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일반적인 미적분학 문제
derivative f(x)=(x^2+3)/x
derivative
f
(
x
)
=
x
2
+
3
x
(dy}{dx}(2y)+\frac{(1+y^2))/x =1
dy
dx
(
2
y
)
+
(
1
+
y
2
)
x
=
1
(\partial)/(\partial t)(sin(x)cos(ct))
∂
∂
t
(
sin
(
x
)
cos
(
ct
)
)
integral of 18sin^2(x)cos^3(x)
∫
1
8
sin
2
(
x
)
cos
3
(
x
)
dx
derivative of arcsin(10x)
d
dx
(
arcsin
(
1
0
x
)
)
integral from 2 to 3 of x+x^2
∫
2
3
x
+
x
2
dx
derivative of-(3x/(8-5x))
d
dx
(
−
3
x
8
−
5
x
)
limit as n approaches infinity of (\sqrt[n]{n})/(ln(n))
lim
n
→
∞
(
n
√
n
ln
(
n
)
)
limit as x approaches 4 of 4x+2x^2
lim
x
→
4
(
4
x
+
2
x
2
)
integral of cos^5(9-x)sin(9-x)
∫
cos
5
(
9
−
x
)
sin
(
9
−
x
)
dx
integral of 1/(3x-x^2-2)
∫
1
3
x
−
x
2
−
2
dx
integral of 3cot^5(θ)sin^4(θ)
∫
3
cot
5
(
θ
)
sin
4
(
θ
)
d
θ
경사지 x^2-2x+1
slope
x
2
−
2
x
+
1
derivative of \sqrt[3]{1-x^3+ln(x})
d
dx
(
3
√
1
−
x
3
+
ln
(
x
)
)
derivative arctan(x-pi/2)
derivative
arctan
(
x
−
π
2
)
integral of x^3sqrt(x^2+35)
∫
x
3
√
x
2
+
3
5
dx
테일러 e^{(x^3)}
taylor
e
(
x
3
)
지역 x^2,x=0,x=1
area
x
2
,
x
=
0
,
x
=
1
derivative tan^2(sin^4(t))
derivative
tan
2
(
sin
4
(
t
)
)
inverse라플라스 3/(s(s^2+8s+18))
inverselaplace
3
s
(
s
2
+
8
s
+
1
8
)
limit as x approaches 2-of x^2-4
lim
x
→
2
−
(
x
2
−
4
)
integral from 1 to 5 of 2/(x^2+2x+1)
∫
1
5
2
x
2
+
2
x
+
1
dx
integral of e^{-st}*(t^2-3t+1)
∫
e
−
st
·
(
t
2
−
3
t
+
1
)
dt
derivative ln(e^x+xe^x)
derivative
ln
(
e
x
+
xe
x
)
derivative of (3sqrt(x)+x(2-x^2))
d
dx
(
(
3
√
x
+
x
)
(
2
−
x
2
)
)
integral from 1 to 6 of 8x
∫
1
6
8
xdx
derivative (5x)/(1+x^2)
derivative
5
x
1
+
x
2
(\partial)/(\partial x)(xy+x)
∂
∂
x
(
xy
+
x
)
derivative of-2sin(x+2sin(2x))
d
dx
(
−
2
sin
(
x
)
+
2
sin
(
2
x
)
)
integral of (cos(x)-sec(x))
∫
(
cos
(
x
)
−
sec
(
x
)
)
dx
derivative (t+5)^{2/3}(3t^2-2)^3
derivative
(
t
+
5
)
2
3
(
3
t
2
−
2
)
3
(dy)/(dx)+5y=70,y(1)=110
dy
dx
+
5
y
=
7
0
,
y
(
1
)
=
1
1
0
limit as x approaches 10 of (7x^2-70x)/(x^2-100)
lim
x
→
1
0
(
7
x
2
−
7
0
x
x
2
−
1
0
0
)
integral of cos(0.5x)
∫
cos
(
0
.
5
x
)
dx
테일러 e^{-x/2}
taylor
e
−
x
2
derivative te^t
derivative
te
t
y^'-2y=x^2e^{2x}
y
′
−
2
y
=
x
2
e
2
x
derivative of e^{5x-3}
d
dx
(
e
5
x
−
3
)
integral of (1+x^2)^{1/2}
∫
(
1
+
x
2
)
1
2
dx
integral of 2(sin(2x))^2
∫
2
(
sin
(
2
x
)
)
2
dx
(\partial)/(\partial x)(xy*e^{xy})
∂
∂
x
(
xy
·
e
xy
)
derivative of 3x^2-e^x
d
dx
(
3
x
2
−
e
x
)
integral of 4^tsin(4^t)
∫
4
t
sin
(
4
t
)
dt
derivative of sqrt(y-x+1)+sqrt(x-y+1)
d
dx
(
√
y
−
x
+
1
+
√
x
−
y
+
1
)
derivative f(x)=ln(sqrt(x+9))
derivative
f
(
x
)
=
ln
(
√
x
+
9
)
derivative-4ln(+1/x-4)
derivative
−
4
ln
(
+
1
x
−
4
)
(x^2+2y^2)dx=xydy
(
x
2
+
2
y
2
)
dx
=
xydy
integral of (sin(1/(x^4)))/(x^5)
∫
sin
(
1
x
4
)
x
5
dx
integral from 0.2 to 0.4 of 150x
∫
0
.
2
0
.
