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일반적인 미적분학 문제
y^'=(x-3)/(y+1)
y
′
=
x
−
3
y
+
1
(\partial)/(\partial x)(4x^3y^3-1)
∂
∂
x
(
4
x
3
y
3
−
1
)
integral of 4cos(3x)
∫
4
cos
(
3
x
)
dx
integral of 7t^4
∫
7
t
4
dt
integral of (x^2)/(x+1)
∫
x
2
x
+
1
dx
derivative (0.07e^x)/(sin(x))
derivative
0
.
0
7
e
x
sin
(
x
)
sum from k=1 to infinity of k/(7^k)
∑
k
=
1
∞
k
7
k
derivative of x(arcsin(x)^2)
d
dx
(
x
(
arcsin
(
x
)
)
2
)
derivative 8e^x
derivative
8
e
x
limit as x approaches infinity of 2x^3-1
lim
x
→
∞
(
2
x
3
−
1
)
(dy)/(dx)=((1+xy))/(1+x)
dy
dx
=
(
1
+
xy
)
1
+
x
derivative x/(x+9)
derivative
x
x
+
9
integral of (e^{2x}+3)^4*e^{2x}
∫
(
e
2
x
+
3
)
4
·
e
2
x
dx
y^{''}+121y=cos(4t)
y
′
′
+
1
2
1
y
=
cos
(
4
t
)
derivative of 9e^x+8/(\sqrt[3]{x})
d
dx
(
9
e
x
+
8
3
√
x
)
d/(dt)(10te^{-5t})
d
dt
(
1
0
te
−
5
t
)
테일러 ln(1-4y),0
taylor
ln
(
1
−
4
y
)
,
0
xy^'=y+sqrt(x^2+y^2)
xy
′
=
y
+
√
x
2
+
y
2
integral of-5x^3
∫
−
5
x
3
dx
limit as x approaches 0 of (sin(kt))/t
lim
x
→
0
(
sin
(
kt
)
t
)
tangent 5x^3
tangent
5
x
3
limit as x approaches-1 of ln(x^2-1)
lim
x
→
−
1
(
ln
(
x
2
−
1
)
)
테일러 (2^k)/(3k)x^k
taylor
2
k
3
k
x
k
derivative of 2sec(cos(x))
d
dx
(
2
sec
(
cos
(
x
)
)
)
derivative of 3a^2x
d
dx
(
3
a
2
x
)
derivative qx+r
derivative
qx
+
r
derivative f(x)=-(18)/(x^3)
derivative
f
(
x
)
=
−
1
8
x
3
derivative of 2*tan(x)
d
dx
(
2
·
tan
(
x
)
)
derivative ln(6x)
derivative
ln
(
6
x
)
(\partial)/(\partial c)(16dc^2)
∂
∂
c
(
1
6
dc
2
)
(dy)/(dx)+y/x =3x^3y^2
dy
dx
+
y
x
=
3
x
3
y
2
integral of 3sec^2(x)+2
∫
3
sec
2
(
x
)
+
2
dx
(\partial)/(\partial y)(xye^{7y})
∂
∂
y
(
xye
7
y
)
3x^2y^2dx+(2x^3y+4y^3)dy=0
3
x
2
y
2
dx
+
(
2
x
3
y
+
4
y
3
)
dy
=
0
(dy)/(dx)+(5/x)y=-2x-2
dy
dx
+
(
5
x
)
y
=
−
2
x
−
2
integral from 0 to 1 of 10cos(x^2)
∫
0
1
1
0
cos
(
x
2
)
dx
integral of (x+3)(x-5)
∫
(
x
+
3
)
(
x
−
5
)
dx
integral from 2 to 6 of 1/(sqrt(3x-2))
∫
2
6
1
√
3
x
−
2
dx
d/(dt)(2cos(t)+2sin(t))
d
dt
(
2
cos
(
t
)
+
2
sin
(
t
)
)
derivative F(x)=(9x^6+4x^3)^4
derivative
F
(
x
)
=
(
9
x
6
+
4
x
3
)
4
y^{''}-2y^'-3y=16x^2e^{-x}
y
′
′
−
2
y
′
−
3
y
=
1
6
x
2
e
−
x
y^{''}+4y^'+5y=e^x+5x
y
′
′
+
4
y
′
+
5
y
=
e
x
+
5
x
inverse라플라스 1/((s^2+4)*s^2*e)
inverselaplace
1
(
s
2
+
4
)
·
s
2
·
e
(\partial)/(\partial x)(sec^2(x))
∂
∂
x
(
sec
2
(
x
)
)
(\partial)/(\partial x)(6x^2)
∂
∂
x
(
6
x
2
)
tangent f(x)=3x*cos(x),\at x=pi
tangent
f
(
x
)
=
3
x
·
cos
(
x
)
,
at
x
=
π
integral of 3cos(nx)
∫
3
cos
(
nx
)
dx
integral of (x-1)/2
∫
x
−
1
2
dx
integral of x^4*ln(x)
∫
x
4
·
ln
(
x
)
dx
integral of i/x
∫
i
x
dx
derivative of ln(x^2-10x)
d
dx
(
ln
