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일반적인 미적분학 문제
derivative of sin(2x+cos(3x))
d
dx
(
sin
(
2
x
)
+
cos
(
3
x
)
)
tangent f(x)=pi^{3x+3},\at x=2
tangent
f
(
x
)
=
π
3
x
+
3
,
at
x
=
2
121y^{''}+88y^'+12y=0
1
2
1
y
′
′
+
8
8
y
′
+
1
2
y
=
0
derivative sqrt(4+cot^2(x))
derivative
√
4
+
cot
2
(
x
)
derivative sqrt(x+5)
derivative
√
x
+
5
integral from 0 to N of e^{-st}e^{5t}
∫
0
N
e
−
st
e
5
t
dt
limit as x approaches 2 of-x+6
lim
x
→
2
(
−
x
+
6
)
limit as h approaches 0 of 2+h
lim
h
→
0
(
2
+
h
)
integral of e^rr+e^r
∫
e
r
r
+
e
r
dr
integral of cos^3(x)*sin(x)
∫
cos
3
(
x
)
·
sin
(
x
)
dx
y^{''}-3y^'-4y=3e^{2x}
y
′
′
−
3
y
′
−
4
y
=
3
e
2
x
integral from 2 to 3 of 3x
∫
2
3
3
xdx
integral from 0 to pi/4 of (tan(x))^2
∫
0
π
4
(
tan
(
x
)
)
2
dx
derivative of-6x^3
d
dx
(
−
6
x
3
)
limit as x approaches-1 of 3f(x)-2h(x)
lim
x
→
−
1
(
3
f
(
x
)
−
2
h
(
x
)
)
derivative ln(sqrt((x+7)/(x-7)))
derivative
ln
(
√
x
+
7
x
−
7
)
derivative of (2x+1e^{-x})
d
dx
(
(
2
x
+
1
)
e
−
x
)
sum from n=0 to infinity of 2/(n^2+2n)
∑
n
=
0
∞
2
n
2
+
2
n
integral of (x^2+3)/(x^3+2x)
∫
x
2
+
3
x
3
+
2
x
dx
derivative of ln(3x^2-y^3-3)
d
dx
(
ln
(
3
x
2
−
y
3
−
3
)
)
derivative of 3^{x^2cot(2x})
d
dx
(
3
x
2
cot
(
2
x
)
)
derivative of 8/(\sqrt[3]{x})
d
dx
(
8
3
√
x
)
derivative (x+3)/(x-3)
derivative
x
+
3
x
−
3
integral of 7e^{10x}
∫
7
e
1
0
x
dx
integral of 4cos(θ)
∫
4
cos
(
θ
)
d
θ
integral of (3x+1)\sqrt[3]{3x^2+2x}
∫
(
3
x
+
1
)
3
√
3
x
2
+
2
x
dx
integral of (x^3+x^2+x-2)/(x^3-x^2)
∫
x
3
+
x
2
+
x
−
2
x
3
−
x
2
dx
지역 4-x^2, 1/4 x^3-2,1,2
area
4
−
x
2
,
1
4
x
3
−
2
,
1
,
2
(dy)/(dx)=(8x^2)/(sqrt(9+x^3))
dy
dx
=
8
x
2
√
9
+
x
3
derivative h^2+7h+40
derivative
h
2
+
7
h
+
4
0
y^'=xy^8
y
′
=
xy
8
integral from 0 to x of x
∫
0
x
xdx
tangent f(x)= 5/(2sqrt(5x+4)),\at x=9
tangent
f
(
x
)
=
5
2
√
5
x
+
4
,
at
x
=
9
(\partial)/(\partial x)(sin(pi(2x-4y)))
∂
∂
x
(
sin
(
π
(
2
x
−
4
y
)
)
)
(\partial)/(\partial x)(arcsin(x/y))
∂
∂
x
(
arcsin
(
x
y
)
)
limit as x approaches 0 of-((1+x^2)^{cot(x)})
lim
x
→
0
(
−
(
(
1
+
x
2
)
cot
(
x
)
)
)
d/(dt)(((sqrt(2)ty))/3)
d
dt
(
(
√
2
ty
)
3
)
지역 y=e^x,y=2e^{-x}+1,x=0
area
y
=
e
x
,
y
=
2
e
−
x
+
1
,
x
=
0
(\partial)/(\partial x)(-4sin(2x))
∂
∂
x
(
−
4
sin
(
2
x
)
)
implicit (dy)/(dx),x^3+y^3=36
implicit
dy
dx
,
x
3
+
y
3
=
3
6
경사지 (0,1),(1,-3)
slope
(
0
,
1
)
,
(
1
,
−
3
)
limit as x approaches-infinity of x-4
lim
x
→
−
∞
(
x
−
4
)
inverse라플라스 2/(s^3(s^2+9))
inverselaplace
2
s
3
(
s
2
+
9
)
integral of (1/(x^6))
∫
(
1
x
6
)
dx
(\partial)/(\partial x)(0.1sqrt(x)*y)
∂
∂
x
(
0
.
1
√
x
·
y
)
(dx)/(dt)+2tx=t
dx
dt
+
2
tx
=
t
xy^'+2y=-2cos(x)
xy
′
+
2
y
=
−
2
cos
(
x
)
limit as x approaches (5pi)/6 of (sin(x))/(cos(x))
lim
x
→
5
π
6
(
sin
(
x
)
cos
(
x
)
)
경사지 (2.1)(-14.7)
slope
(
2
.
1
)
(
−
1
4
.
7
)
derivative 640(1.06)^t
derivative
6
4
0
(
1
.
