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일반적인 미적분학 문제
implicit x^5+x^2y^3=0
implicit
x
5
+
x
2
y
3
=
0
integral of ((ln(x^7)))/x
∫
(
ln
(
x
7
)
)
x
dx
y^'=(3x^2-e^x)/(2y-5)
y
′
=
3
x
2
−
e
x
2
y
−
5
(\partial)/(\partial x)(sqrt(x^2+y^2+1))
∂
∂
x
(
√
x
2
+
y
2
+
1
)
derivative y=4ln(cos(x))
derivative
y
=
4
ln
(
cos
(
x
)
)
integral of (sqrt(x^2-4))/(x^4)
∫
√
x
2
−
4
x
4
dx
derivative (sqrt(x))/(x+6)
derivative
√
x
x
+
6
integral of (2x^2-3)^5x
∫
(
2
x
2
−
3
)
5
xdx
derivative y=24(x^3+6x)^{3/8}
derivative
y
=
2
4
(
x
3
+
6
x
)
3
8
integral of x(x-1)(3-x)
∫
x
(
x
−
1
)
(
3
−
x
)
dx
integral of 1/(\sqrt[8]{x)}
∫
1
8
√
x
dx
integral from 2 to 3 of x/(sqrt(x^2-1))
∫
2
3
x
√
x
2
−
1
dx
(\partial)/(\partial x)((2x)/(x^2+y^4))
∂
∂
x
(
2
x
x
2
+
y
4
)
integral of (e^{6x})/(e^{12x)+49}
∫
e
6
x
e
1
2
x
+
4
9
dx
(\partial)/(\partial x)(sin(z))
∂
∂
x
(
sin
(
z
)
)
tangent cos(3x)
tangent
cos
(
3
x
)
derivative y=(7x-1)/(8x+3)
derivative
y
=
7
x
−
1
8
x
+
3
(\partial)/(\partial x)(xe^{3y})
∂
∂
x
(
xe
3
y
)
derivative of 2x^2(x-4x^3)
d
dx
(
2
x
2
(
x
−
4
x
3
)
)
sum from n=0 to infinity of 2(-2/3)
∑
n
=
0
∞
2
(
−
2
3
)
(dx)/(dt)+t^3x^5+x/t =0
dx
dt
+
t
3
x
5
+
x
t
=
0
integral of x^2ln(x+4)
∫
x
2
ln
(
x
+
4
)
dx
derivative of e^{3x}cos(x+e^{3x}sin(x))
d
dx
(
e
3
x
cos
(
x
)
+
e
3
x
sin
(
x
)
)
integral of x^3e^{-x^2}
∫
x
3
e
−
x
2
dx
limit as x approaches+2 of 3x^2+4x-3
lim
x
→
+
2
(
3
x
2
+
4
x
−
3
)
지역 y=-x^2+2x+5,y=(x^2)/2-4x+5
area
y
=
−
x
2
+
2
x
+
5
,
y
=
x
2
2
−
4
x
+
5
limit as x approaches 0 of ln(1+1/x)
lim
x
→
0
(
ln
(
1
+
1
x
)
)
integral of e^{-7t}
∫
e
−
7
t
dt
16y^{''}+2y=0
1
6
y
′
′
+
2
y
=
0
derivative f(x)=-9x^2
derivative
f
(
x
)
=
−
9
x
2
derivative of x^2-2x^3
d
dx
(
x
2
−
2
x
3
)
derivative of (x^5/6)
d
dx
(
x
5
6
)
derivative sin((pix)/6)
derivative
sin
(
π
x
6
)
(dy)/(dx)=3
dy
dx
=
3
derivative f(x)=(-x^2-9)/((x^2-9)^2)
derivative
f
(
x
)
=
−
x
2
−
9
(
x
2
−
9
)
2
tangent 2x^2,\at x=1
tangent
2
x
2
,
at
x
=
1
integral from 3 to infinity of e^{-2x}
∫
3
∞
e
−
2
x
dx
integral of e^{-sx}*x
∫
e
−
sx
·
xdx
derivative f(x)=(x^2-9)/(x^2+3x)
derivative
f
(
x
)
=
x
2
−
9
x
2
+
3
x
지역 y=x,y=2xsqrt(100-x^2)
area
y
=
x
,
y
=
2
x
√
1
0
0
−
x
2
derivative f(x)=186.7
derivative
f
(
x
)
=
1
8
6
.
