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일반적인 미적분학 문제
tangent f(x)=x^3-4x^2-9x+11
tangent
f
(
x
)
=
x
3
−
4
x
2
−
9
x
+
1
1
integral from-infinity to infinity of x^2e^{(-x^2)/2}
∫
−
∞
∞
x
2
e
−
x
2
2
dx
implicit (dy)/(dx),xy+4e^y=4e
implicit
dy
dx
,
xy
+
4
e
y
=
4
e
integral of (5-e^x)/(e^{6x)}
∫
5
−
e
x
e
6
x
dx
integral of x^2(x^3+5)^{10}
∫
x
2
(
x
3
+
5
)
1
0
dx
y^{''}+2y^'+y=3-e^{-t}
y
′
′
+
2
y
′
+
y
=
3
−
e
−
t
derivative of sec^2(x+tan^2(x))
d
dx
(
sec
2
(
x
)
+
tan
2
(
x
)
)
integral of cos^8(x)
∫
cos
8
(
x
)
dx
경사지 (6.4)(2.7)
slope
(
6
.
4
)
(
2
.
7
)
derivative (x^{-2}+x^{-3})(x^5-2x^2)
derivative
(
x
−
2
+
x
−
3
)
(
x
5
−
2
x
2
)
limit as x approaches-1 of x^2+6
lim
x
→
−
1
(
x
2
+
6
)
derivative f(x)=5x+9
derivative
f
(
x
)
=
5
x
+
9
y^3-(14x+6)+3xy^2y^'=0
y
3
−
(
1
4
x
+
6
)
+
3
xy
2
y
′
=
0
integral from 0 to 1 of 3^{4x}
∫
0
1
3
4
x
dx
integral from 0 to 3 of x^2+6x+9
∫
0
3
x
2
+
6
x
+
9
dx
integral of ((2x^2+6))/((x^2-2x+2)^2)
∫
(
2
x
2
+
6
)
(
x
2
−
2
x
+
2
)
2
dx
경사지intercept (8.7)(0.3)
slopeintercept
(
8
.
7
)
(
0
.
3
)
integral of 2/(sqrt(25-100x^2))
∫
2
√
2
5
−
1
0
0
x
2
dx
derivative y=(arctan(2x))/x
derivative
y
=
arctan
(
2
x
)
x
(\partial)/(\partial x)((x^2+y^2)/(z^2))
∂
∂
x
(
x
2
+
y
2
z
2
)
integral from 2 to 3 of (2x)/((x^2+1)^3)
∫
2
3
2
x
(
x
2
+
1
)
3
dx
limit as h approaches 0 of-2x-h+8
lim
h
→
0
(
−
2
x
−
h
+
8
)
limit as x approaches 1 of (x+1)/(x^3-1)
lim
x
→
1
(
x
+
1
x
3
−
1
)
sum from n=5 to infinity of 2/((n^2-1))
∑
n
=
5
∞
2
(
n
2
−
1
)
(dP)/(dt)=P-P^2
dP
dt
=
P
−
P
2
(dy)/(dx)= 3/(x^2y-8y)
dy
dx
=
3
x
2
y
−
8
y
(\partial)/(\partial x)(sqrt(R(x)^2+x^2)-x)
∂
∂
x
(
√
R
(
x
)
2
+
x
2
−
x
)
derivative f(0)=(x^4+3x)(4x^5+4x-2)
derivative
f
(
0
)
=
(
x
4
+
3
x
)
(
4
x
5
+
4
x
−
2
)
derivative-2/(x^2)
derivative
−
2
x
2
derivative y=ln((x-3)/(x+3))
derivative
y
=
ln
(
x
−
3
x
+
3
)
integral of (y^5-5y)
∫
(
y
5
−
5
y
)
dy
테일러 e^{sin(x)}
taylor
e
sin
(
x
)
tangent f(x)=x^3+3x-2,\at x=3
tangent
f
(
x
)
=
x
3
+
3
x
−
2
,
at
x
=
3
integral of (x^{1.7}+9x^{3.5})
∫
(
x
1
.
7
+
9
x
3
.
5
)
dx
derivative of sqrt(4+x^2)
d
dx
(
√
4
+
x
2
)
tangent y=(1+5x)^9,(0,1)
tangent
y
=
(
1
+
5
x
)
9
,
(
0
,
1
)
y^2y^'+5=x^2
y
2
y
′
+
5
=
x
2
integral of (7x-5)/(x^2+16)
∫
7
x
−
5
x
2
+
1
6
dx
tangent f(x)=6-x^2,\at x=7
tangent
f
(
x
)
=
6
−
x
2
,
at
x
=
7
integral of 1/(tan(x)-1)
∫
1
tan
(
x
)
−
1
dx
integral from-5 to 6 of x
∫
−
5
6
xdx
derivative f(x)=(x^2-1)(1-e^x)
derivative
f
(
x
)
=
(
x
2
−
1
)
(
1
−
e
x
)
integral of 4sin^2(xco)s^3x
∫
4
sin
2
(
xco
)
s
3
xdx
integral of sqrt(17)
∫
√
1
7
dx
integral from-6 to 0 of (2+sqrt(36-x^2))
∫
−
6
0
(
2
+
√
3
6
−
x
2
)
dx
(\partial)/(\partial y)(x^2y^2z)
∂
∂
y
(
x
2
y
2
z
)
y^'+6y=t+e^{-5t}
y
′
+
6
y
=
t
+
e
−
5
t
integral of sin^4(x)*cos^4(x)
∫
sin
4
(
x
)
·
cos
4
(
x
)
dx
integral of (sec^2(ln(x)))/(2x)
∫
sec
2
(
ln
(
x
)
)
2
x
dx
limit as x approaches 1 of 3x
lim
x
→
1
(
3
x
)
(dx)/(dt)+5x=cos(2t)
dx
dt
+
5
x
=
cos
(
2
t
)
integral of 1/(36e^{-6x)+e^{6x}}
∫
1
3
6
e
−
6
x
+
e
6
x
dx
derivative 2/(2x-3)
derivative
2
2
x
−
3
integral of cos(x)sin(kx)
∫
cos
(
x
)
sin
(
kx
)
dx
derivative 0.0588s^{1.125}
derivative
0
.