(
x
2
−
1
0
x
)
)
(\partial)/(\partial x)(e^{-x/a})
∂
∂
x
(
e
−
x
a
)
(\partial)/(\partial y)(2x+3y-4)
∂
∂
y
(
2
x
+
3
y
−
4
)
(\partial)/(\partial y)(e^xy^3+2ye^{2x})
∂
∂
y
(
e
x
y
3
+
2
ye
2
x
)
(dy)/(dx)=-y/(10)
dy
dx
=
−
y
1
0
tangent f(x)=x^2-8,(2,-4)
tangent
f
(
x
)
=
x
2
−
8
,
(
2
,
−
4
)
integral of tan(x)sqrt(1+sec^4(x))
∫
tan
(
x
)
√
1
+
sec
4
(
x
)
dx
derivative sin(ax)
derivative
sin
(
ax
)
integral of tan^5(x)sec^4(x)
∫
tan
5
(
x
)
sec
4
(
x
)
dx
integral of t/(sqrt(t+1))
∫
t
√
t
+
1
dt
dy+e^{3y}dx=0
dy
+
e
3
y
dx
=
0
derivative of 4sec(x-3x)
d
dx
(
4
sec
(
x
)
−
3
x
)
integral of (x^2-2)^2
∫
(
x
2
−
2
)
2
dx
derivative of (x^6-1/(x-1))
d
dx
(
x
6
−
1
x
−
1
)
integral from 0 to 1 of 3x^4e^{-x}
∫
0
1
3
x
4
e
−
x
dx
경사지 y=-5x^2,(1,-5)
slope
y
=
−
5
x
2
,
(
1
,
−
5
)
derivative 20ln(3x+1)-x/3
derivative
2
0
ln
(
3
x
+
1
)
−
x
3
derivative y=8x-x^2
derivative
y
=
8
x
−
x
2
integral of 1/(2e^x)
∫
1
2
e
x
dx
integral from 0 to 8 of x/(sqrt(x^2+36))
∫
0
8
x
√
x
2
+
3
6
dx
derivative of sqrt(x/(1-x))
d
dx
(
√
x
1
−
x
)
derivative of (sqrt(x^2-1)/x)
d
dx
(
√
x
2
−
1
x
)
inverse라플라스 (e^{-5s})/(s^2-4s+13)
inverselaplace
e
−
5
s
s
2
−
4
s
+
1
3
y^{''}=2+x
y
′
′
=
2
+
x
(1+x)(dy)/(dx)=4y
(
1
+
x
)
dy
dx
=
4
y
x(x-2)(dy)/(dx)+2y=0
x
(
x
−
2
)
dy
dx
+
2
y
=
0
derivative of 4x^3+1/(x^2)
d
dx
(
4
x
3
+
1
x
2
)
limit as x approaches 0 of-x^8
lim
x
→
0
(
−
x
8
)
derivative of ((x+4/(x-4))^5)
d
dx
(
(
x
+
4
x
−
4
)
5
)
integral of 1/x x
∫
1
x
xdx
integral of (1+cos(2x))
∫
(
1
+
cos
(
2
x
)
)
dx
limit as x approaches 1 of 2-1/x
lim
x
→
1
(
2
−
1
x
)
integral of (sqrt(x^2-36))/x
∫
√
x
2
−
3
6
x
dx
derivative ((1-3x))/(2+x)
derivative
(
1
−
3
x
)
2
+
x
derivative of 8sin(x-x)
d
dx
(
8
sin
(
x
)
−
x
)
derivative of ({f}(x{g}(x))/({f)(x)-{g}(x)})
d
dx
(
f
(
x
)
g
(
x
)
f
(
x
)
−
g
(
x
)
)
integral of e^{-xy}sin(x)
∫
e
−
xy
sin
(
x
)
dx
integral of xsin(3x+1)
∫
x
sin
(
3
x
+
1
)
dx
inverse라플라스 (e^{-pis})/(s^3+s)
inverselaplace
e
−
π
s
s
3
+
s
y^'=0.5x-450
y
′
=
0
.
5
x
−
4
5
0
limit as x approaches-1 of (2-5x)/(2+2x)
lim
x
→
−
1
(
2
−
5
x
2
+
2
x
)
derivative of 3x^5ln(x)
d
dx
(
3
x
5
ln
(
x
)
)
tangent f(x)=(4x^2)/(x+2)
tangent
f
(
x
)
=
4
x
2
x
+
2
derivative 3+6cos(3t)
derivative
3
+
6
cos
(
3
t
)
derivative-1/2 t^4+48t^2
derivative
−
1
2
t
4
+
4
8
t
2
tangent f(x)= 1/x ,\at x=2
tangent
f
(
x
)
=
1
x
,
at
x
=
2
derivative of (dy/(dx))+4y=2sin(2x)
d
dx
(
dy
dx
)
+
4
y
=
2
sin
(
2
x
)
2x^{''}+12x^'+50x=0
2
x
′
′
+
1
2
x
′
+
5
0
x
=
0
테일러 80*22^{t/(20)}
taylor
8
0
·
2
2
t
2
0
integral of 6/(9+6x)
∫
6
9
+
6
x
dx
1
..
1483
1484
1485
1486
1487
..
2459