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일반적인 미적분학 문제
derivative of (1-x^{-1}^{-1})
d
dx
(
(
1
−
x
−
1
)
−
1
)
y^'=((4+5*y))/6
y
′
=
(
4
+
5
·
y
)
6
integral of x*x^{1/2}
∫
x
·
x
1
2
dx
limit as x approaches 0 of (x^2)*ln(x)
lim
x
→
0
(
(
x
2
)
·
ln
(
x
)
)
y^'+1/x y=0
y
′
+
1
x
y
=
0
tangent f(x)=3x^3-3x^2+7,(2,19)
tangent
f
(
x
)
=
3
x
3
−
3
x
2
+
7
,
(
2
,
1
9
)
derivative of 3^xlog_{5}(x)
d
dx
(
3
x
log
5
(
x
)
)
integral from 0 to x of 1/(1-x)
∫
0
x
1
1
−
x
dx
d/(dθ)(1/θ)
d
d
θ
(
1
θ
)
(\partial)/(\partial x)(6e^{x^3y})
∂
∂
x
(
6
e
x
3
y
)
integral of sqrt(26)
∫
√
2
6
dx
tangent f(x)=3x^3-x^2+8,(2,28)
tangent
f
(
x
)
=
3
x
3
−
x
2
+
8
,
(
2
,
2
8
)
derivative of sqrt(8-x^2)
d
dx
(
√
8
−
x
2
)
derivative y=(sqrt(t))^t
derivative
y
=
(
√
t
)
t
limit as x approaches 1/3 of (x+3)/(x+4)
lim
x
→
1
3
(
x
+
3
x
+
4
)
derivative of (x^2dx)
d
dx
(
(
x
2
)
dx
)
limit as x approaches-3 of (x^2+x)/(x+3)
lim
x
→
−
3
(
x
2
+
x
x
+
3
)
integral of 3y^3e^{xy}
∫
3
y
3
e
xy
dx
integral of x^2e^{2x+1}
∫
x
2
e
2
x
+
1
dx
tangent f(x)=-3x^2-5,\at x=0
tangent
f
(
x
)
=
−
3
x
2
−
5
,
at
x
=
0
derivative of (x-1/(x-2))
d
dx
(
x
−
1
x
−
2
)
integral of (tan(θ))/(sec^2(θ))
∫
tan
(
θ
)
sec
2
(
θ
)
d
θ
단순화 8/(sqrt(x))
simplify
8
√
x
derivative of a(1-cos^2(x/2)^2)
d
dx
(
a
(
1
−
cos
2
(
x
2
)
)
2
)
확장 (x-2)(x-7)(x+1)
expand
(
x
−
2
)
(
x
−
7
)
(
x
+
1
)
laplace변환 27t^2sin(6t-60)
laplacetransform
2
7
t
2
sin
(
6
t
−
6
0
)
(\partial)/(\partial x)(3e^{x/y})
∂
∂
x
(
3
e
x
y
)
tangent y= 6/(sqrt(x)),(1, 6/1)
tangent
y
=
6
√
x
,
(
1
,
6
1
)
derivative of (cos(sqrt(x))/x)
d
dx
(
cos
(
√
x
)
x
)
(2xy^2-3)dx+(2x^2y+4)dy=0
(
2
xy
2
−
3
)
dx
+
(
2
x
2
y
+
4
)
dy
=
0
derivative of x/((1+x^2^2))
d
dx
(
x
(
1
+
x
2
)
2
)
(d^2)/(dx^2)((x^2+8)^9)
d
2
dx
2
(
(
x
2
+
8
)
9
)
derivative of ((x^2)/2)
d
dx
(
(
x
2
)
2
)
tangent (sqrt(3))^x
tangent
(
√
3
)
x
(\partial)/(\partial x)(5ye^x-ln(z))
∂
∂
x
(
5
ye
x
−
ln
(
z
)
)
integral of 1/(x^4)-1/(\sqrt[4]{x)}-4
∫
1
x
4
−
1
4
√
x
−
4
dx
derivative f(x)=sec^2(pix)
derivative
f
(
x
)
=
sec
2
(
π
x
)
integral of-1/4 x
∫
−
1
4
xdx
laplace변환 e^{-2t}cos(3t)
laplacetransform
e
−
2
t
cos
(
3
t
)
(\partial)/(\partial y)(y+1)
∂
∂
y
(
y
+
1
)
inverse라플라스 6/((s+1)(2s^2+5s+3))
inverselaplace
6
(
s
+
1
)
(
2
s
2
+
5
s
+
3
)
integral from 0 to 1 of (x^2)/((x+3)^2)
∫
0
1
x
2
(
x
+
3
)
2
dx
integral of e^{10x}*5x
∫
e
1
0
x
·
5
xdx
지역 x=4y,x=y^2-5
area
x
=
4
y
,
x
=
y
2
−
5
integral from-4 to 4 of (2x^7+1)
∫
−
4
4
(
2
x
7
+
1
)
dx
derivative (1/(y^2)-9/(y^4))(y+3y^3)
derivative
(
1
y
2
−
9
y
4
)
(
y
+
3
y
3
)
integral from 2 to 4 of f(x)
∫
2
4
f
(
x
)
dx
f^'(x)= 4/x
f
′
(
x
)
=
4
x
d/(dt)(sin(6t))
d
dt
(
sin
(
6
t
)
)
integral of 1/(sqrt(36x^2+2))
∫
1
√
3
6
x
2
+
2
dx
integral from 0 to 1/2 of cos^3(pix)