0
5
8
8
s
1
.
1
2
5
integral from 0 to 1/2 of 4cos(pix)
∫
0
1
2
4
cos
(
π
x
)
dx
integral of x*1/(x^2)
∫
x
·
1
x
2
dx
limit as x approaches-3 of-2x^3
lim
x
→
−
3
(
−
2
x
3
)
tangent f(x)=sqrt(x+2),\at x=-1
tangent
f
(
x
)
=
√
x
+
2
,
at
x
=
−
1
limit as x approaches 1+of x^2-3
lim
x
→
1
+
(
x
2
−
3
)
derivative of-6e^{5x}
d
dx
(
−
6
e
5
x
)
integral of (ln(4x))
∫
(
ln
(
4
x
)
)
dx
integral of tan^8(x)sec^6(x)
∫
tan
8
(
x
)
sec
6
(
x
)
dx
d/(dt)(1+sqrt(t))
d
dt
(
1
+
√
t
)
derivative of (ax^2+bx+c*e^{(-x)/4})
d
dx
(
(
ax
2
+
bx
+
c
)
·
e
−
x
4
)
integral of sin^{10}(θ)cos^3(θ)
∫
sin
1
0
(
θ
)
cos
3
(
θ
)
d
θ
integral of ((sqrt(x)-2)^2)/(x^3)
∫
(
√
x
−
2
)
2
x
3
dx
integral of 1/((5x-2)^{2/3)}
∫
1
(
5
x
−
2
)
2
3
dx
derivative of x^4-2x^2-3
d
dx
(
x
4
−
2
x
2
−
3
)
integral of (x+7)/(x^2+25)
∫
x
+
7
x
2
+
2
5
dx
integral of xcos(3x^2)
∫
x
cos
(
3
x
2
)
dx
limit as x approaches 0 of (1+x)/x
lim
x
→
0
(
1
+
x
x
)
derivative y=(5x^2+x)(x-x^2)
derivative
y
=
(
5
x
2
+
x
)
(
x
−
x
2
)
지역 y=-x^2+2x+6,y=-x+6
area
y
=
−
x
2
+
2
x
+
6
,
y
=
−
x
+
6
integral of x^2+sin(x)+1
∫
x
2
+
sin
(
x
)
+
1
dx
limit as x approaches-infinity of (8x^3)/(9x^4)
lim
x
→
−
∞
(
8
x
3
9
x
4
)
integral of-cos(x)2x
∫
−
cos
(
x
)
2
xdx
단순화 x^2+(16)/x
simplify
x
2
+
1
6
x
derivative of (x-5/(3x-4))
d
dx
(
x
−
5
3
x
−
4
)
derivative of-(ln(2)/(x(x+ln(2))))
d
dx
(
−
ln
(
2
)
x
(
x
+
ln
(
2
)
)
)
(dx)/(dy)=-x^2+7x-8
dx
dy
=
−
x
2
+
7
x
−
8
integral of (x^4-2x^2+3)/(x^2)
∫
x
4
−
2
x
2
+
3
x
2
dx
integral of sqrt(x+4y)
∫
√
x
+
4
y
dx
sum from n=1 to infinity of (n^n)/(n!)
∑
n
=
1
∞
n
n
n
!
4(dy)/(dx)+28y=7
4
dy
dx
+
2
8
y
=
7
integral of 4cos^3(2x)
∫
4
cos
3
(
2
x
)
dx
(x^{ln(x)})^'
(
x
ln
(
x
)
)
′
inverse라플라스 ((s+3))/((s^2))
inverselaplace
(
s
+
3
)
(
s
2
)
integral of cos(x)tan(x)
∫
cos
(
x
)
tan
(
x
)
dx
integral from 0 to pi/3 of xtan^2(x)
∫
0
π
3
x
tan
2
(
x
)
dx
derivative of ln((1+x/(1-x)))
d
dx
(
ln
(
1
+
x
1
−
x
)
)
tangent 5x+4cos(x)
tangent
5
x
+
4
cos
(
x
)
derivative y=5e^{4x}cos(5x)
derivative
y
=
5
e
4
x
cos
(
5
x
)
inverse라플라스 s/((s^2+4)^2)
inverselaplace
s
(
s
2
+
4
)
2
tangent f(x)=6sin(x)+4cos(x),\at x=0
tangent
f
(
x
)
=
6
sin
(
x
)
+
4
cos
(
x
)
,
at
x
=
0
integral of ((arctan(x))^7)/(1+x^2)
∫
(
arctan
(
x
)
)
7
1
+
x
2
dx
limit as x approaches 1 of (1-x)/(x-1)
lim
x
→
1
(
1
−
x
x
−
1
)
derivative f(x)=5x^4e^x+e^xx^5
derivative
f
(
x
)
=
5
x
4
e
x
+
e
x
x
5
테일러 4+x^2+4x^4,-3
taylor
4
+
x
2
+
4
x
4
,
−
3
f(t)=sin(4t)
f
(
t
)
=
sin
(
4
t
)
1
..
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