7
y^{''}-y^'+y=3sin(t)-15e^{2t}
y
′
′
−
y
′
+
y
=
3
sin
(
t
)
−
1
5
e
2
t
derivative of (9x-1^{-2})
d
dx
(
(
9
x
−
1
)
−
2
)
integral of (x^2)/(e^{x+1)}
∫
x
2
e
x
+
1
dx
derivative of x^{1/5}(x+6)
d
dx
(
x
1
5
(
x
+
6
)
)
integral of p^4ln(p)
∫
p
4
ln
(
p
)
dp
3(dx)/(dt)-6x=sin(2t),x(0)=1
3
dx
dt
−
6
x
=
sin
(
2
t
)
,
x
(
0
)
=
1
derivative of sqrt(x/y)
d
dx
(
√
x
y
)
derivative 1-sin^2(x)
derivative
1
−
sin
2
(
x
)
integral of (13xe^{2x})/((1+2x)^2)
∫
1
3
xe
2
x
(
1
+
2
x
)
2
dx
(\partial)/(\partial x)(3sin(x))
∂
∂
x
(
3
sin
(
x
)
)
integral of 4x^2-sin(x)+2
∫
4
x
2
−
sin
(
x
)
+
2
dx
derivative (1-4/(x+2))^3
derivative
(
1
−
4
x
+
2
)
3
tangent 5tan(x),\at x= pi/3
tangent
5
tan
(
x
)
,
at
x
=
π
3
derivative of arctan(x/y)
d
dx
(
arctan
(
x
y
)
)
maclaurin (x^2)/(e^x)
maclaurin
x
2
e
x
integral from 0 to 1 of e^{-4x}
∫
0
1
e
−
4
x
dx
derivative of Ce^{-2x}
d
dx
(
Ce
−
2
x
)
integral of 3^{sin(x)}cos(x)
∫
3
sin
(
x
)
cos
(
x
)
dx
P^'=kP
P
′
=
kP
derivative 9t
derivative
9
t
derivative of 16x^{3/2}
d
dx
(
1
6
x
3
2
)
derivative of 2x^{3/4}+4x^{-1/4}
d
dx
(
2
x
3
4
+
4
x
−
1
4
)
tangent (3x)/(x^2-6)(3.3)
tangent
3
x
x
2
−
6
(
3
.
3
)
integral of 1/(2-x)
∫
1
2
−
x
dx
지역 y^2= 1/8 x,y=8x^2
area
y
2
=
1
8
x
,
y
=
8
x
2
tangent f(x)=-x^3-5x^2+2,\at x=-1
tangent
f
(
x
)
=
−
x
3
−
5
x
2
+
2
,
at
x
=
−
1
단순화 e^{rx}
simplify
e
rx
derivative of (x^2-3x^2)
d
dx
(
(
x
2
−
3
x
)
2
)
integral from 1 to infinity of 4/(1+x^2)
∫
1
∞
4
1
+
x
2
dx
integral of 1/(2cos(x))
∫
1
2
cos
(
x
)
dx
derivative (110)/(x^{12)}
derivative
1
1
0
x
1
2
x^{''}=-9x
x
′
′
=
−
9
x
derivative of ((2x^2-x^{-2}/(4x+3))^{3/4})
d
dx
(
(
2
x
2
−
x
−
2
4
x
+
3
)
3
4
)
테일러 1/x ,4
taylor
1
x
,
4
integral of e^{8x-9}
∫
e
8
x
−
9
dx
tangent f(x)=ln(x),\at x=e^{-7}
tangent
f
(
x
)
=
ln
(
x
)
,
at
x
=
e
−
7
integral of 1/((1/3 x-8)^5)
∫
1
(
1
3
x
−
8
)
5
dx
(d^2)/(dx^2)(3x^2+4x)
d
2
dx
2
(
3
x
2
+
4
x
)
(\partial)/(\partial x)(xe^{sqrt(3xy)})
∂
∂
x
(
xe
√
3
xy
)
sum from n=1 to infinity of (5n)/(2n+1)
∑
n
=
1
∞
5
n
2
n
+
1
derivative of sqrt(18+x)
d
dx
(
√
1
8
+
x
)
integral of (3x+1)/(x^2+3x-10)
∫
3
x
+
1
x
2
+
3
x
−
1
0
dx
derivative (8e^{2w}+3e^w)/(e^w)
derivative
8
e
2
w
+
3
e
w
e
w
integral of (3x^2+5x-4)/((x^2-1)(x+1))
∫
3
x
2
+
5
x
−
4
(
x
2
−
1
)
(
x
+
1
)
dx
integral of 2/(3\sqrt[3]{x)}
∫
2
3
3
√
x
dx
(\partial)/(\partial x)(-4sin(x))
∂
∂
x
(
−
4
sin
(
x
)
)
derivative of ((-3x+1^4-5)^3)
d
dx
(
(
(
−
3
x
+
1
)
4
−
5
)
3
)
derivative of ((-2x-3^7)/((4x+2)^4))
d
dx
(
(
−
2
x
−
3
)
7
(
4
x
+
2
)
4
)
derivative 2-2x^2
derivative
2
−
2
x
2
integral of y/((y^2+1)^2)
∫
y
(
y
2
+
1
)
2
dy
sum from n=0 to infinity of (2n)/(3n+1)
∑
n
=
0
∞
2
n
3
n
+
1
y^'= y/(sqrt(t))+1
y
′
=
y
√
t
+
1
(dx)/(dt)=x(1-0.0008x)
dx
dt
=
x
(
1
−
0
.
0
0
0
8
x
)
derivative of (1/(x^2-5/(x^4))(x+7x^3))
d
dx
(
(
1
x
2
−
5
x
4
)
(
x
+
7
x
3
)
)
integral from 3 to 4 of 5log_{6}(t)
∫
3
4
5
log
6
(
t
)
dt
integral of 1/(3-y)
∫
1
3
−
y
dy
limit as x approaches 4 of (x^2-2)/(x-4)
lim
x
→
4
(
x
2
−
2
x
−
4
)
(dy)/(dx)-y=1
dy
dx
−
y
=
1
integral of 3cos(x)+e^{-x}+4
∫
3
cos
(
x
)
+
e
−
x
+
4
dx
1
..
1212
1213
1214
1215
1216
..
2459