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일반적인 미적분학 문제
(\partial)/(\partial y)(x^2*sin(2y))
∂
∂
y
(
x
2
·
sin
(
2
y
)
)
derivative f(x)=sqrt(x)-\sqrt[3]{x}
derivative
f
(
x
)
=
√
x
−
3
√
x
derivative f(x)=x^2+x-9
derivative
f
(
x
)
=
x
2
+
x
−
9
limit as x approaches 1/8 of 1/x+x^{-1}
lim
x
→
1
8
(
1
x
+
x
−
1
)
integral of 1/(t^2+9)
∫
1
t
2
+
9
dt
implicit (dy)/(dx),x^2+y^2=36
implicit
dy
dx
,
x
2
+
y
2
=
3
6
integral of (4x^3+x^2)(3x^4+x^3)^8
∫
(
4
x
3
+
x
2
)
(
3
x
4
+
x
3
)
8
dx
integral of 1/(z^3sqrt(z^2-100))
∫
1
z
3
√
z
2
−
1
0
0
dz
(\partial)/(\partial x)(x^2y-3xy+xy^2)
∂
∂
x
(
x
2
y
−
3
xy
+
xy
2
)
integral of ln^2(x^2)
∫
ln
2
(
x
2
)
dx
integral of (2-1/x)ln(x)
∫
(
2
−
1
x
)
ln
(
x
)
dx
derivative of 10sin(x+10sqrt(3)cos(x))
d
dx
(
1
0
sin
(
x
)
+
1
0
√
3
cos
(
x
)
)
tangent y=9x-6sqrt(x),(1,3)
tangent
y
=
9
x
−
6
√
x
,
(
1
,
3
)
limit as x approaches 1 of x^4-1
lim
x
→
1
(
x
4
−
1
)
integral of (x^5-x^4+4x^2-x)/(x^3+1)
∫
x
5
−
x
4
+
4
x
2
−
x
x
3
+
1
dx
limit as x approaches 0 of xcos(7/x)
lim
x
→
0
(
x
cos
(
7
x
)
)
derivative (sqrt(x)+x)/(x^2)
derivative
√
x
+
x
x
2
derivative of ln(4+x)
d
dx
(
ln
(
4
+
x
)
)
integral of xe^x-e^x
∫
xe
x
−
e
x
dx
(dy)/(dx)=2xy+6/(sqrt(pi))
dy
dx
=
2
xy
+
6
√
π
integral of 1/(x^4sqrt(9-x^2))
∫
1
x
4
√
9
−
x
2
dx
sum from n=1 to infinity of 1-3/(7^n)
∑
n
=
1
∞
1
−
3
7
n
(dy)/(dt)= 1/2 t
dy
dt
=
1
2
t
y^{''}+6y^'+9y=12e^{-3x}
y
′
′
+
6
y
′
+
9
y
=
1
2
e
−
3
x
integral of 50sin(120pi)x
∫
5
0
sin
(
1
2
0
π
)
xdx
x*dy=dx,y(-1)=3
x
·
dy
=
dx
,
y
(
−
1
)
=
3
derivative of 7^xlog_{7}(x)
d
dx
(
7
x
log
7
(
x
)
)
(\partial)/(\partial x)(8x^2-7x+4)
∂
∂
x
(
8
x
2
−
7
x
+
4
)
확장 2e^{-x}x-e^{-x}(x^2-8)
expand
2
e
−
x
x
−
e
−
x
(
x
2
−
8
)
integral of xsin(y)
∫
x
sin
(
y
)
dy
integral of (-2)/(x^3-x)
∫
−
2
x
3
−
x
dx
integral from 1 to b of 1/((x+4)^2)
∫
1
b
1
(
x
+
4
)
2
dx
integral of 1/6 sin(6t)
∫
1
6
sin
(
6
t
)
dt
f(x)=sqrt(3+x^2)
f
(
x
)
=
√
3
+
x
2
tangent y=sqrt(x^2-x+2),\at x=2
tangent
y
=
√
x
2
−
x
+
2
,
at
x
=
2
derivative of (x+3^2)
d
dx
(
(
x
+
3
)
2
)
limit as x approaches 0 of xsin(8/x)
lim
x
→
0
(
x
sin
(
8
x
)
)
(6+x)(dy)/(dx)=3y
(
6
+
x
)
dy
dx
=
3
y
derivative of 4/(x+2)
d
dx
(
4
x
+
2
)
(\partial)/(\partial x)(sqrt(4x^2+y^2))
∂
∂
x
(
√
4
x
2
+
y
2
)
integral of (2-u)/(u^2+2u+3)
∫
2
−
u
u
2
+
2
u
+
3
du
limit as x approaches 4-of 2x-5
lim
x
→
4
−
(
2
x
−
5
)
derivative f(1)=x^6+4e^x
derivative
f
(
1
)
=
x
6
+
4
e
x
derivative of \sqrt[4]{3x^5}
d
dx
(
4
√
3
x
5
)
derivative of sin^2(cos(2x))
d
dx
(
sin
2
(
cos
(
2
x
)
)
)
integral of 2x^3(x^4-3)^5
∫
2
x
3
(
x
4
−
3
)
5
dx
경사지 (x^2)/(x+9)
slope
x
2
x
+
9
derivative of (x^3-\sqrt[4]{x^3}/(2x))
d
dx
(
x
3
−
4
√
x
3
2
x
)
sum from n=1 to infinity of 9^nx^nn!