∫
0
1
2
cos
3
(
π
x
)
dx
derivative of (x^4+9x^2-7^8)
d
dx
(
(
x
4
+
9
x
2
−
7
)
8
)
derivative of ln((7x^{ln(2x)}))
d
dx
(
ln
(
(
7
x
)
ln
(
2
x
)
)
)
(\partial)/(\partial z)(8ze^{xyz})
∂
∂
z
(
8
ze
xyz
)
d/(dt)(ccos(t)+t^2sin(t))
d
dt
(
c
cos
(
t
)
+
t
2
sin
(
t
)
)
integral of 6/(x^2(x^2+25))
∫
6
x
2
(
x
2
+
2
5
)
dx
limit as x approaches 0 of x^2+x+1
lim
x
→
0
(
x
2
+
x
+
1
)
derivative y=x^6f(x)
derivative
y
=
x
6
f
(
x
)
e^{x-y}y^'=x-3
e
x
−
y
y
′
=
x
−
3
(\partial)/(\partial z)(x^2+y^2z)
∂
∂
z
(
x
2
+
y
2
z
)
laplace변환-8e^{pi-t}
laplacetransform
−
8
e
π
−
t
derivative (x^3+2x^2)^{-1}
derivative
(
x
3
+
2
x
2
)
−
1
sum from n=1 to infinity of arctan(n+1)
∑
n
=
1
∞
arctan
(
n
+
1
)
limit as z approaches i of z(z+1)
lim
z
→
i
(
z
(
z
+
1
)
)
derivative f(x)=ln(4x+1)
derivative
f
(
x
)
=
ln
(
4
x
+
1
)
derivative of 1/(ln^2(x))
d
dx
(
1
ln
2
(
x
)
)
integral of 1/(xsqrt(9x^2+16))
∫
1
x
√
9
x
2
+
1
6
dx
integral of t^2sqrt(t^3+1)
∫
t
2
√
t
3
+
1
dt
integral of (r^3)/(sqrt(4+r^2))
∫
r
3
√
4
+
r
2
dr
limit as x approaches 2-of (1-x)/(x-2)
lim
x
→
2
−
(
1
−
x
x
−
2
)
xy^'-2y=12x^2
xy
′
−
2
y
=
1
2
x
2
derivative of x^2+5x-8
d
dx
(
x
2
+
5
x
−
8
)
-18y^{''}-14y^'=0,y(3)=-3,y^'(3)=-3
−
1
8
y
′
′
−
1
4
y
′
=
0
,
y
(
3
)
=
−
3
,
y
′
(
3
)
=
−
3
integral of (3x)/(sqrt(x^2-11))
∫
3
x
√
x
2
−
1
1
dx
integral of (4xe^x+e^{4x})/(e^{3x)}
∫
4
xe
x
+
e
4
x
e
3
x
dx
integral from 1 to 4 of f(x)
∫
1
4
f
(
x
)
dx
derivative of x(x^5+1^3)
d
dx
(
x
(
x
5
+
1
)
3
)
(\partial)/(\partial y)(xe^y-ln(x))
∂
∂
y
(
xe
y
−
ln
(
x
)
)
derivative-x-1/x
derivative
−
x
−
1
x
limit as x approaches 0 of x^{-1}
lim
x
→
0
(
x
−
1
)
integral from-2 to 3 of (14)/(x^4)
∫
−
2
3
1
4
x
4
dx
derivative of xe^xsin(y)
d
dx
(
xe
x
sin
(
y
)
)
y^{''}+3y^'-7y=x^4e^x
y
′
′
+
3
y
′
−
7
y
=
x
4
e
x
지역 y=x^2-2x+2,y=4
area
y
=
x
2
−
2
x
+
2
,
y
=
4
limit as x approaches 0 of xcot(1/4 x)
lim
x
→
0
(
x
cot
(
1
4
x
)
)
x^{''}+2x^'+5x=0
x
′
′
+
2
x
′
+
5
x
=
0
derivative (e^x+e^{-x})/(e^x-e^{-x)}
derivative
e
x
+
e
−
x
e
x
−
e
−
x
integral of y/(sqrt(16-9y^4))
∫
y
√
1
6
−
9
y
4
dy
integral of (2x^3+x)(x^4+x^2)
∫
(
2
x
3
+
x
)
(
x
4
+
x
2
)
dx
derivative f(x)=-2x+7
derivative
f
(
x
)
=
−
2
x
+
7
integral of 7x^9-3x^6+10x^3
∫
7
x
9
−
3
x
6
+
1
0
x
3
dx
integral of 1/((x+1)^5)
∫
1
(
x
+
1
)
5
dx
limit as x approaches 0 of (e^{bx}-1)/x
lim
x
→
0
(
e
bx
−
1
x
)
limit as x approaches+1 of x/((x-1))
lim
x
→
+
1
(
x
(
x
−
1
)
)
limit as x approaches 0 of (x-6)/(x-2)
lim
x
→
0
(
x
−
6
x
−
2
)
(d^3)/(dx^3)(sqrt(1+x))
d
3
dx
3
(
√
1
+
x
)
(dy)/(dx)=12
dy
dx
=
1
2
derivative of x+1/(x+2)
d
dx
(
x
+
1
x
+
2
)
derivative f(x)=sqrt(x)(x+3)
derivative
f
(
x
)
=
√
x
(
x
+
3
)
derivative of sqrt(6-3x)
d
dx
(
√
6
−
3
x
)
1
..
1194
1195
1196
1197
1198
..
2459