0
6
)
t
derivative f(x)=2x^2-32
derivative
f
(
x
)
=
2
x
2
−
3
2
laplace변환 f(t)=5+4*\delta(t)
laplacetransform
f
(
t
)
=
5
+
4
·
δ
(
t
)
derivative of ln(1+sin(x))
d
dx
(
ln
(
1
+
sin
(
x
)
)
)
derivative of (f(x(6x))^2-2)
d
dx
(
(
f
(
x
)
(
6
x
)
)
2
−
2
)
limit as x approaches 0+of 2+ln(x)
lim
x
→
0
+
(
2
+
ln
(
x
)
)
integral of (cos(3x))^3
∫
(
cos
(
3
x
)
)
3
dx
derivative of-e^{4x}
d
dx
(
−
e
4
x
)
(y^2+1)dx=(1+xy)dy
(
y
2
+
1
)
dx
=
(
1
+
xy
)
dy
derivative sin(x)*tan(x)
derivative
sin
(
x
)
·
tan
(
x
)
integral of-8e^{-8x}
∫
−
8
e
−
8
x
dx
integral of 1/((9+x^2)^2)
∫
1
(
9
+
x
2
)
2
dx
y(1+x^2)y^'-x(5+y^2)=0
y
(
1
+
x
2
)
y
′
−
x
(
5
+
y
2
)
=
0
integral from 0 to 1 of 6e^{-2x}
∫
0
1
6
e
−
2
x
dx
derivative e^8
derivative
e
8
laplace변환 2((e^{2t}+e^{-2t})/2)sin(2t)
laplacetransform
2
(
e
2
t
+
e
−
2
t
2
)
sin
(
2
t
)
(\partial)/(\partial x)(z^2x^3)
∂
∂
x
(
z
2
x
3
)
derivative f(x)=sqrt(x^2+3)
derivative
f
(
x
)
=
√
x
2
+
3
integral of 2arctan(sqrt(x))
∫
2
arctan
(
√
x
)
dx
지역 f(x)=x^5+4,g(x)=x+4
area
f
(
x
)
=
x
5
+
4
,
g
(
x
)
=
x
+
4
tangent f(x)=-1/(2sqrt(1-x)),\at x=-8
tangent
f
(
x
)
=
−
1
2
√
1
−
x
,
at
x
=
−
8
integral of 1/(usqrt(7-u^2))
∫
1
u
√
7
−
u
2
du
f^'(x)=(8x^5-6x^9)/(x^4)
f
′
(
x
)
=
8
x
5
−
6
x
9
x
4
derivative of ln(1+e^{2x})
d
dx
(
ln
(
1
+
e
2
x
)
)
limit as x approaches-1 of (x^2-x)/x
lim
x
→
−
1
(
x
2
−
x
x
)
integral from 2 to infinity of 1/(x^2-1)
∫
2
∞
1
x
2
−
1
dx
(dy)/(dx)+y=y^2,y(0)=2
dy
dx
+
y
=
y
2
,
y
(
0
)
=
2
integral of sqrt(y/4)
∫
√
y
4
dy
derivative of ((sqrt(x))/(7+x))
d
dx
(
(
√
x
)
7
+
x
)
(2xy+3x^2)dx+(x^2-1)dy=0
(
2
xy
+
3
x
2
)
dx
+
(
x
2
−
1
)
dy
=
0
integral of pisin(8pix)
∫
π
sin
(
8
π
x
)
dx
integral of (1/(13x))
∫
(
1
1
3
x
)
dx
integral from 0 to 2 of x^2e^{-5x}
∫
0
2
x
2
e
−
5
x
dx
derivative of 2sin^2(3x+2cos^2(3x))
d
dx
(
2
sin
2
(
3
x
)
+
2
cos
2
(
3
x
)
)
(\partial)/(\partial y)(x^2-xy)
∂
∂
y
(
x
2
−
xy
)
integral from 0 to ln(5) of xe^x
∫
0
ln
(
5
)
xe
x
dx
laplace변환 e^tcos(2t)
laplacetransform
e
t
cos
(
2
t
)
derivative of e^{0x}
d
dx
(
e
0
x
)
f(x)=(pix)/2
f
(
x
)
=
π
x
2
derivative of 64x-(x^3/3)
d
dx
(
6
4
x
−
x
3
3
)
derivative of ln(6x^2+3x)
d
dx
(
ln
(
6
x
2
+
3
x
)
)
limit as x approaches 1 of (x-2)^2
lim
x
→
1
(
(
x
−
2
)
2
)
sum from n=1 to infinity of (1/2)^{n+1}
∑
n
=
1
∞
(
1
2
)
n
+
1
(\partial)/(\partial x)(ln(x^2+2x))
∂
∂
x
(
ln
(
x
2
+
2
x
)
)
(\partial)/(\partial x)(-3y^3+3x^2y^2-y)
∂
∂
x
(
−
3
y
3
+
3
x
2
y
2
−
y
)
y^'=24x^2e^{-y}
y
′
=
2
4
x
2
e
−
y
integral of 4-3(1-x^2)^{-1}
∫
4
−
3
(
1
−
x
2
)
−
1
dx
derivative of y-y=4
d
dx
y
−
y
=
4
derivative f(x)=(-2x)/(x^2+1)
derivative
f
(
x
)
=
−
2
x
x
2
+
1
integral of (5-50x)/(sqrt(4-25x^2))
∫
5
−
5
0
x
√
4
−
2
5
x
2
dx
integral of 2^{sqrt(x)}
∫
2
√
x
dx
1
..
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1485
1486
1487
1488
..
2459