∑
n
=
1
∞
9
n
x
n
n
!
limit as x approaches 100 of 7
lim
x
→
1
0
0
(
7
)
(\partial)/(\partial x)(e^{ax+by})
∂
∂
x
(
e
ax
+
by
)
derivative of e^x+e^{xx}
d
dx
(
e
x
+
e
xx
)
derivative of 0.5x^3+1.5
d
dx
(
0
.
5
x
3
+
1
.
5
)
integral of k
∫
k
laplace변환 3e^{4t-5}
laplacetransform
3
e
4
t
−
5
derivative of 20e^{-x}
d
dx
(
2
0
e
−
x
)
derivative of (2x+x^2/((1+x)^2))
d
dx
(
2
x
+
x
2
(
1
+
x
)
2
)
y^'+35y=7
y
′
+
3
5
y
=
7
derivative-2t^2-8t+9
derivative
−
2
t
2
−
8
t
+
9
limit as x approaches 6-of (x-6)/(|x-6|)
lim
x
→
6
−
(
x
−
6
|
x
−
6
|
)
derivative of ln(x^x)
d
dx
(
ln
(
x
x
)
)
integral of 4xe^{-2x^2}
∫
4
xe
−
2
x
2
dx
derivative of (cos(x+2)^3)
d
dx
(
(
cos
(
x
)
+
2
)
3
)
integral of (4x)/((x^2+6)^2)
∫
4
x
(
x
2
+
6
)
2
dx
(dy)/(dx)=(x+y)^2-1
dy
dx
=
(
x
+
y
)
2
−
1
derivative of-2/(9x^{5/3})
d
dx
(
−
2
9
x
5
3
)
integral of 2x^2+1
∫
2
x
2
+
1
dx
integral from 0 to pi/2 of 30cos^5(x)
∫
0
π
2
3
0
cos
5
(
x
)
dx
tangent f(x)=3x^2+2x,\at x=1
tangent
f
(
x
)
=
3
x
2
+
2
x
,
at
x
=
1
sum from n=1 to infinity of (-0.3)^n
∑
n
=
1
∞
(
−
0
.
3
)
n
limit as x approaches 0 of 1/3 x
lim
x
→
0
(
1
3
x
)
tangent f(x)=3x-cos(x),\at x=0
tangent
f
(
x
)
=
3
x
−
cos
(
x
)
,
at
x
=
0
integral of (9x+5)^2
∫
(
9
x
+
5
)
2
dx
derivative f(x)=x^{-5}
derivative
f
(
x
)
=
x
−
5
경사지 x^2-8x+9
slope
x
2
−
8
x
+
9
limit as x approaches 0 of (2^{2x}-1)/x
lim
x
→
0
(
2
2
x
−
1
x
)
integral of ln(z)
∫
ln
(
z
)
dz
integral of ((xe^x))/((x+1)^2)
∫
(
xe
x
)
(
x
+
1
)
2
dx
integral of x*sin(3x)
∫
x
·
sin
(
3
x
)
dx
테일러 xcos(pi)x,x=0
taylor
x
cos
(
π
)
x
,
x
=
0
derivative f(-1)=x^2+2-1
derivative
f
(
−
1
)
=
x
2
+
2
−
1
derivative f(x)= 1/(sqrt(2x+3))
derivative
f
(
x
)
=
1
√
2
x
+
3
integral of (x^3+2x)^5(6x^2+4)
∫
(
x
3
+
2
x
)
5
(
6
x
2
+
4
)
dx
derivative of ln(x/(2e))
d
dx
(
ln
(
x
2
e
)
)
tangent f(x)=x^2+9,(-2,13)
tangent
f
(
x
)
=
x
2
+
9
,
(
−
2
,
1
3
)
integral from 0 to 2 of 1/(x-1)
∫
0
2
1
x
−
1
dx
integral of (x/(sqrt(x+1)))
∫
(
x
√
x
+
1
)
dx
(\partial)/(\partial x)(y-1)
∂
∂
x
(
y
−
1
)
limit as x approaches-infinity of 5
lim
x
→
−
∞
(
5
)
integral of (e^{-x})^2
∫
(
e
−
x
)
2
dx
h(x)=-x^3e^x
h
(
x
)
=
−
x
3
e
x
inverse라플라스 (s^2+2s+3)/((s+1)^3)
inverselaplace
s
2
+
2
s
+
3
(
s
+
1
)
3
integral of ((8x^2+9x+8))/((x^2+1)^2)
∫
(
8
x
2
+
9
x
+
8
)
(
x
2
+
1
)
2
dx
integral of x*cos(5x)
∫
x
·
cos
(
5
x
)
dx
limit as x approaches 0 of 1/(1+x^2)
lim
x
→
0
(
1
1
+
x
2
)
derivative of (x^{-2}+x^3(4x)^{-2x})
d
dx
(
(
x
−
2
+
x
)
3
(
4
x
)
−
2
x
)
xy^'=4x^4cos(2x)+3y
xy
′
=
4
x
4
cos
(
2
x
)
+
3
y
limit as x approaches 0 of xsin(pi/x)
lim
x
→
0
(
x
sin
(
π
x
)
)
지역 y=5x-x^2,y=2x,(3,6)
area
y
=
5
x
−
x
2
,
y
=
2
x
,
(
3
,
6
)
(\partial)/(\partial x)(4y-3x^2)
∂
∂
x
(
4
y
−
3
x
2
)
1
..
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1205
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..
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