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일반적인 미적분학 문제
경사지 (-1,3),(13,1)
slope
(
−
1
,
3
)
,
(
1
3
,
1
)
integral of (tan(x))/(cos^2(x))
∫
tan
(
x
)
cos
2
(
x
)
dx
8t(dy)/(dt)+y=t^4
8
t
dy
dt
+
y
=
t
4
(\partial)/(\partial y)(x+sqrt(x^2+y^2))
∂
∂
y
(
x
+
√
x
2
+
y
2
)
derivative of (6x-1/(4x+3))
d
dx
(
6
x
−
1
4
x
+
3
)
(\partial)/(\partial v)(uv^2)
∂
∂
v
(
uv
2
)
derivative of 1/((x+8^2))
d
dx
(
1
(
x
+
8
)
2
)
integral of 1/(x^2(x-2))
∫
1
x
2
(
x
−
2
)
dx
integral from 0 to 3 of 3x^3
∫
0
3
3
x
3
dx
derivative 1/(2+t)
derivative
1
2
+
t
integral of 8csc(x)
∫
8
csc
(
x
)
dx
tangent f(x)=sqrt(5x+39),\at x=5
tangent
f
(
x
)
=
√
5
x
+
3
9
,
at
x
=
5
derivative x/(5+x^2)
derivative
x
5
+
x
2
inverse라플라스 (20)/(-5s+3)
inverselaplace
2
0
−
5
s
+
3
derivative of 1/x+2sqrt(x)
d
dx
(
1
x
+
2
√
x
)
laplace변환 sin(t-pi/2)
laplacetransform
sin
(
t
−
π
2
)
derivative f(x)=sqrt(3-4x)
derivative
f
(
x
)
=
√
3
−
4
x
sum from n=0 to infinity of 1/3*(1/3)^n
∑
n
=
0
∞
1
3
·
(
1
3
)
n
integral of x^2sin(zx)
∫
x
2
sin
(
zx
)
dx
y^'+4/x y=x^9
y
′
+
4
x
y
=
x
9
limit as x approaches infinity of arctan(((1-x^2))/((1+x)))
lim
x
→
∞
(
arctan
(
(
1
−
x
2
)
(
1
+
x
)
)
)
(dy)/(dx)=0.067y(1-y/(2800))
dy
dx
=
0
.
0
6
7
y
(
1
−
y
2
8
0
0
)
tangent f(x)=x^3,(1,1)
tangent
f
(
x
)
=
x
3
,
(
1
,
1
)
(2x-y)+(2y-x)y^'=0
(
2
x
−
y
)
+
(
2
y
−
x
)
y
′
=
0
integral of (5x^2+11x+4)/(x^3+3x^2+3x+1)
∫
5
x
2
+
1
1
x
+
4
x
3
+
3
x
2
+
3
x
+
1
dx
derivative of 1/((4x+5^2))
d
dx
(
1
(
4
x
+
5
)
2
)
integral of (xln(x^2+4))/(x^2+4)
∫
x
ln
(
x
2
+
4
)
x
2
+
4
dx
integral of x^2sqrt(x^3+37)
∫
x
2
√
x
3
+
3
7
dx
integral of (x+2)/(x-1)
∫
x
+
2
x
−
1
dx
tangent f(x)=sqrt(7x+2),\at x=2
tangent
f
(
x
)
=
√
7
x
+
2
,
at
x
=
2
경사지 (0,1),(5,4)
slope
(
0
,
1
)
,
(
5
,
4
)
(21+x^2)y^'-2xy=0
(
2
1
+
x
2
)
y
′
−
2
xy
=
0
(\partial)/(\partial y)(xy^3+x^2y^2)
∂
∂
y
(
xy
3
+
x
2
y
2
)
y^'=9.8-(3y)/(3.5)
y
′
=
9
.
8
−
3
y
3
.
5
limit as x approaches infinity of (n^{1.5})/(ln(n))
lim
x
→
∞
(
n
1
.
5
ln
(
n
)
)
derivative x^4-18x^2+81
derivative
x
4
−
1
8
x
2
+
8
1
derivative of-3tan^3(sin(x))
d
dx
(
−
3
tan
3
(
sin
(
x
)
)
)
(6+x)((dy)/(dx))=9y
(
6
+
x
)
(
dy
dx
)
=
9
y
d/(dt)(e^tsin(t))
d
dt
(
e
t
sin
(
t
)
)
derivative 400x^{10}+40x^5+1
derivative
4
0
0
x
1
0
+
4
0
x
5
+
1
y^'=(4sec(y))/((x-6)^2)
y
′
=
4
sec
(
y
)
(
x
−
6
)
2
확장 ((x^2-a)^3)/(ax)
expand
(
x
2
−
a
)
3
ax
derivative (x+x^{-1})^3
derivative
(
x
+
x
−
1
)
3
derivative f(x)=-x+1/x+1
derivative
f
(
x
)
=
−
x
+
1
x
+
1
derivative of 2/(1-x^3)
d
dx
(
2
1
−
x
3
)
derivative of e^{-5/x}
d
dx
(
e
−
5
x
)
integral of x(3x+1)
∫
x
(
3
x
+
1
)
dx
sum from n=1 to infinity of cos^n(0.8)
∑
n
=
1
∞
cos
n
(
0
.
