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일반적인 미적분학 문제
y'=0.027y(1-y/(1527))
y
′
=
0
.
0
2
7
y
(
1
−
y
1
5
2
7
)
derivative ln(3)+e^{x^e}
derivative
ln
(
3
)
+
e
x
e
y^{''}-5y^'=10x+3
y
′
′
−
5
y
′
=
1
0
x
+
3
xyy^'+x^2+y^2=0
xyy
′
+
x
2
+
y
2
=
0
integral of (5x^4+6)/(x^5+6x)
∫
5
x
4
+
6
x
5
+
6
x
dx
limit as x approaches 5+of 4/(x-5)
lim
x
→
5
+
(
4
x
−
5
)
limit as x approaches 0 of x^8-1/x
lim
x
→
0
(
x
8
−
1
x
)
derivative of sin^3(2x-cos(2x))
d
dx
(
sin
3
(
2
x
)
−
cos
(
2
x
)
)
integral of e^{-v}sin(wv)
∫
e
−
v
sin
(
wv
)
dv
(dy)/(dt)=-t/y ,y(0)=4
dy
dt
=
−
t
y
,
y
(
0
)
=
4
derivative of (x^2+2x/(1-x^2))
d
dx
(
x
2
+
2
x
1
−
x
2
)
tangent x^4+6x^2-x
tangent
x
4
+
6
x
2
−
x
integral of (sin(y))/(cos(y))
∫
sin
(
y
)
cos
(
y
)
dy
(\partial)/(\partial y)(-e^{-x}sin(y))
∂
∂
y
(
−
e
−
x
sin
(
y
)
)
(\partial)/(\partial y)(4x^2+4xy-3y^2+4y-1)
∂
∂
y
(
4
x
2
+
4
xy
−
3
y
2
+
4
y
−
1
)
limit as x approaches 1 of x-1
lim
x
→
1
(
x
−
1
)
integral of sec^2(x)+sec(2x)tan(2x)
∫
sec
2
(
x
)
+
sec
(
2
x
)
tan
(
2
x
)
dx
derivative p(θ)=sqrt(7θ)
derivative
p
(
θ
)
=
√
7
θ
f(x)=ln(x+4)
f
(
x
)
=
ln
(
x
+
4
)
integral of 1/(2sin(x)-3cos(x)-5)
∫
1
2
sin
(
x
)
−
3
cos
(
x
)
−
5
dx
limit as x approaches infinity of 0/0
lim
x
→
∞
(
0
0
)
inverse라플라스 (s+3)/((s+1)^2)
inverselaplace
s
+
3
(
s
+
1
)
2
(dy)/(dt)=-4(y-2)
dy
dt
=
−
4
(
y
−
2
)
d/(dy)(6y)
d
dy
(
6
y
)
derivative y=ln(sqrt((a+bx)/(a-bx)))
derivative
y
=
ln
(
√
a
+
bx
a
−
bx
)
테일러 cos(x+1)
taylor
cos
(
x
+
1
)
(\partial)/(\partial x)(12y^5x^3+35y^8x^6)
∂
∂
x
(
1
2
y
5
x
3
+
3
5
y
8
x
6
)
6(t+1)(dy)/(dt)-5y=5t
6
(
t
+
1
)
dy
dt
−
5
y
=
5
t
limit as x approaches 0 of ((x^2-2))/x
lim
x
→
0
(
(
x
2
−
2
)
x
)
d/(d{x)}({x}^4+{y}^4+{z}^4-4{x}{y}{z})
d
d
x
(
x
4
+
y
4
+
z
4
−
4
x
y
z
)
integral of x/(x-3)
∫
x
x
−
3
dx
derivative of-x^3+x
d
dx
(
−
x
3
+
x
)
지역 4cos(7x),4-4cos(7x),0, pi/7
area
4
cos
(
7
x
)
,
4
−
4
cos
(
7
x
)
,
0
,
π
7
inverse라플라스 ((s+1))/(s^2+1)
