
x
+
1
)
derivative of arctan(sqrt(x^2-1))
d
dx
(
arctan
(
√
x
2
−
1
)
)
derivative-(6x)/y
derivative
−
6
x
y
limit as t approaches 0 of t/(tan(3t))
lim
t
→
0
(
t
tan
(
3
t
)
)
derivative of arcsin(x/6)
d
dx
(
arcsin
(
x
6
)
)
derivative of e^{sqrt(xy)}
d
dx
(
e
√
xy
)
d/(dθ)(csc(θ)cot(θ))
d
d
θ
(
csc
(
θ
)
cot
(
θ
)
)
derivative of csc(x-cot(x))
d
dx
(
csc
(
x
)
−
cot
(
x
)
)
integral of (18x+4)(9x^2+4x)^5
∫
(
1
8
x
+
4
)
(
9
x
2
+
4
x
)
5
dx
(\partial)/(\partial x)(-4y^5sin(4x))
∂
∂
x
(
−
4
y
5
sin
(
4
x
)
)
(\partial)/(\partial x)(7x^5y^7+3x^8y^6)
∂
∂
x
(
7
x
5
y
7
+
3
x
8
y
6
)
tangent f(x)=4(x-1/x)^4,\at x=2
tangent
f
(
x
)
=
4
(
x
−
1
x
)
4
,
at
x
=
2
sum from n=1 to infinity of 1/(6n)
∑
n
=
1
∞
1
6
n
tangent \sqrt[4]{x}-x
tangent
4
√
x
−
x
inverse라플라스 2/((s^2+2)(s^2+1))
inverselaplace
2
(
s
2
+
2
)
(
s
2
+
1
)
(\partial)/(\partial z)(xz+yz)
∂
∂
z
(
xz
+
yz
)
derivative f(x)=(x(x^5+9)^3)
derivative
f
(
x
)
=
(
x
(
x
5
+
9
)
3
)
integral of e^{4θ}sin(5θ)
∫
e
4
θ
sin
(
5
θ
)
d
θ
(dN)/(dt)=kN
dN
dt
=
kN
integral of ln((2-3x)^4)
∫
ln
(
(
2
−
3
x
)
4
)
dx
derivative of \sqrt[3]{x^2}+5sqrt(x^3)
d
dx
(
3
√
x
2
+
5
√
x
3
)
지역 sqrt(6x-x^2),0,6
area
√
6
x
−
x
2
,
0
,
6
0.5y^{''}+10y^'+100y=150,y(0)=0,y^'(0)=0
0
.
5
y
′
′
+
1
0
y
′
+
1
0
0
y
=
1
5
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
derivative f(x)=(7x+2)/(8x-3)
derivative
f
(
x
)
=
7
x
+
2
8
x
−
3
derivative f(x)=(3x+4)/(3x-4)
derivative
f
(
x
)
=
3
x
+
4
3
x
−
4
derivative arcsin(4x+1)
derivative
arcsin
(
4
x
+
1
)
integral of (sin(2x))^3(cos(2x))^2
∫
(
sin
(
2
x
)
)
3
(
cos
(
2
x
)
)
2
dx
integral of (1+x^2)e^{-x}
∫
(
1
+
x
2
)
e
−
x
dx
sum from n=0 to infinity of n/(3n^3+1)
∑
n
=
0
∞
n
3
n
3
+
1
(dy)/(dx)=((x+y))/(3x+3y-4)
dy
dx
=
(
x
+
y
)
3
x
+
3
y
−
4
(2x+3y)dx+(3x+2y)dy=0
(
2
x
+
3
y
)
dx
+
(
3
x
+
2
y
)
dy
=
0
tangent sqrt(9-6x)
tangent
√
9
−
6
x
derivative of ln(x+y-ln(x-y))
d
dx
(
ln
(
x
+
y
)
−
ln
(
x
−
y
)
)
(\partial)/(\partial x)(cos(x)-xcos(y))
∂
∂
x
(
cos
(
x
)
−
x
cos
(
y
)
)
integral of 5t^2+e^{0.39t}+2
∫
5
t
2
+
e
0
.
3
9
t
+
2
dt
integral of t/(a+bt^2)
∫
t
a
+
bt
2
dt
integral of 9e^{-9x}
∫
9
e
−
9
x
dx
지역 sin^2(x),sin^3(x)
area
sin
2
(
x
)
,
sin
3
(
x
)
derivative of sin(1/x x^3)
d
dx
(
sin
(
1
x
)
x
3
)
tangent g(x)=ln(x^2),(e,2)
tangent
g
(
x
)
=
ln
(
x
2
)
,
(
e
,
2
)
integral from 0 to 8 of t+2t^3
∫
0
8
t
+
2
t
3
dt
경사지 (8.2)(-10.4)
slope
(
8
.
2
)
(
−
1
0
.
4
)
integral of (x+2)/(x^2-4x)
∫
x
+
2
x
2
−
4
x
dx
(\partial)/(\partial y)(x^3+y^2-yx^2-xy)
∂
∂
y
(
x
3
+
y
2
−
yx
2
−
xy
)
limit as x approaches 1-of (x-1)|x-1|
lim
x
→
1
−
(
(
x
−
1
)
|
x
−
1
|
)
derivative f(x)=4-6x
derivative
f
(
x
)
=
4
−
6
x
integral from 2 to 2 of x^3
∫
2
2
x
3
dx
(dy)/(dt)=(te^t)/(ysqrt(1+y^2))
dy
dt
=
te
t
y
√
1
+
y
2
derivative of-16ax^2+a+1/3
d
dx
(
−
1
6
ax
2
+
a
+
1
3
)
integral of xcos(5)x^2
∫
x
cos
(
5
)
x
2
dx
integral of (4x)/(x^2+9)
∫
4
x
x
2
+
9
dx
derivative y=2xsin(x)+x^2e^x
derivative
y
=
2
x
sin
(
x
)
+
x
2
e
x
derivative of-2x^2-5x+2
d
dx
(
−
2
x
2
−
5
x
+
2
)
integral of 1/(sqrt(x^2-81))
∫
1
√
x
2
−
8
1
dx
y^'=-(3y)/t-2-t^{-4},y(1)=4
y
′
=
−
3
y
t
−
2
−
t
−
4
,
y
(
1
)
=
4
(\partial)/(\partial y)((x-3)/(y^2+1))
∂
∂
y
(
x
−
3
y
2
+
1
)
1
..
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1176
1177
1178
1179
..
2459