8
)
sum from n=0 to infinity of n(5/6)^{n-1}
∑
n
=
0
∞
n
(
5
6
)
n
−
1
derivative of x^2y+3x*y^3+x
d
dx
(
x
2
y
+
3
x
·
y
3
+
x
)
integral of cot(6x)
∫
cot
(
6
x
)
dx
(\partial)/(\partial z)(x^3)
∂
∂
z
(
x
3
)
derivative x^2sin^2(5x)
derivative
x
2
sin
2
(
5
x
)
derivative y=5e^x
derivative
y
=
5
e
x
integral of (sqrt(x))/(sqrt(x-1))
∫
√
x
√
x
−
1
dx
derivative (((3x^2))/(2x+4))^3
derivative
(
(
3
x
2
)
2
x
+
4
)
3
limit as x approaches 0 of x*ln^2(x)
lim
x
→
0
(
x
·
ln
2
(
x
)
)
limit as x approaches 0 of (3e^x-3)/x
lim
x
→
0
(
3
e
x
−
3
x
)
limit as x approaches infinity of-5x^6-6x^4-x^3+7x
lim
x
→
∞
(
−
5
x
6
−
6
x
4
−
x
3
+
7
x
)
integral of ((ln(x^9)))/x
∫
(
ln
(
x
9
)
)
x
dx
derivative of 2x^3-3x^2-12x+1
d
dx
(
2
x
3
−
3
x
2
−
1
2
x
+
1
)
derivative 1/(5x^2+6x)
derivative
1
5
x
2
+
6
x
(\partial)/(\partial x)(16sqrt(3y)+2x)
∂
∂
x
(
1
6
√
3
y
+
2
x
)
(\partial)/(\partial x)(xe)
∂
∂
x
(
xe
)
(\partial)/(\partial y)(yln(x)+1/9 y^3)
∂
∂
y
(
y
ln
(
x
)
+
1
9
y
3
)
limit as x approaches 0 of (3cos(x))/x
lim
x
→
0
(
3
cos
(
x
)
x
)
derivative of (1-sec(x)/(tan(x)))
d
dx
(
1
−
sec
(
x
)
tan
(
x
)
)
tangent f(x)=5x-2sqrt(x),(1,3)
tangent
f
(
x
)
=
5
x
−
2
√
x
,
(
1
,
3
)
implicit (dy)/(dx),y=x^3+7
implicit
dy
dx
,
y
=
x
3
+
7
derivative of-x^3
d
dx
(
−
x
3
)
integral of cot(5x)
∫
cot
(
5
x
)
dx
inverse라플라스-(12)/(s^2-5)
inverselaplace
−
1
2
s
2
−
5
integral of 17θsec^2(θ)
∫
1
7
θ
sec
2
(
θ
)
d
θ
derivative y=e^{cx}
derivative
y
=
e
cx
integral from 0 to 4 of (5-x)sqrt(x)
∫
0
4
(
5
−
x
)
√
x
dx
뿌리 xe^y
roots
xe
y
integral of 1/(sqrt(x^2+4x-5))
∫
1
√
x
2
+
4
x
−
5
dx
t^2y^'+2ty=y^3
t
2
y
′
+
2
ty
=
y
3
y^'=(2sec(y))/((x-2)^2)
y
′
=
2
sec
(
y
)
(
x
−
2
)
2
derivative f(x)=(t^2+3)/(t^4-2t+4)
derivative
f
(
x
)
=
t
2
+
3
t
4
−
2
t
+
4
limit as x approaches 0 of sqrt(x+2)
lim
x
→
0
(
√
x
+
2
)
integral of z^{31}+z^8
∫
z
3
1
+
z
8
dz
integral of (10)/(x^{0.5)}
∫
1
0
x
0
.
5
dx
normal y=x^2-4x,(7,21)
normal
y
=
x
2
−
4
x
,
(
7
,
2
1
)
derivative 4-3x
derivative
4
−
3
x
integral of (x^2-18)^8(2x)
∫
(
x
2
−
1
8
)
8
(
2
x
)
dx
implicit (dy)/(dx),3(x^2+y^2)^2=100xy
implicit
dy
dx
,
3
(
x
2
+
y
2
)
2
=
1
0
0
xy
derivative of (a^2x/((x+b)^2))
d
dx
(
a
2
x
(
x
+
b
)
2
)
integral of (6x^3)
∫
(
6
x
3
)
dx
derivative of \sqrt[3]{(3x/(4pi)})
d
dx
(
3
√
3
x
4
π
)
f(x)=(cos(x))/(cos(x)+1)
f
(
x
)
=
cos
(
x
)
cos
(
x
)
+
1
derivative y=(6x)/(x^2+1)
derivative
y
=
6
x
x
2
+
1
integral of (1-sin(x))/(1-sin^2(x))
∫
1
−
sin
(
x
)
1
−
sin
2
(
x
)
dx
tangent y=x^2+3,(-1,4)
tangent
y
=
x
2
+
3
,
(
−
1
,
4
)
integral from-4 to 4 of |x|
∫
−
4
4
|
x
|
dx
limit as x approaches-3 of (4x-5)/(3x+9)
lim
x
→
−
3
(
4
x
−
5
3
x
+
9
)
limit as x approaches 1 of [3x+1]
lim
x
→
1
(
[
3
x
+
1
]
)
derivative 4x
derivative
4
x
integral of (1+6x)^4(6)
∫
(
1
+
6
x
)
4
(
6
)
dx
integral of e^{4*ln(x)}
∫
e
4
·
ln
(
x
)
dx
1
..
1381
1382
1383
1384
1385
..
2459