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일반적인 미적분학 문제
derivative e^{-x}
derivative
e
−
x
limit as s approaches 5 of 5/((s-5)^2)
lim
s
→
5
(
5
(
s
−
5
)
2
)
derivative of sin(2^{sqrt(1+1/x)})
d
dx
(
sin
(
2
√
1
+
1
x
)
)
derivative of 2-ln(x)
d
dx
(
2
−
ln
(
x
)
)
integral of ((ln(x))^n)/x
∫
(
ln
(
x
)
)
n
x
dx
tangent y=sqrt(x^2-x+7),\at x=2
tangent
y
=
√
x
2
−
x
+
7
,
at
x
=
2
integral from-2 to 2 of 1/(36+x^2)
∫
−
2
2
1
3
6
+
x
2
dx
2y^{''}+5y^'-3y=0,y(0)=1,y^'(0)=25
2
y
′
′
+
5
y
′
−
3
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
5
(\partial)/(\partial x)(2xsqrt(y))
∂
∂
x
(
2
x
√
y
)
integral of 4x^3+3x^2
∫
4
x
3
+
3
x
2
dx
integral of (cos(x))/(sqrt(2sin(x)))
∫
cos
(
x
)
√
2
sin
(
x
)
dx
limit as x approaches 0 of (1/(5x))-(1/(e^{5x)}-1)
lim
x
→
0
(
(
1
5
x
)
−
(
1
e
5
x
−
1
)
)
derivative 3(5^x)
derivative
3
(
5
x
)
integral from 0 to 2 of (2x-5)^2
∫
0
2
(
2
x
−
5
)
2
dx
derivative of ((3x+2/(x-1))^7)
d
dx
(
(
3
x
+
2
x
−
1
)
7
)
y^'=(3x^4+y^4)/(xy^3)
y
′
=
3
x
4
+
y
4
xy
3
tangent f(x)= 1/(5+3x),(-1, 1/2)
tangent
f
(
x
)
=
1
5
+
3
x
,
(
−
1
,
1
2
)
derivative of pi\sqrt[5]{x}cos(x)
d
dx
(
π
5
√
x
cos
(
x
)
)
derivative of Ce^x
d
dx
(
Ce
x
)
(\partial)/(\partial x)(yln(x^2+y^2+4))
∂
∂
x
(
y
ln
(
x
2
+
y
2
+
4
)
)
derivative of x^3-3/x+e^2
d
dx
(
x
3
−
3
x
+
e
2
)
integral of (cos^2(x)*sin(x))
∫
(
cos
2
(
x
)
·
sin
(
x
)
)
dx
integral of (12x^3)/(x^4+7)
∫
1
2
x
3
x
4
+
7
dx
tangent y=x^3,\at x=-1
tangent
y
=
x
3
,
at
x
=
−
1
derivative f(x)=(2x)/(sin(x)+cos(x))
derivative
f
(
x
)
=
2
x
sin
(
x
)
+
cos
(
x
)
integral of ((y^2+1)^2)/(y^2)
∫
(
y
2
+
1
)
2
y
2
dy
limit as x approaches 2 of 3/x
lim
x
→
2
(
3
x
)
(\partial)/(\partial x)(3xe^y-x^3-e^{3y})
∂
∂
x
(
3
xe
y
−
x
3
−
e
3
y
)
integral of 3x^2y+e^xsin(y)
∫
3
x
2
y
+
e
x
sin
(
y
)
dx
y^'+((x-2))/(x-1)y=0
y
′
+
(
x
−
2
)
x
−
1
y
=
0
derivative of x^2*ln(2x)
d
dx
(
x
2
·
ln
(
2
x
)
)
inverse라플라스 s/(s^2+25)
inverselaplace
s
s
2
+
2
5
integral from 0 to pi/3 of sin^4(3x)
∫
0
π
3
sin
4
(
3
x
)
dx
derivative ln((x+3)/(x-1))
derivative
ln
(
x
+
3
x
−
1
)
121y^{''}-16y=0
1
2
1
y
′
′
−
1
6
y
=
0
(\partial)/(\partial x)((x+y)^2)
∂
∂
x
(
(
x
+
y
)
2
)
sum from n=1 to infinity of 1/(n^2+3n+2)
∑
n
=
1
∞
1
n
2
+
3
n
+
2
integral of ((x+1))/((x^2+2x))
∫
(
x
+
1
)
(
x
2
+
2
x
)
dx
integral of (6x^3-12x^2+8)/(x^2-2x)
∫
6
x
3
−
1
2
x
2
+
8
x
2
−
2
x
dx
integral from 0 to 1 of ((x+2)(x-3))
∫
0
1
(
(
x
+
2
)
(
x
−
3
)
)
dx
테일러 e^{x+2}
taylor
e
x
+
2
(4+x)y^'=7y
(
4
+
x
)
y
′
=
7
y
limit as x approaches 0 of (e^{-8x}-1)/x
lim
x
→
0
(
e
−
8
x
−
1
x
)
limit as x approaches 0 of 3x^2+2x
lim
x
→
0
(
3
x
2
+
2
x
)
integral of \sqrt[7]{x^2}
∫
7
√
x
2
dx
derivative of x^2(5x-1^3)
d
dx
(
x
2
(
5
x
−
1
)
3
)
derivative f(x)=(x^2+1)(x^3+1)
derivative
f
(
x
)
=
(
x
2
+
1
)
(
x
3
+
1
)
(\partial)/(\partial z)(x+e^z+y)
∂
∂
z
(
x
+
e
z
+
y
)
xy^'+ln(x)y=0
xy
′
+
ln
(
