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일반적인 미적분학 문제
(\partial)/(\partial x)(\sqrt[3]{x^4})
∂
∂
x
(
3
√
x
4
)
derivative of ((x^3/(x^8+9))^2)
d
dx
(
(
x
3
x
8
+
9
)
2
)
2yy^'+2=y^2+2x
2
yy
′
+
2
=
y
2
+
2
x
derivative of (x^2/4)
d
dx
(
x
2
4
)
derivative (sin(x))/x
derivative
sin
(
x
)
x
integral of (12)/(x^4)
∫
1
2
x
4
dx
derivative arctan(x/2)
derivative
arctan
(
x
2
)
(dy)/(dx)-50y=-y^2
dy
dx
−
5
0
y
=
−
y
2
integral from 2 to x of 1/8 (x-2)
∫
2
x
1
8
(
x
−
2
)
dx
sum from n=1 to infinity of (-6)^nx^n
∑
n
=
1
∞
(
−
6
)
n
x
n
integral of (x^2)/(1-2x^3)
∫
x
2
1
−
2
x
3
dx
derivative of (e^x/(7x^2+9))
d
dx
(
e
x
7
x
2
+
9
)
limit as x approaches-7 of 12
lim
x
→
−
7
(
1
2
)
derivative x^2-8x+17
derivative
x
2
−
8
x
+
1
7
integral of (x^2+5)(x-3)
∫
(
x
2
+
5
)
(
x
−
3
)
dx
derivative x/(sqrt(x^2+1))
derivative
x
√
x
2
+
1
integral of e^{-st}*t^2
∫
e
−
st
·
t
2
dt
integral of 3x^2-4
∫
3
x
2
−
4
dx
지역 5x-x^2,2x,[0,3]
area
5
x
−
x
2
,
2
x
,
[
0
,
3
]
derivative of arcsec(x+3)
d
dx
(
arcsec
(
x
+
3
)
)
integral of 2sin^3(3xco)s^33x
∫
2
sin
3
(
3
xco
)
s
3
3
xdx
integral of x^4e^{-x}
∫
x
4
e
−
x
dx
(\partial)/(\partial t)(-t)
∂
∂
t
(
−
t
)
tangent f(x)=sqrt(1-x),\at x=0
tangent
f
(
x
)
=
√
1
−
x
,
at
x
=
0
limit as x approaches 0 of 5
lim
x
→
0
(
5
)
(dy)/(dx)=e^y(x^2-x)
dy
dx
=
e
y
(
x
2
−
x
)
derivative of (2x/(9-tan(x)))
d
dx
(
2
x
9
−
tan
(
x
)
)
sum from n=1 to infinity of 4(2/3)^n
∑
n
=
1
∞
4
(
2
3
)
n
derivative of-2sin(4x)
d
dx
(
−
2
sin
(
4
x
)
)
integral of (sqrt(x^2-169))/x
∫
√
x
2
−
1
6
9
x
dx
derivative of (-2/(x^2))
d
dx
(
−
2
x
2
)
derivative ln(1+5x)
derivative
ln
(
1
+
5
x
)
implicit (dy)/(dx),y=13^x
implicit
dy
dx
,
y
=
1
3
x
derivative of-2/(sqrt(e^x))
d
dx
(
−
2
√
e
x
)
derivative of (cos(x)/(e^x))
d
dx
(
cos
(
x
)
e
x
)
derivative of x^4-2x^2+1
d
dx
(
x
4
−
2
x
2
+
1
)
limit as x approaches infinity of x^{-3}
lim
x
→
∞
(
x
−
3
)
limit as x approaches pi+of x/(sin(x))
lim
x
→
π
+
(
x
sin
(
x
)
)
derivative of 15ln(x)
d
dx
(
1
5
ln
(
x
)
)
derivative f(x)=8x(x^2+3)^3
derivative
f
(
x
)
=
8
x
(
x
2
+
3
)
3
derivative sin^8(x)
derivative
sin
8
(
x
)
integral of (e^{2x})/4
∫
e
2
x
4
dx
(\partial)/(\partial x)(xy^2e^{3x^2y-y^2})
∂
∂
x
(
xy
2
e
3
x
2
y
−
y
2
)
derivative of 3e^2
d
dx
(
3
e
2
)
derivative ((sqrt(x)+x))/(x^2)
derivative
(
√
x
+
x
)
x
2
integral of x^3sqrt(x^2+20)
∫
x
3
√
x
2
+
2
0
dx
integral of (7x^3)/(sqrt(3+x^2))
∫
7
x
3
√
3
+
x
2
dx
inverse라플라스 8/(9s^2+9s+4)
inverselaplace
8
9
s
2
+
9
s
+
4
derivative (x^2+32sqrt(x))/8
derivative
x
2
+
3
2
√
x
8
inverse라플라스 8/(s-1)-3/s
inverselaplace
8
s
−
1
−
3
s
derivative (2x^2)+(sqrt(x-8))
derivative
(
2
x
2
)
+
(
√
x
−
8
)
limit as x approaches 5 of (x+5)/(x-5)
lim
x
→
5
(
x
+
5
x
−
5
)
limit as x approaches 0 of x/(x^2+4x)
lim
x
→
0
(
x
x
2
+
4
x
)
sum from n=1 to infinity of (1-3/n)^n
∑
n
=
1
∞
(
1
−
3
n
)
n
integral of (e^{x/2})
∫
(
e
x
2
)
dx
(\partial)/(\partial x)(2xyz-ye^{2xyz})
∂
∂
x
(
2
xyz
−
ye
2
xyz
)
경사지 (3.1)(1.7)
slope
(
3
.
