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일반적인 미적분학 문제
derivative of x^3+5x
d
dx
(
x
3
+
5
x
)
derivative of 2x+2xln(x)
d
dx
(
2
x
+
2
x
ln
(
x
)
)
tangent (4x+4)^{1/3},\at x=2
tangent
(
4
x
+
4
)
1
3
,
at
x
=
2
tangent y=(-6x)/(x^2+1),(-1,3)
tangent
y
=
−
6
x
x
2
+
1
,
(
−
1
,
3
)
y^{''}+4y^'-32y=0
y
′
′
+
4
y
′
−
3
2
y
=
0
derivative of 2x^3sqrt(2-3x^2)
d
dx
(
2
x
3
√
2
−
3
x
2
)
derivative of h({g}(xk(x)))
d
dx
(
h
(
g
(
x
)
k
(
x
)
)
)
inverse라플라스 ((s+1))/(s^2+s+1)
inverselaplace
(
s
+
1
)
s
2
+
s
+
1
integral of (x^3+4x)^2(3x^2+4)
∫
(
x
3
+
4
x
)
2
(
3
x
2
+
4
)
dx
integral of (x^3+7)/(x^2+5x+6)
∫
x
3
+
7
x
2
+
5
x
+
6
dx
(\partial)/(\partial x)(sqrt(4x^2+4y+2z^2))
∂
∂
x
(
√
4
x
2
+
4
y
+
2
z
2
)
derivative of (x^2+2x/((x+1)^2))
d
dx
(
x
2
+
2
x
(
x
+
1
)
2
)
derivative y=a^4+cos^4(x)
derivative
y
=
a
4
+
cos
4
(
x
)
integral of [5sin^2(3x)+tan(2x)]
∫
[
5
sin
2
(
3
x
)
+
tan
(
2
x
)
]
dx
derivative of 4x+8+(14400/x)
d
dx
(
4
x
+
8
+
1
4
4
0
0
x
)
integral of 2x+4e^x
∫
2
x
+
4
e
x
dx
integral from 0 to 1 of x/2
∫
0
1
x
2
dx
integral of (x^2)/(sqrt(x+4))
∫
x
2
√
x
+
4
dx
derivative of 3sin^5(x)
d
dx
(
3
sin
5
(
x
)
)
derivative of (x+1(x+2))
d
dx
(
(
x
+
1
)
(
x
+
2
)
)
(\partial)/(\partial x)(y^2-2ycos(x))
∂
∂
x
(
y
2
−
2
y
cos
(
x
)
)
d/(dt)({v}(t))
d
dt
(
v
(
t
)
)
derivative of ({f}(x)/({g)(x)})
d
dx
(
f
(
x
)
g
(
x
)
)
y^{''}+9y=2cos(3x)
y
′
′
+
9
y
=
2
cos
(
3
x
)
derivative 1/4 e^{3x}
derivative
1
4
e
3
x
limit as x approaches 1-of sqrt(x^2-1)
lim
x
→
1
−
(
√
x
2
−
1
)
(\partial)/(\partial x)(9x^{5y})
∂
∂
x
(
9
x
5
y
)
(d^8)/(dx^8)(sqrt(1-x^2))
d
8
dx
8
(
√
1
−
x
2
)
inverse라플라스 (3s)/((s^2+1))
inverselaplace
3
s
(
s
2
+
1
)
extreme f(x)=rx+n
extreme
f
(
x
)
=
rx
+
n
(\partial)/(\partial t)(t-s)
∂
∂
t
(
t
−
s
)
derivative-2x^4+5x^2-3
derivative
−
2
x
4
+
5
x
2
−
3
derivative f(x)=e^{4tsin(2t)}
derivative
f
(
x
)
=
e
4
t
sin
(
2
t
)
y^'=e^{(t+y)},y(0)=0
y
′
=
e
(
t
+
y
)
,
y
(
0
)
=
0
x^2((dy)/(dx))+4xy-y^3=0
x
2
(
dy
dx
)
+
4
xy
−
y
3
=
0
limit as x approaches 2 of (3x-1)^{x^2-3x+4}
lim
x
→
2
(
(
3
x
−
1
)
x
2
−
3
x
+
4
)
(\partial)/(\partial y)(ln(x/y))
∂
∂
y
(
ln
(
x
y
)
)
(\partial)/(\partial y)(xe^y+ye^z+ze^x)
∂
∂
y
(
xe
y
+
ye
z
+
ze
x
)
limit as x approaches 0 of 2/x-2/x
lim
x
→
0
(
2
x
−
2
x
)
지역 2/x , 2/(x^2),x=4
area
2
x
,
2
x
2
,
x
=
4
derivative f(x)=6sec(x)-5x
derivative
f
(
x
)
=
6
sec
(
x
)
−
5
x
derivative of sqrt(sec(5x^2))
d
dx
(
√
sec
(
5
)
x
2
)
sum from n=1 to infinity of 7/(n^5)
∑
n
=
1
∞
7
n
5
derivative y=5x^2
derivative
y
=
5
x
2
derivative of (4e^x/x)
d
dx
(
4
e
x
x
)
derivative f(x)=x^{2cos(x)}
derivative
f
(
x
)
=
x
2
cos
(
x
)
(\partial)/(\partial y)(4x^{2y})
∂
∂
y
(
4
x
2
y
)
(d^2y)/(dx^2)=x
d
2
y
dx
2
=
x
tangent f(x)= x/(x^2+1)
tangent
f
(
x
)
=
x
x
2
+
1
derivative of (cot(x)/(1+cot(x)))
d
dx
(
cot
(
x
)
1
+
cot
(
x
)
)
implicit (dy)/(dx),y-5xy^3+8=5sin(y^3+2x^2)
