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일반적인 미적분학 문제
derivative of (4x^2-8x+8e^{-6x})
d
dx
(
(
4
x
2
−
8
x
+
8
)
e
−
6
x
)
derivative x=tsin(t)
derivative
x
=
t
sin
(
t
)
derivative 8e^t
derivative
8
e
t
limit as x approaches 0-of x^2sin(1/x)
lim
x
→
0
−
(
x
2
sin
(
1
x
)
)
integral of e^x(1/2 x^2+x)
∫
e
x
(
1
2
x
2
+
x
)
dx
ty^'=y^2+1
ty
′
=
y
2
+
1
integral of xcos(bx)
∫
x
cos
(
bx
)
dx
implicit (dy)/(dx),y= 6/x
implicit
dy
dx
,
y
=
6
x
(2x+ln(y))dx+(x/y)dy=0
(
2
x
+
ln
(
y
)
)
dx
+
(
x
y
)
dy
=
0
경사지intercept (3.11)(11.8)
slopeintercept
(
3
.
1
1
)
(
1
1
.
8
)
integral from-pi/2 to pi/2 of sin(x)
∫
−
π
2
π
2
sin
(
x
)
dx
지역 4x+y^2=12,y=x
area
4
x
+
y
2
=
1
2
,
y
=
x
limit as x approaches 0 of (sin(2x))/(3x)
lim
x
→
0
(
sin
(
2
x
)
3
x
)
integral of 4pir^2
∫
4
π
r
2
dr
integral from 1 to 2 of 3x
∫
1
2
3
xdx
(dy)/(dx)-tan(x)y=sin(x)
dy
dx
−
tan
(
x
)
y
=
sin
(
x
)
integral of xsqrt(4x^2-5)
∫
x
√
4
x
2
−
5
dx
derivative f(x)=(3x^4+8)^{4/3}
derivative
f
(
x
)
=
(
3
x
4
+
8
)
4
3
integral from 0 to 1 of 2(1+sqrt(x))^4
∫
0
1
2
(
1
+
√
x
)
4
dx
derivative of cos(x^2-2x^2sin(x^2))
d
dx
(
cos
(
x
2
)
−
2
x
2
sin
(
x
2
)
)
derivative of 1-tan^2(x)
d
dx
(
1
−
tan
2
(
x
)
)
derivative y=1-cos^2(x)
derivative
y
=
1
−
cos
2
(
x
)
derivative of-sin(x/2)
d
dx
(
−
sin
(
x
2
)
)
y^'=13.2-(6y)/(740-2t)
y
′
=
1
3
.
2
−
6
y
7
4
0
−
2
t
(\partial)/(\partial y)(sqrt(x^2+2y^2))
∂
∂
y
(
√
x
2
+
2
y
2
)
(dy)/(dx)=4x-y
dy
dx
=
4
x
−
y
integral of (x^2-3x+1)/(x+1)
∫
x
2
−
3
x
+
1
x
+
1
dx
(\partial)/(\partial y)(3xe^{-2xy})
∂
∂
y
(
3
xe
−
2
xy
)
((dy)/(dx))=sqrt(y)-y
(
dy
dx
)
=
√
y
−
y
integral of 1/(sqrt(x^2+4x+8))
∫
1
√
x
2
+
4
x
+
8
dx
derivative of (3x-5^4)
d
dx
(
(
3
x
−
5
)
4
)
5e^{2x}(dy)/(dx)=-10 x/(y^2)
5
e
2
x
dy
dx
=
−
1
0
x
y
2
tangent f(x)= 1/(2sqrt(x)),\at x=49
tangent
f
(
x
)
=
1
2
√
x
,
at
x
=
4
9
derivative f(x)=9-4/(x^2)
derivative
f
(
x
)
=
9
−
4
x
2
derivative of x^2sec(1/x)
d
dx
(
x
2
sec
(
1
x
)
)
integral of x^{3.4}-2x^{sqrt(2)-1}
∫
x
3
.
4
−
2
x
√
2
−
1
dx
integral from-2 to 0 of sqrt(4-x^2)
∫
−
2
0
√
4
−
x
2
dx
integral of x^3sin(x)
∫
x
3
sin
(
x
)
dx
(\partial)/(\partial t)(t^4e^{-x})
∂
∂
t
(
t
4
e
−
x
)
테일러 2/(1-2x)
taylor
2
1
−
2
x
limit as x approaches 4 of (x-5)/(x+1)
lim
x
→
4
(
x
−
5
x
+
1
)
(\partial)/(\partial x)((2x-1)^3)
∂
∂
x
(
(
2
x
−
1
)
3
)
9y^{''}+6y=0
9
y
′
′
+
6
y
=
0
integral of (-cos(2x)-1)/4
∫
−
cos
(
2
x
)
−
1
4
dx
integral of 3/98 x^2
∫
3
9
8
x
2
dx
f(x)=cos^2(3x)
f
(
x
)
=
cos
2
(
3
x
)
y^'=8x^3*y^2
y
′
=
8
x
3
·
y
2
limit as x approaches 0 of (sin(7x))/(tan(5x))
lim
x
→
0
(
sin
(
7
x
)
tan
(
5
x
)
)
y^'+1/x y-e^{-x^2}=0,y(1)=0
y
′
+
1
x
y
−
e
−
x
2
=
0
,
y
(
1
)
=
0
sum from n=0 to infinity of 2^nn^2x^n
∑
n
=
0
∞
2
n
n
2
x
n
integral of ln(3)e^x
∫
ln
(
3
)
e
x
dx
integral of (x^4+9)/(x^4+9x^2)
∫
x
4
+
9
x
4
+
9
x
2
dx
inverse라플라스 1/((s+6)(s-4))
inverselaplace
1
(
s
+
6
)
(
s
−
4
)
derivative of 4^{(8x^4+cos(x)^3})
d
dx
(
4
(
8
x
4
+
cos
(
x
)
)
3
)
integral of 4x^3-3x^2+4x-3
∫
4
x
3
−
3
x
2
+
4
x
−
3
dx
t^2-t*y*y^'+y^2=0
t
2
−
t
·
y
·
y
′
+
y
2
=
0
derivative (t^6)/((t^3+1)^2)
derivative
t
6
(
t
3
+
1
)
2
integral of 6tan^5(x)sec^2(x)
∫
6
tan
5
(
x
)
sec
2
(
x
)
dx
limit as x approaches 0-of 8/(5x^{1/5)}
lim
x
→
0
−
(
8
5
x
1
5
)
integral of (x^2)/(x-5)
∫
x
2
x
−
5
dx
(dy)/(dx)=0.2*y+200
dy
dx
=
0
.