1
)
(
1
.
7
)
sum from n=1 to infinity of (-3)^nx^n
∑
n
=
1
∞
(
−
3
)
n
x
n
derivative of-sin(x^22x)
d
dx
(
−
sin
(
x
2
)
2
x
)
(dy)/(dx)+9(tan(9x))y=cos(9x)
dy
dx
+
9
(
tan
(
9
x
)
)
y
=
cos
(
9
x
)
limit as x approaches 4-of (|2x|)/x
lim
x
→
4
−
(
|
2
x
|
x
)
derivative-32t
derivative
−
3
2
t
derivative of sqrt(2)cos(x)
d
dx
(
√
2
cos
(
x
)
)
tangent f(x)=sqrt(7-4x),\at x=-1
tangent
f
(
x
)
=
√
7
−
4
x
,
at
x
=
−
1
integral of sqrt(1+cos(2x))
∫
√
1
+
cos
(
2
x
)
dx
(d^2y)/(dx^2)+5(dy)/(dx)+4y=0
d
2
y
dx
2
+
5
dy
dx
+
4
y
=
0
(dy)/(dx)=y^2(x+1)
dy
dx
=
y
2
(
x
+
1
)
integral of 1/(9e^y+e^{-y)}
∫
1
9
e
y
+
e
−
y
dy
derivative of (\sqrt[5]{x^2}/(sin(x)))
d
dx
(
5
√
x
2
sin
(
x
)
)
sum from n=1 to infinity of (2^n)/(n^3)
∑
n
=
1
∞
2
n
n
3
derivative of x^2+10x+25
d
dx
(
x
2
+
1
0
x
+
2
5
)
integral of (sin(3x))^2
∫
(
sin
(
3
x
)
)
2
dx
(\partial)/(\partial x)(-yln(y)sin(xln(y)))
∂
∂
x
(
−
y
ln
(
y
)
sin
(
x
ln
(
y
)
)
)
limit as x approaches-1 of x^2-2ln(x)
lim
x
→
−
1
(
x
2
−
2
ln
(
x
)
)
(\partial)/(\partial x)(4z-18xy)
∂
∂
x
(
4
z
−
1
8
xy
)
integral of (1+cos(7x))/6
∫
1
+
cos
(
7
x
)
6
dx
y^{1/2}(dy)/(dx)+y^{3/2}=1
y
1
2
dy
dx
+
y
3
2
=
1
(\partial)/(\partial x)((x^2)/(1+t^2))
∂
∂
x
(
x
2
1
+
t
2
)
integral of 8cos^4(x)
∫
8
cos
4
(
x
)
dx
integral of 12x^2+2
∫
1
2
x
2
+
2
dx
integral of (x^4)/(sqrt(4x^2-9))
∫
x
4
√
4
x
2
−
9
dx
derivative x^2-5x+3
derivative
x
2
−
5
x
+
3
limit as x approaches-1 of (x-31)^{2/5}
lim
x
→
−
1
(
(
x
−
3
1
)
2
5
)
(\partial)/(\partial x)(x^{x^2+y^2+z^2})
∂
∂
x
(
x
x
2
+
y
2
+
z
2
)
sin(2x)dx+cos(6y)dy=0,y(pi/2)= pi/6
sin
(
2
x
)
dx
+
cos
(
6
y
)
dy
=
0
,
y
(
π
2
)
=
π
6
integral of e^{3x+5}
∫
e
3
x
+
5
dx
(\partial)/(\partial y)((xy^2)/(x^2+y^2))
∂
∂
y
(
xy
2
x
2
+
y
2
)
integral of 1/(x^{-0.1)}
∫
1
x
−
0
.
1
dx
limit as x approaches infinity of x*(arctan(e^x)-pi/2)
lim
x
→
∞
(
x
·
(
arctan
(
e
x
)
−
π
2
)
)
(d^2)/(dx^2)(e^{-2x})
d
2
dx
2
(
e
−
2
x
)
integral of 1/((x^4-1)^2)
∫
1
(
x
4
−
1
)
2
dx
동등성 y=sqrt(x+\sqrt{x+\sqrt{x)}}
parity
y
=
√
x
+
√
x
+
√
x
(\partial)/(\partial y)(-e^{-x}sin(yz))
∂
∂
y
(
−
e
−
x
sin
(
yz
)
)
integral of 1/(v^2+2v)
∫
1
v
2
+
2
v
dv
integral of 1/((x^2+1)^{3/2)}
∫
1
(
x
2
+
1
)
3
2
dx
derivative of-(3x+2cos(2x))
d
dx
(
−
(
3
x
+
2
)
cos
(
2
x
)
)
f(x)=sin(x)+1/2 cot(x)
f
(
x
)
=
sin
(
x
)
+
1
2
cot
(
x
)
sum from n=0 to infinity of n/(2n+4)
∑
n
=
0
∞
n
2
n
+
4
integral of-(sin(x)tan(x))/1
∫
−
sin
(
x
)
tan
(
x
)
1
dx
(dy)/(dt)-(4t)/((1+4t^2))y=4t
dy
dt
−
4
t
(
1
+
4
t
2
)
y
=
4
t
1
..
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