inverselaplace
(
s
+
1
)
s
2
+
1
derivative 9/x
derivative
9
x
limit as x approaches 0-of 3^{1/x}
lim
x
→
0
−
(
3
1
x
)
integral of (x^2)/(xsqrt(x^2-x+1))
∫
x
2
x
√
x
2
−
x
+
1
dx
integral of xcos(1/2 x)
∫
x
cos
(
1
2
x
)
dx
y^{''}+3y^'+2y=x+6e^x,y(0)=0,y^'(0)=1
y
′
′
+
3
y
′
+
2
y
=
x
+
6
e
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
tangent y=sin(xy)+pi,(1,pi)
tangent
y
=
sin
(
xy
)
+
π
,
(
1
,
π
)
7(d^2y)/(dx^2)+4(dy)/(dx)+9y=0
7
d
2
y
dx
2
+
4
dy
dx
+
9
y
=
0
tangent f(x)=x^4+3x^2-x,(1,3)
tangent
f
(
x
)
=
x
4
+
3
x
2
−
x
,
(
1
,
3
)
integral from 0 to a of x
∫
0
a
xdx
integral from 0 to 1 of 6x^2+4x-3+4e^{4x}
∫
0
1
6
x
2
+
4
x
−
3
+
4
e
4
x
dx
y^{''}-5y^'+6y=2e^t
y
′
′
−
5
y
′
+
6
y
=
2
e
t
경사지 (5,2),(2,-3)
slope
(
5
,
2
)
,
(
2
,
−
3
)
derivative of x/(x^4+1)
d
dx
(
x
x
4
+
1
)
tangent y=(x^3-16x)^{14},(4,0)
tangent
y
=
(
x
3
−
1
6
x
)
1
4
,
(
4
,
0
)
derivative 1/(\sqrt[3]{(5-x^3)^5)}
derivative
1
3
√
(
5
−
x
3
)
5
y^'+4xy=x^3e^{x^2},y(0)=-1
y
′
+
4
xy
=
x
3
e
x
2
,
y
(
0
)
=
−
1
integral of xcosh(2x^2-3)
∫
x
cosh
(
2
x
2
−
3
)
dx
inverse라플라스 (e^{-s})/((s+1)^2+1)
inverselaplace
e
−
s
(
s
+
1
)
2
+
1
integral from 0 to pi of 2sin^4(x)
∫
0
π
2
sin
4
(
x
)
dx
integral of (x^3)/(x^2+x+1)
∫
x
3
x
2
+
x
+
1
dx
x^2y^{''}-7xy^'-20y=0
x
2
y
′
′
−
7
xy
′
−
2
0
y
=
0
y^{''}+9y=30sin(t)
y
′
′
+
9
y
=
3
0
sin
(
t
)
derivative f(x)=e^xsqrt(x)
derivative
f
(
x
)
=
e
x
√
x
지역 y=8cos(3x),y=8sin(3x),(0, pi/(12))
area
y
=
8
cos
(
3
x
)
,
y
=
8
sin
(
3
x
)
,
(
0
,
π
1
2
)
tangent f(x)= 5/(sqrt(x)),(1,5)
tangent
f
(
x
)
=
5
√
x
,
(
1
,
5
)
derivative of (x^2+x^3^4)
d
dx
(
(
x
2
+
x
3
)
4
)
(\partial)/(\partial x)(x*y^2*e^z)
∂
∂
x
(
x
·
y
2
·
e
z
)
derivative y=cos^3(pit-16)
derivative
y
=
cos
3
(
π
t
−
1
6
)
tangent f(x)=x^4+2x^2-x,(1,2)
tangent
f
(
x
)
=
x
4
+
2
x
2
−
x
,
(
1
,
2
)
derivative of x,x^2-y,x+y^2
d
dx
(
x
,
x
2
−
y
,
x
+
y
2
)
integral of 5/((8z-1)^{7/8)}
∫
5
(
8
z
−
1
)