2
·
y
+
2
0
0
(x^3+y^3)dx-xy^2dy=0
(
x
3
+
y
3
)
dx
−
xy
2
dy
=
0
derivative of (x^2ln(sqrt(x))/(1+2x))
d
dx
(
x
2
ln
(
√
x
)
1
+
2
x
)
derivative sqrt(x-7)
derivative
√
x
−
7
-10x^2y+(dy)/(dx)=-7x^2
−
1
0
x
2
y
+
dy
dx
=
−
7
x
2
integral of 1000x
∫
1
0
0
0
xdx
integral from 0 to 1 of (4x)/((x^2+1)^2)
∫
0
1
4
x
(
x
2
+
1
)
2
dx
limit as x approaches 5 of (3x+5)/(5x+6)
lim
x
→
5
(
3
x
+
5
5
x
+
6
)
integral of 3/((x^2+1)^2)
∫
3
(
x
2
+
1
)
2
dx
integral of (inx)/(x^2)
∫
inx
x
2
dx
d/(dt)(3sin^3(t))
d
dt
(
3
sin
3
(
t
)
)
7(dy)/(dx)=y^2
7
dy
dx
=
y
2
tangent f(x)=3x^3-x^2+4,(1,6)
tangent
f
(
x
)
=
3
x
3
−
x
2
+
4
,
(
1
,
6
)
derivative of-6/5 e^{-20x}
d
dx
(
−
6
5
e
−
2
0
x
)
integral of e^{3x}-sin(x)+7/(1+x^2)
∫
e
3
x
−
sin
(
x
)
+
7
1
+
x
2
dx
(\partial)/(\partial x)(ln(x^2+2y^2+2))
∂
∂
x
(
ln
(
x
2
+
2
y
2
+
2
)
)
y^'t^4=0
y
′
t
4
=
0
integral from 0 to pi of x^2sin(x)
∫
0
π
x
2
sin
(
x
)
dx
laplace변환 e^{-4t}*cos(t)
laplacetransform
e
−
4
t
·
cos
(
t
)
integral of (-2/(x^2)+3sqrt(x))
∫
(
−
2
x
2
+
3
√
x
)
dx
integral of 1/(sqrt(3-x^2-2x))
∫
1
√
3
−
x
2
−
2
x
dx
integral of tan(sqrt(x-7)) 1/(sqrt(x-7))
∫
tan
(
√
x
−
7
)
1
√
x
−
7
dx
integral of e^{ax+7}
∫
e
ax
+
7
dx
(\partial)/(\partial y)(-x)
∂
∂
y
(
−
x
)
tangent f(x)=x^4-17x^2+16,\at x=1
tangent
f
(
x
)
=
x
4
−
1
7
x
2
+
1
6
,
at
x
=
1
지역 sin^2(x),sin^3(x),[0,pi]
area
sin
2
(
x
)
,
sin
3
(
x
)
,
[
0
,
π
]
지역 y=2x^3,x=0,x=2
area
y
=
2
x
3
,
x
=
0
,
x
=
2
지역 y=x^3-13x^2+36x,y=-x^3+13x^2-36x
area
y
=
x
3
−
1
3
x
2
+
3
6
x
,
y
=
−
x
3
+
1
3
x
2
−
3
6
x
derivative of ln|ln(3x|)
d
dx
(
ln
|
ln
(
3
x
)
|
)
derivative of e^{2x-4}
d
dx
(
e
2
x
−
4
)
derivative of sqrt((3x^{2/3)-2})
d
dx
(
√
(
3
x
)
2
3
−
2
)
derivative f(x)=(2x)/(x^2+4)
derivative
f
(
x
)
=
2
x
x
2
+
4
integral of-9x^2sec(3x^3+1)tan(3x^3+1)
∫
−
9
x
2
sec
(
3
x
3
+
1
)
tan
(
3
x
3
+
1
)
dx
integral of inx
∫
inxdx
(\partial)/(\partial x)(y{f}(x)+2x^3)
∂
∂
x
(
y
f
(
x
)
+
2
x
3
)
derivative e^{1-x}*(5-x^2)
derivative
e
1
−
x
·
(
5
−
x
2
)
derivative f(x)=(7x^4-6x^3-5x)^8
derivative
f
(
x
)
=
(
7
x
4
−
6
x
3
−
5
x
)
8
integral of 120x*(2x+1)^4
∫
1
2
0
x
·
(
2
x
+
1
)
4
dx
integral of 1/3 e^{-x/2}(x+1)
∫
1
3
e
−
x
2
(
x
+
1
)
dx
integral of sec^8(t)anx
∫
sec
8
(
t
)
anxdx
1
..
1386
1387
1388
1389
1390
..
2459