implicit
dy
dx
,
y
−
5
xy
3
+
8
=
5
sin
(
y
3
+
2
x
2
)
(\partial)/(\partial x)(x(y+1))
∂
∂
x
(
x
(
y
+
1
)
)
integral from 0 to 2pi of sin^4(x)
∫
0
2
π
sin
4
(
x
)
dx
derivative of sin(9x+(sin(9x))^2)
d
dx
(
sin
(
9
x
)
+
(
sin
(
9
x
)
)
2
)
derivative f(2x)=5x-3
derivative
f
(
2
x
)
=
5
x
−
3
(\partial)/(\partial x)(x+sqrt(y))
∂
∂
x
(
x
+
√
y
)
(t+y+1)dt-dy=0
(
t
+
y
+
1
)
dt
−
dy
=
0
derivative f(x)=2x-4
derivative
f
(
x
)
=
2
x
−
4
derivative of ((x+1/(x-1))^4)
d
dx
(
(
x
+
1
x
−
1
)
4
)
integral of ln(x)-9x^2
∫
ln
(
x
)
−
9
x
2
dx
laplace변환 3sin^2(t)
laplacetransform
3
sin
2
(
t
)
(\partial)/(\partial x)(y^2+6x-x^2y+36)
∂
∂
x
(
y
2
+
6
x
−
x
2
y
+
3
6
)
integral of sqrt(2t)
∫
√
2
t
dt
integral of (4x+4)sqrt(2x^2+4x)
∫
(
4
x
+
4
)
√
2
x
2
+
4
x
dx
integral of 50x
∫
5
0
xdx
지역 sqrt(x-1),x-1
area
√
x
−
1
,
x
−
1
integral from 0 to pi of 3e^xsin(x)
∫
0
π
3
e
x
sin
(
x
)
dx
derivative of 1/(sqrt(9-x^2))
d
dx
(
1
√
9
−
x
2
)
inverse라플라스 1/((s+1)^2*(s-1))
inverselaplace
1
(
s
+
1
)
2
·
(
s
−
1
)
limit as h approaches 0 of (8^h-1)/h
lim
h
→
0
(
8
h
−
1
h
)
derivative f(x)=(x^2+2x-3)/((x+1)^2)
derivative
f
(
x
)
=
x
2
+
2
x
−
3
(
x
+
1
)
2
integral from-infinity to 0 of 1/(6-4x)
∫
−
∞
0
1
6
−
4
x
dx
y^{''}+7y^'+14y=1096e^{2t}cos(8t)
y
′
′
+
7
y
′
+
1
4
y
=
1
0
9
6
e
2
t
cos
(
8
t
)
limit as x approaches 4-of x/(x^2-16)
lim
x
→
4
−
(
x
x
2
−
1
6
)
(dy)/(dx)= x/(25y),y(5)=1
dy
dx
=
x
2
5
y
,
y
(
5
)
=
1
derivative of sqrt(9x+1)
d
dx
(
√
9
x
+
1
)
laplace변환 cos(t)*e^t
laplacetransform
cos
(
t
)
·
e
t
integral of (tan^3(x))/(sec^2(x)-1)
∫
tan
3
(
x
)
sec
2
(
x
)
−
1
dx
derivative y=ln(xln(x))
derivative
y
=
ln
(
x
ln
(
x
)
)
integral from 0 to 9 of 1/(sqrt(81+x^2))
∫
0
9
1
√
8
1
+
x
2
dx
integral of sec^5(t)
∫
sec
5
(
t
)
dt
(\partial ^2)/(\partial x^2)(x^2-e^{y^2})
∂
2
∂
x
2
(
x
2
−
e
y
2
)
derivative ln|sec(θ)+tan(θ)|
derivative
ln
|
sec
(
θ
)
+
tan
(
θ
)
|
integral from 0 to 1 of (x^4+2)/x
∫
0
1
x
4
+
2
x
dx
derivative (sqrt(s)-1)/(sqrt(s)+1)
derivative
√
s
−
1
√
s
+
1
(\partial)/(\partial x)(e^ye^x)
∂
∂
x
(
e
y
e
x
)
(\partial)/(\partial x)(ye^{-2x})
∂
∂
x
(
ye
−
2
x
)
laplace변환-2t
laplacetransform
−
2
t
(\partial)/(\partial x)(ln((x+y)/(x-y)))
∂
∂
x
(
ln
(
x
+
y
x
−
y
)
)
integral from 0 to 1 of v^2cos(v^3)
∫
0
1
v
2
cos
(
v
3
)
dv
derivative of (d/(dx(x^3))^2)
d
dx
(
(
d
dx
(
x
3
)
)
2
)
derivative of sqrt(3x^2-4x+2)
d
dx
(
√
3
x
2
−
4
x
+
2
)
(dy)/(dx)+y=e^{6x}
dy
dx
+
y
=
e
6
x
derivative of cos^2(sin(2x))
d
dx
(
cos
2
(
sin
(
2
x
)
)
)
derivative of (x^2+1^{ln(x)})
d
dx
(
(
x
2
+
1
)
ln
(
x
)
)
sum from i=1 to infinity of 4(2)^{i-1}
∑
i
=
1
∞
4
(
2
)
i
−
1
integral of (ln(x)-2)/(xln(x)(ln(x)-1))
∫
ln
(
x
)
−
2
x
ln
(
x
)
(
ln
(
x
)
−
1
)
dx
integral of sin(x)ln(x)cos(x)
∫
sin
(
x
)
ln
(
x
)
cos
(
x
)
dx
laplace변환 e^{mt}
laplacetransform
e
mt
integral of x/(sqrt(5+4x))
∫
x
√
5
+
4
x
dx
1
..
1164
1165
1166
1167
1168
..
2459