x
)
y
=
0
derivative f(x)=2x^3+3x^2-12x+2
derivative
f
(
x
)
=
2
x
3
+
3
x
2
−
1
2
x
+
2
limit as x approaches 4-of (x+5)/(x-4)
lim
x
→
4
−
(
x
+
5
x
−
4
)
tangent y=x^2+2x-1,(1,2)
tangent
y
=
x
2
+
2
x
−
1
,
(
1
,
2
)
지역 sqrt(x),y=2,x=0
area
√
x
,
y
=
2
,
x
=
0
(\partial)/(\partial x)(sin(x)+cos(y))
∂
∂
x
(
sin
(
x
)
+
cos
(
y
)
)
derivative f(x)=(x^3)/(x-1)
derivative
f
(
x
)
=
x
3
x
−
1
sum from n=0 to infinity of (2/7)^{n/2}
∑
n
=
0
∞
(
2
7
)
n
2
y^{'''}+2y^{''}-y^'-2y=0
y
′
′
′
+
2
y
′
′
−
y
′
−
2
y
=
0
(1-cos(t))^'
(
1
−
cos
(
t
)
)
′
integral from 0 to 2 of sqrt(1+16x^2)
∫
0
2
√
1
+
1
6
x
2
dx
integral of 1/(x^{15)}
∫
1
x
1
5
dx
limit as x approaches pi of \sqrt[5]{(x-pi)/(x+pi)}
lim
x
→
π
(
5
√
x
−
π
x
+
π
)
(dy)/(dx)+4y=60
dy
dx
+
4
y
=
6
0
단순화 2pisqrt(x/g)
simplify
2
π
√
x
g
derivative of (-ln(x+1)/(x^2))
d
dx
(
−
ln
(
x
)
+
1
x
2
)
integral of (30)/(\sqrt[3]{x^2)}
∫
3
0
3
√
x
2
dx
derivative of (x^2-3/x)
d
dx
(
x
2
−
3
x
)
integral of (5t^2)/2
∫
5
t
2
2
dt
integral of (300)/(sqrt(2q+25))
∫
3
0
0
√
2
q
+
2
5
dq
limit as x approaches-5 of 10x+3
lim
x
→
−
5
(
1
0
x
+
3
)
derivative of 4x-sin(2x)
d
dx
(
4
x
−
sin
(
2
x
)
)
derivative-3cot(x)csc(x)
derivative
−
3
cot
(
x
)
csc
(
x
)
integral of e^{x^2}*xln(x)
∫
e
x
2
·
x
ln
(
x
)
dx
y^'+(3y)/(100-x)= 4/5
y
′
+
3
y
1
0
0
−
x
=
4
5
integral of (tan^3(ln(x)))/(4x)
∫
tan
3
(
ln
(
x
)
)
4
x
dx
integral of tcos^2(t)
∫
t
cos
2
(
t
)
dt
derivative ln(sqrt(2))
derivative
ln
(
√
2
)
(\partial)/(\partial x)(xyz+xy^3+yz^3+zx^3)
∂
∂
x
(
xyz
+
xy
3
+
yz
3
+
zx
3
)
(dx)/(dt)=tx^{1/3}
dx
dt
=
tx
1
3
integral from 0 to 1 of (x-3)e^x
∫
0
1
(
x
−
3
)
e
x
dx
derivative f(x)=8x^5-8cos(x)
derivative
f
(
x
)
=
8
x
5
−
8
cos
(
x
)
derivative of x^{xcos(x})
d
dx
(
x
x
cos
(
x
)
)
derivative x^2+4ln^2(x)
derivative
x
2
+
4
ln
2
(
x
)
tangent ln(x^2)
tangent
ln
(
x
2
)
derivative (-3x^5-x^4-x^3+4x^2)/(x^2)
derivative
−
3
x
5
−
x
4
−
x
3
+
4
x
2
x
2
x(dy)/(dx)=4y
x
dy
dx
=
4
y
지역 y=x^3,x=-1,x=2,y=0
area
y
=
x
3
,
x
=
−
1
,
x
=
2
,
y
=
0
(\partial)/(\partial x)(3/4 (2-3x)^{4/3})
∂
∂
x
(
3
4
(
2
−
3
x
)
4
3
)
limit as x approaches 2 of 2x(x^2-3)
lim
x
→
2
(
2
x
(
x
2
−
3
)
)
(dy)/(dx)=(e^{x+y})/(y-1)
dy
dx
=
e
x
+
y
y
−
1
지역 y=3x^2,y=x^4-x^2
area
y
=
3
x
2
,
y
=
x
4
−
x
2
tangent f(x)=3+4x^2-2x^3
tangent
f
(
x
)
=
3
+
4
x
2
−
2
x
3
integral of 1/(x^2-y)
∫
1
x
2
−
y
dx
f(x)=tan(sqrt(x))
f
(
x
)
=
tan
(
√
x
)
derivative-1/2 cos^2(x)
derivative
−
1
2
cos
2
(
x
)
tangent y=x^2-3x-4,(2,-6)
tangent
y
=
x
2
−
3
x
−
4
,
(
2
,
−
6
)
integral from 0 to 2 of 5^x
∫
0
2
5
x
dx
integral of arccot(x)
∫
arccot
(
x
)
dx
y^'+2y=te^{-2t}
y
′
+
2
y
=
te
−
2
t
x^2y^{''}+2xy^'+100.25y=0
x
2
y
′
′
+
2
xy
′
+
1
0
0
.
2
5
y
=
0
derivative of (150x/(x+8))
d
dx
(
1
5
0
x
x
+
8
)
1
..
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1395
1396
1397
1398
..
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