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일반적인 미적분학 문제
(d^2y)/(dx^2)=-49y
d
2
y
dx
2
=
−
4
9
y
derivative ln(tan(x^3))
derivative
ln
(
tan
(
x
3
)
)
(dx)/(dt)=-t/x
dx
dt
=
−
t
x
laplacetransform e^{2t}sin(4t)
laplacetransform
e
2
t
sin
(
4
t
)
derivative (x^3-2)^2
derivative
(
x
3
−
2
)
2
derivative of sqrt(x)-6x
d
dx
(
√
x
−
6
x
)
limit as x approaches 1 of x^3
lim
x
→
1
(
x
3
)
limit as x approaches+3 of 5/(x^2-9)
lim
x
→
+
3
(
5
x
2
−
9
)
(dy)/(dt)=20-y/(230+16t)
dy
dt
=
2
0
−
y
2
3
0
+
1
6
t
(dy)/(dx)=e^x-6x^2
dy
dx
=
e
x
−
6
x
2
tangent y=x^3+x
tangent
y
=
x
3
+
x
integral of x^2ex
∫
x
2
exdx
derivative (sin(θ))/3+c/θ
derivative
sin
(
θ
)
3
+
c
θ
derivative 3z
derivative
3
z
derivative of 1/4 x^4
d
dx
(
1
4
x
4
)
integral of 3xcos(4x)
∫
3
x
cos
(
4
x
)
dx
integral of (3x^2-1)/((x-1)x^2)
∫
3
x
2
−
1
(
x
−
1
)
x
2
dx
derivative of e^{cos(x})
d
dx
(
e
cos
(
x
)
)
integral of xe^{bx}
∫
xe
bx
dx
integral of sec^5(3x)
∫
sec
5
(
3
x
)
dx
derivative of (2xy/((2-x^2)))
d
dx
(
2
xy
(
2
−
x
2
)
)
derivative cos(6y)
derivative
cos
(
6
y
)
derivative of (ax+b/(cx+d))
d
dx
(
ax
+
b
cx
+
d
)
limit as x approaches 1 of arccos(x)
lim
x
→
1
(
arccos
(
x
)
)
d/(ds)(6/(s^2+36))
d
ds
(
6
s
2
+
3
6
)
(d^2)/(dx^2)(sqrt(x^2+16))
d
2
dx
2
(
√
x
2
+
1
6
)
integral of (3x^2+1)/(2x)
∫
3
x
2
+
1
2
x
dx
integral of (5x^3+7x)/(x-1)
∫
5
x
3
+
7
x
x
−
1
dx
integral of 1/((x+4)(x-4))
∫
1
(
x
+
4
)
(
x
−
4
)
dx
derivative y=2xarccos(x)-2sqrt(1-x^2)
derivative
y
=
2
x
arccos
(
x
)
−
2
√
1
−
x
2
sum from n=0 to infinity of ((n))/(n+1)
∑
n
=
0
∞
(
n
)
n
+
1
y/(x^2)(dy)/(dx)+e^{2x^3+y^2}=0
y
x
2
dy
dx
+
e
2
x
3
+
y
2
=
0
limit as x approaches infinity of 4/x-12
lim
x
→
∞
(
4
x
−
1
2
)
(\partial)/(\partial y)(3x+2ysin(x))
∂
∂
y
(
3
x
+
2
y
sin
(
x
)
)
limit as x approaches 20 of sin(70-x)
lim
x
→
2
0
(
sin
(
7
0
−
x
)
)
f(x)=(2x^4-1)(5x^3+6x)
f
(
x
)
=
(
2
x
4
−
1
)
(
5
x
3
+
6
x
)
derivative ((x^2-5)^3)/(x^2+2)
derivative
(
x
2
−
5
)
3
x
2
+
2
limit as x approaches 5 of ln(x^2-25)
lim
x
→
5
(
ln
(
x
2
−
2
5
)
)
integral of 5e^x-cos(x)+3x^2-1/x
∫
5
e
x
−
cos
(
x
)
+
3
x
2
−
1
x
dx
integral of 1/(xsqrt(36x^2-4))
∫
1
x
√
3
6
x
2
−
4
dx
derivative of x^2+3x+2
d
dx
(
x
2
+
3
x
+
2
)
derivative 6*6^t+2*2t
derivative
6
·
6
t
+
2
·
2
t
integral of (sin(3x))/(csc^2(4x))
∫
sin
(
3
x
)
csc
2
(
4
x
)
dx
(dy)/(dx)=(1-y)/(1-x)
dy
dx
=
1
−
y
1
−
x
(\partial)/(\partial v)(2vsin(u))
∂
∂
v
(
2
v
sin
(
u
)
)
inverselaplace 1/(s^2-s)
inverselaplace
1
s
2
−
s
limit as x approaches 1/5 of x/(10x-2)
lim
x
→
1
5
(
x
1
0
x
−
2
)
derivative of (cos(x)^3)
d
dx
(
(
cos
(
x
)
)
3
)
x^'+2/(1+t)x=(e^t)/(1+t)
x
′
+
2
1
+
t
x
=
e
t
1
+
t
integral from-1 to 1 of 3x^2sqrt(x^3+5)
∫
−
1
1
3
x
2
√
x
3
+
5
dx
(x^2+2x)^'
(
x
2
+
2
x
)
′