7
8
dz
derivative e^2+ln(4)
derivative
e
2
+
ln
(
4
)
limit as x approaches 0-of 1/x
lim
x
→
0
−
(
1
x
)
limit as x approaches 2 of (x-2)/(4-x^2)
lim
x
→
2
(
x
−
2
4
−
x
2
)
(\partial}{\partial x}(\frac{x^2-y^2)/2)
∂
∂
x
(
x
2
−
y
2
2
)
(\partial)/(\partial x)(1/((x+3y)))
∂
∂
x
(
1
(
x
+
3
y
)
)
derivative of 9/(4(1+x^{5/2)})
d
dx
(
9
4
(
1
+
x
)
5
2
)
integral of x/(sqrt(3-x^4))
∫
x
√
3
−
x
4
dx
derivative (x^{3/2})/3-x^{1/2}
derivative
x
3
2
3
−
x
1
2
derivative of {f}(x*e^{1/({f)(x)}})
d
dx
(
f
(
x
)
·
e
1
f
(
x
)
)
derivative 6(x+2)^{1/2}
derivative
6
(
x
+
2
)
1
2
integral from 0 to 6 of x^2sqrt(36-x^2)
∫
0
6
x
2
√
3
6
−
x
2
dx
y=(3x^5-7x^2-4)/(x^2)
y
=
3
x
5
−
7
x
2
−
4
x
2
derivative of 4^{e^x}
d
dx
(
4
e
x
)
derivative e^{-,\at}
derivative
e
−
,
at
y^{''}+4y=3sec(2x)
y
′
′
+
4
y
=
3
sec
(
2
x
)
derivative (3x^2+1)(2x+2)^2
derivative
(
3
x
2
+
1
)
(
2
x
+
2
)
2
integral of ((x+5))/((x+3)(x-2)^2)
∫
(
x
+
5
)
(
x
+
3
)
(
x
−
2
)
2
dx
(\partial)/(\partial x)(e^x+sin(y))
∂
∂
x
(
e
x
+
sin
(
y
)
)
limit as x approaches 0+of ln(sinh(x))
lim
x
→
0
+
(
ln
(
sinh
(
x
)
)
)
derivative of-2sin(x-x)
d
dx
(
−
2
sin
(
x
)
−
x
)
f(x)=x+sin(x)
f
(
x
)
=
x
+
sin
(
x
)
derivative (89t)/(99t-89)
derivative
8
9
t
9
9
t
−
8
9
integral from 0 to 5 of 1/(x^2)
∫
0
5
1
x
2
dx
limit as x approaches pi/2 of 9sin(x)
lim
x
→
π
2
(
9
sin
(
x
)
)
derivative log_{e}(7x^2)
derivative
log
e
(
7
x
2
)
derivative of x^{sin(x})
d
dx
(
x
sin
(
x
)
)
limit as h approaches 0 of (ln(1+h))/h
lim
h
→
0
(
ln
(
1
+
h
)
h
)
maclaurin e^{-3x}
maclaurin
e
−
3
x
(f(x)(x^2))'
(
f
(
x
)
(
x
2
)
)
′
f(x)=(sin(sqrt(x)))/(cos(ln(-x)))
f
(
x
)
=
sin
(
√
x
)
cos
(
ln
(
−
x
)
)
경사지 xy-4y^2=8
slope
xy
−
4
y
2
=
8
integral of \sqrt[5]{x^3}
∫
5
√
x
3
dx
integral of ((2t^2+tsqrt(t)-1))/(t^2)
∫
(
2
t
2
+
t
√
t
−
1
)
t
2
dt
integral of 1/(sin(y)+1)
∫
1
sin
(
y
)
+
1
dy
지역 y=x^3,x=y^2-2
area
y
=
x
3
,
x
=
y
2
−
2
1
..
1173
1174
1175
1176
1177
..
2459