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일반적인 미적분학 문제
(\partial)/(\partial x)(1.2x^{0.6}y^{0.4})
∂
∂
x
(
1
.
2
x
0
.
6
y
0
.
4
)
테일러 sin(x-pi/4)
taylor
sin
(
x
−
π
4
)
integral of u^n
∫
u
n
du
integral of 5/(x+2)-3/((x+2)^2)
∫
5
x
+
2
−
3
(
x
+
2
)
2
dx
integral of x^2(1+x^3)^{1/4}
∫
x
2
(
1
+
x
3
)
1
4
dx
(\partial)/(\partial x)(5xy^2)
∂
∂
x
(
5
xy
2
)
derivative f(x)=2x^2-6x^{1/3}
derivative
f
(
x
)
=
2
x
2
−
6
x
1
3
지역 y=3x(-x+1),y=-3x
area
y
=
3
x
(
−
x
+
1
)
,
y
=
−
3
x
derivative of e^{mx}
d
dx
(
e
mx
)
derivative 7+2x+x^3(5x^2+1)^5
derivative
7
+
2
x
+
x
3
(
5
x
2
+
1
)
5
limit as x approaches 0 of 1/(3xsin(x))
lim
x
→
0
(
1
3
x
sin
(
x
)
)
derivative of ln(sqrt((3x^4+2/(4x))))
d
dx
(
ln
(
√
3
x
4
+
2
4
x
)
)
integral of (cos(x))/(x^2)
∫
cos
(
x
)
x
2
dx
derivative 6^{4-x^2}
derivative
6
4
−
x
2
derivative of (2-3x-x^2/(x^2-4))
d
dx
(
2
−
3
x
−
x
2
x
2
−
4
)
(dy)/(dx)=4e^{3x-4y}
dy
dx
=
4
e
3
x
−
4
y
derivative of 6/(2^x)
d
dx
(
6
2
x
)
derivative of x/(sqrt(x+5))
d
dx
(
x
√
x
+
5
)
x(dy)/(dx)=y(y+1)
x
dy
dx
=
y
(
y
+
1
)
tangent f(x)=(6x)/(x+2),(4,4)
tangent
f
(
x
)
=
6
x
x
+
2
,
(
4
,
4
)
derivative f(x)=-1/6 (x^{-6}+x^{12})
derivative
f
(
x
)
=
−
1
6
(
x
−
6
+
x
1
2
)
derivative (x^2-36)/(x-6)
derivative
x
2
−
3
6
x
−
6
y^{''}+y=sin(2x)
y
′
′
+
y
=
sin
(
2
x
)
derivative of (2x^2-1+(5x-6))
d
dx
(
(
2
x
2
−
1
)
+
(
5
x
−
6
)
)
f(x)=12x^2
f
(
x
)
=
1
2
x
2
(\partial)/(\partial x)(10x^{1/4}*2y^{3/4})
∂
∂
x
(
1
0
x
1
4
·
2
y
3
4
)
limit as x approaches 1 of 4x^2-2x-6
lim
x
→
1
(
4
x
2
−
2
x
−
6
)
integral of (1-x)^{3/2}
∫
(
1
−
x
)
3
2
dx
derivative sec^5(x)
derivative
sec
5
(
x
)
integral from 1200 to 1210 of x*0.1
∫
1
2
0
0
1
2
1
0
x
·
0
.
1
dx
derivative ((4x^3+5)/(-5x^2+1))^{1/4}
derivative
(
4
x
3
+
5
−
5
x
2
+
1
)
1
4
derivative (x^2)/(5(4-x))
derivative
x
2
5
(
4
−
x
)
integral from-3 to 0 of 1/(sqrt(1-x))
∫
−
3
0
1
√
1
−
x
dx
integral of-x^2y^2sin(x)+2xy^2cos(x)
∫
−
x
2
y
2
sin
(
x
)
+
2
xy
2
cos
(
x
)
dx
경사지 (-10,9),(-2,-5)
slope
(
−
1
0
,
9
)
,
(
−
2
,
−
5
)
inverse라플라스 {(10)/(s(s+2))}
inverselaplace
{
1
0
s
(
s
+
2
)
}
derivative of 7(x^3-x^4)
d
dx
(
7
(
x
3
−
x
)
4
)
integral of (3x^4-5x)
∫
(
3
x
4
−
5
x
)
dx
derivative of 6x+29cos((3x/4)+5x^2+3)
d
dx
(
6
x
+
2
9
cos
(
3
x
4
)
+
5
x
2
+
3
)
integral of (2x-3)^5
∫
(
2
x
−
3
)
5
dx
limit as y approaches x of (y^{2/3}-x^{2/3})/(y-x)
lim
y
→
x
(
y
2
3
−
x
2
3
y
−
x
)
tangent f(x)=x^2,\at x=5
tangent
f
(
x
)
=
x
2
,
at
x
=
5
integral of sqrt(1-cos(4x))
∫
√
1
−
cos
(
4
x
)
dx
derivative of 1+xsqrt(x)
d
dx
(
1
+
x
√
x
)
derivative 5/(2x^6)
derivative
5
2
x
6
limit as x approaches-2 of (x+1)^7(3x^2)
lim
x
→
−
2
(
(
x
+
1
)
7
(
3
x
2
)
)
integral of-x/y
∫
−
x
y
dx
y^'ln(y)+x^2y=0
y
′
ln
(
y
)
+
x
2
y
=
0
지역 x=y,x=y^2
area
x
=
y
,
x
=
y
2
integral of (19-19x)/(1-sqrt(x))