limit as x approaches 1+of 5/(x^3-1)
lim
x
→
1
+
(
5
x
3
−
1
)
integral of (x+5)/(x^2+10x)
∫
x
+
5
x
2
+
1
0
x
dx
integral from 0 to 1 of pi(1-x^2)
∫
0
1
π
(
1
−
x
2
)
dx
inverselaplace (-5)/(s(s^2-5s+4))
inverselaplace
−
5
s
(
s
2
−
5
s
+
4
)
derivative y=-3x-2
derivative
y
=
−
3
x
−
2
x^{''}+6x^'+7x=0,x(0)=0,x^'(0)=1
x
′
′
+
6
x
′
+
7
x
=
0
,
x
(
0
)
=
0
,
x
′
(
0
)
=
1
integral from 2 to 5 of (4x-2)
∫
2
5
(
4
x
−
2
)
dx
(sqrt(x))^'
(
√
x
)
′
integral of (180x^2)/((3x+1)(3x+5)(x+2))
∫
1
8
0
x
2
(
3
x
+
1
)
(
3
x
+
5
)
(
x
+
2
)
dx
f(x)=cos(ln(x))
f
(
x
)
=
cos
(
ln
(
x
)
)
integral from 0 to 4 of 1/(x^2)
∫
0
4
1
x
2
dx
(\partial)/(\partial x)(ln(x^2))
∂
∂
x
(
ln
(
x
2
)
)
integral of-2cos(t)
∫
−
2
cos
(
t
)
dt
tangent f(x)=8\sqrt[4]{x},\at x=1
tangent
f
(
x
)
=
8
4
√
x
,
at
x
=
1
derivative of (3x+5^3-5x)
d
dx
(
(
3
x
+
5
)
3
−
5
x
)
(\partial)/(\partial x)(xe^{(y/x)})
∂
∂
x
(
xe
(
y
x
)
)
integral of 1/(cos^2(b)x)
∫
1
cos
2
(
b
)
x
dx
limit as x approaches 2 of-5
lim
x
→
2
(
−
5
)
integral of-cos(2t)
∫
−
cos
(
2
t
)
dt
integral of 1/((1-x)(2-x))
∫
1
(
1
−
x
)
(
2
−
x
)
dx
derivative 1/(cos^2(x))
derivative
1
cos
2
(
x
)
(dx)/(dt)=x
dx
dt
=
x
(\partial)/(\partial y)(2x-y)
∂
∂
y
(
2
x
−
y
)
limit as x approaches infinity of (((log_{2}(x))^2))/(sqrt(x))
lim
x
→
∞
(
(
(
log
2
(
x
)
)
2
)
√
x
)
xyy^'=x^6+3y^2
xyy
′
=
x
6
+
3
y
2
integral of 3xsin(x)cos(x)
∫
3
x
sin
(
x
)
cos
(
x
)
dx
derivative of ln(x*sqrt(x^2-1))
d
dx
(
ln
(
x
·
√
x
2
−
1
)
)
derivative f(x)=x^9cos(x)
derivative
f
(
x
)
=
x
9
cos
(
x
)
laplacetransform t^2e^{-3t}
laplacetransform
t
2
e
−
3
t
derivative of y^2x+2yx^3
d
dx
(
y
2
x
+
2
yx
3
)
경사지 (0,-2),(2,2)
slope
(
0
,
−
2
)
,
(
2
,
2
)
integral from 0 to 1 of sqrt(x+16)
∫
0
1
√
x
+
1
6
dx
테일러 sin(x+pi)
taylor
sin
(
x
+
π
)
laplacetransform 2e^{-4t}
laplacetransform
2
e
−
4
t
derivative of ln(y/x)
d
dx
(
ln
(
y
x
)
)
(\partial)/(\partial y)(x^2-2x-xy)
∂
∂
y
(
x
2
−
2
x
−
xy
)
derivative (x^2)/((x^2-1)^4)
derivative
x
2
(
x
2
−
1
)
4
(\partial)/(\partial y)(x^2e^y)
∂
∂
y
(
x
2
e
y
)
slopeintercept (7)(-1.6)
slopeintercept
(
7
)
(
−
1
.
6
)
x^2y^'+2xy=11cos^2(x)
x
2
y
′
+
2
xy
=
1
1
cos
2
(
x
)
derivative y=log_{5}(sqrt(7x+1))
derivative
y
=
log
5
(
√
7
x
+
1
)
derivative of (4x^3/3)
d
dx
(
4
x
3
3
)
(\partial)/(\partial y)(zcos(xz))
∂
∂
y
(
z
cos
(
xz
)
)
derivative of (x-2^4-1)
d
dx
(
(
x
−
2
)
4
−
1
)
integral of xIn(1+x)
∫
xIn
(
1
+
x
)
경사지 (-6,7),(1,-12)
slope
(
−
6
,
7
)
,
(
1
,
−
1
2
)
integral from 0 to 4 of (8t)/((t-5)^2)
∫
0
4
8
t
(
t
−
5
)
2
dt
derivative of (3x^2+5x+8/(\sqrt[3]{x)})
d
dx
(
3
x
2
+
5
x
+
8
3
√
x
)
limit as x approaches 0 of (|x-0|)/(x-0)
lim
x
→
0
(
|
x
−
0
|
x
−
0
)
1
2
3
4
5
6
7
..
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