4
1
5
0
xdx
derivative 5/(sqrt(x)+5)
derivative
5
√
x
+
5
y^'-(2x+1)y=0
y
′
−
(
2
x
+
1
)
y
=
0
integral of 1/(csc(x)(1+sin(x)))
∫
1
csc
(
x
)
(
1
+
sin
(
x
)
)
dx
integral from 0 to x of sqrt(1+36t)
∫
0
x
√
1
+
3
6
t
dt
integral from 1 to n of ln(x)
∫
1
n
ln
(
x
)
dx
derivative of (9+4x-6sqrt(x)/x)
d
dx
(
9
+
4
x
−
6
√
x
x
)
(\partial)/(\partial x)(ln(x*cos(y)))
∂
∂
x
(
ln
(
x
·
cos
(
y
)
)
)
integral of 1/((x^2-441)^{3/2)}
∫
1
(
x
2
−
4
4
1
)
3
2
dx
derivative of \sqrt[3]{(3x^2+5x-1^2})
d
dx
(
3
√
(
3
x
2
+
5
x
−
1
)
2
)
y^{''}-2y^'+5y=e^{-2t}
y
′
′
−
2
y
′
+
5
y
=
e
−
2
t
inverse라플라스 (2s-6)/(s^2+9)
inverselaplace
2
s
−
6
s
2
+
9
derivative of sin^4(2xcos^43x)
d
dx
(
sin
4
(
2
xco
)
s
4
3
x
)
integral of 3xe^{(-2x)}
∫
3
xe
(
−
2
x
)
dx
(\partial)/(\partial y)(sqrt(5x+4y))
∂
∂
y
(
√
5
x
+
4
y
)
derivative of 7/(sqrt(x+1))
d
dx
(
7
√
x
+
1
)
integral from 1 to 5 of w^2ln(w)
∫
1
5
w
2
ln
(
w
)
dw
integral of ({y})/(L{y\)}
∫
{
y
}
L
{
y
}
dL
tangent 5/((x^2+1))
tangent
5
(
x
2
+
1
)
integral of 1+cos(2θ)
∫
1
+
cos
(
2
θ
)
d
θ
integral of (x^2-x-4)/(x^3+2x)
∫
x
2
−
x
−
4
x
3
+
2
x
dx
integral of (x^3)/(sqrt((x+1)^2+4))
∫
x
3
√
(
x
+
1
)
2
+
4
dx
derivative 16^4sqrt(4x^4+4)
derivative
1
6
4
√
4
x
4
+
4
6y^'=x^2
6
y
′
=
x
2
derivative of 1/3 x^3-x^2-8x+1
d
dx
(
1
3
x
3
−
x
2
−
8
x
+
1
)
y^'=(2x^4+y^4)/(xy^3)
y
′
=
2
x
4
+
y
4
xy
3
2x(dy)/(dx)=y^2
2
x
dy
dx
=
y
2
y^'=sqrt(9x+y)-9
y
′
=
√
9
x
+
y
−
9
integral of x/(x-6)
∫
x
x
−
6
dx
(\partial)/(\partial x)(2y-sin(x))
∂
∂
x
(
2
y
−
sin
(
x
)
)
derivative of x^3e^{4x}
d
dx
(
x
3
e
4
x
)
t^2y^{''}+7ty^'+5y=t
t
2
y
′
′
+
7
ty
′
+
5
y
=
t
derivative of 2/5 x^{15}
d
dx
(
2
5
x
1
5
)
laplace변환 t^2cos(2t+30)
laplacetransform
t
2
cos
(
2
t
+
3
0
◦
)
derivative f(x)=5xsin(pix)
derivative
f
(
x
)
=
5
x
sin
(
π
x
)
y^{''}-2y^'+y=e^xtan^{-1}(x)
y
′
′
−
2
y
′
+
y
=
e
x
tan
−
1
(
x
)
limit as x approaches-2 of [f(x)+g(x)]
lim
x
→
−
2
(
[
f
(
x
)
+
g
(
x
)
]
)
laplace변환-5
laplacetransform
−
5
integral from 0 to 2pi of cos^3(θ)
∫
0
2
π
cos
3
(
θ
)
d
θ
derivative of (3x^2-4x+5/(6sqrt(x)))
d
dx
(
3
x
2
−
4
x
+
5
6
√
x
)
x(dy)/(dx)+y=9xy^2
x
dy
dx
+
y
=
9
xy
2
limit as x approaches 2+of 1/((x-2)^2)
lim
x
→
2
+
(
1
(
x
−
2
)
2
)
(\partial)/(\partial x)(x/(x^2+81))
∂
∂
x
(
x
x
2
+
8
1
)
y^'-2y=3x^2
y
′
−
2
y
=
3
x
2
limit as x approaches 4 of x^2-16
lim
x
→
4
(
x
2
−
1
6
)
limit as x approaches-2 of (5x+3)/(2x-9)
lim
x
→
−
2
(
5
x
+
3
2
x
−
9
)
derivative (2x^5-3)^8
derivative
(
2
x
5
−
3
)
8
integral from 0 to 2 of ((x+2))/((x-4))
∫
0
2
(
x
+
2
)
(
x
−
4
)
dx
(\partial)/(\partial x)(36-6x^2-y^2)
∂
∂
x
(
3
6
−
6
x
2
−
y
2
)
테일러 (2x)/(sqrt(e^{2x^2)-1)}
taylor
2
x
√
e
2
x
2
−
1
derivative of 2sqrt(3)sin(x+2cos(x))
d
dx
(
2
√
3
sin
(
x
)
+
2
cos
(
x
)
)
integral from 1 to 2 of 3
∫
1
2
3
dx
1
..
1197
1198
1199
1200
1201
..
2459