∫
1
9
−
1
9
x
1
−
√
x
dx
integral of 3/(x^2sqrt(x^2+16))
∫
3
x
2
√
x
2
+
1
6
dx
sum from n=1 to infinity of 1/(n+1000)
∑
n
=
1
∞
1
n
+
1
0
0
0
d/(dt)((3t^2)/(1+t^3))
d
dt
(
3
t
2
1
+
t
3
)
derivative of x^3+6x^2+8x-96
d
dx
(
x
3
+
6
x
2
+
8
x
−
9
6
)
integral of 1/((x-8)^2)
∫
1
(
x
−
8
)
2
dx
(\partial)/(\partial y)(1/(1+e^{-x-2y)})
∂
∂
y
(
1
1
+
e
−
x
−
2
y
)
derivative of 3(5-8x^5)
d
dx
(
3
(
5
−
8
x
)
5
)
derivative of sqrt(6x+3)
d
dx
(
√
6
x
+
3
)
limit as x approaches 3 of 2x^2-4x+5
lim
x
→
3
(
2
x
2
−
4
x
+
5
)
derivative of In(x+1)
d
dx
(
In
(
x
+
1
)
)
derivative f(x)=4pix^2
derivative
f
(
x
)
=
4
π
x
2
inverse라플라스 ((e^{-s}))/(s^2-4)
inverselaplace
(
e
−
s
)
s
2
−
4
derivative of e^{2x}cos(2x)
d
dx
(
e
2
x
cos
(
2
x
)
)
limit as h approaches 0 of (1+h/x)^{1/h}
lim
h
→
0
(
(
1
+
h
x
)
1
h
)
derivative of 6x^{-5/6}
d
dx
(
6
x
−
5
6
)
(\partial)/(\partial x)(5x+2y)
∂
∂
x
(
5
x
+
2
y
)
limit as x approaches 0 of x^{-5}
lim
x
→
0
(
x
−
5
)
derivative 1/(2sqrt(x))-5/(2x^{3/2)}
derivative
1
2
√
x
−
5
2
x
3
2
derivative f(x)= x/(x+a/x)
derivative
f
(
x
)
=
x
x
+
a
x
integral of e^x+sin(x)
∫
e
x
+
sin
(
x
)
dx
derivative y=(2x^2+2x+4)/(sqrt(x))
derivative
y
=
2
x
2
+
2
x
+
4
√
x
integral of (10)/(x^3)
∫
1
0
x
3
dx
integral of (2x-1)/x
∫
2
x
−
1
x
dx
integral from 0 to 1 of 3x5^x
∫
0
1
3
x
5
x
dx
y^{''}+2y^'-10y=0
y
′
′
+
2
y
′
−
1
0
y
=
0
derivative of x^{10}e^xcsc(x)
d
dx
(
x
1
0
e
x
csc
(
x
)
)
limit as x approaches 0 of 7sin(x)ln(x)
lim
x
→
0
(
7
sin
(
x
)
ln
(
x
)
)
tangent f(x)=4sqrt(x),\at x=2
tangent
f
(
x
)
=
4
√
x
,
at
x
=
2
integral from 1 to 8 of sqrt(x)ln(x)
∫
1
8
√
x
ln
(
x
)
dx
limit as x approaches 0 of (|x-1|)/(x-1)
lim
x
→
0
(
|
x
−
1
|
x
−
1
)
f(x)=sin^2(3x+2)
f
(
x
)
=
sin
2
(
3
x
+
2
)
(e^{2x}+e^{-x})^'
(
e
2
x
+
e
−
x
)
′
경사지 y=-3-5x^2
slope
y
=
−
3
−
5
x
2
laplace변환 tcos(3t)
laplacetransform
t
cos
(
3
t
)
integral of-x^{2/3}
∫
−
x
2
3
dx
integral from 0 to 24 of sqrt(6x)
∫
0
2
4
√
6
x
dx
derivative of 3xln(2x)
d
dx
(
3
x
ln
(
2
x
)
)
tangent f(2.1)=3x^2-4x+1,(2,0)
tangent
f
(
2
.
1
)
=
3
x
2
−
4
x
+
1
,
(
2
,
0
)
integral of cos(x)sin^3(x)
∫
cos
(
x
)
sin
3
(
x
)
dx
derivative (e^{y^2})/((2y+1)^5)
derivative
e
y
2
(
2
y
+
1
)
5
derivative of 2/3 x^{3/2}-1/2 x^{1/2}
d
dx
(
2
3
x
3
2
−
1
2
x
1
2
)
integral of ((1-2x))/(x^2)
∫
(
1
−
2
x
)
x
2
dx
derivative of 1/4 e^{-x}+e^x
d
dx
(
1
4
e
−
x
+
e
x
)
derivative f(x)=xsqrt(x+1)
derivative
f
(
x
)
=
x
√
x
+
1
limit as x approaches 0 of (7^x-1)/x
lim
x
→
0
(
7
x
−
1
x
)
integral of ((5+sqrt(x)+x))/x
∫
(
5
+
√
x
+
x
)
x
dx
y^{''}+y=3sec^3(t)
y
′
′
+
y
=
3
sec
3
(
t
)
integral from-11 to-4 of 1/x
∫
−
1
1
−
4
1
x
dx
limit as x approaches 0-of ([x])/x
lim
x
→
0
−
(
[
x
]
x
)
integral from 0 to 9 of pi(x-1)
∫
0
9
π
(
x
−
1
)
dx
1
..
1202
1203
1204
1205
1206
..
2459