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일반적인 미적분학 문제
tangent f(x)=3x^2+12x-36
tangent
f
(
x
)
=
3
x
2
+
1
2
x
−
3
6
integral from-3 to 1 of x^2+2x-3
∫
−
3
1
x
2
+
2
x
−
3
dx
(dy)/(dx)+y^7x+2y=0
dy
dx
+
y
7
x
+
2
y
=
0
integral of-(10)/(sqrt(x^2+16))
∫
−
1
0
√
x
2
+
1
6
dx
integral of f(u)
∫
f
(
u
)
du
tangent f(x)=(5x)/(x-2),(3,15)
tangent
f
(
x
)
=
5
x
x
−
2
,
(
3
,
1
5
)
-y^{''}+36y=0
−
y
′
′
+
3
6
y
=
0
derivative of x^{7/2}
d
dx
(
x
7
2
)
derivative 6y
derivative
6
y
y^'=k(1-y)^2
y
′
=
k
(
1
−
y
)
2
integral of (1/(x^2))
∫
(
1
x
2
)
dx
integral of (cos^2(2x))/4
∫
cos
2
(
2
x
)
4
dx
limit as x approaches 0+of 15cos(15x)
lim
x
→
0
+
(
1
5
cos
(
1
5
x
)
)
integral of (2x^3+x^2-x-31)/(x^2-x-6)
∫
2
x
3
+
x
2
−
x
−
3
1
x
2
−
x
−
6
dx
derivative of x/(x^2+2x+2)
d
dx
(
x
x
2
+
2
x
+
2
)
derivative 3x^2-12x-15
derivative
3
x
2
−
1
2
x
−
1
5
(\partial)/(\partial x)(e^{-2t}cos(x))
∂
∂
x
(
e
−
2
t
cos
(
x
)
)
derivative of A(e^x+e^{xx})
d
dx
(
A
(
e
x
+
e
xx
)
)
y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0
y
′
′
+
1
3
y
′
+
3
0
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
limit as x approaches infinity of 5/x-2
lim
x
→
∞
(
5
x
−
2
)
integral of (3x+5)^3
∫
(
3
x
+
5
)
3
dx
maclaurin f(x)=x^4sin(4x)
maclaurin
f
(
x
)
=
x
4
sin
(
4
x
)
limit as x approaches 2 of x(2)
lim
x
→
2
(
x
(
2
)
)
integral from 3 to sqrt(14 of)x
∫
3
√
1
4
xdx
integral of cos^2(u)sin(u)
∫
cos
2
(
u
)
sin
(
u
)
du
y^{''}+9y=cos(3x)+sin(3x)
y
′
′
+
9
y
=
cos
(
3
x
)
+
sin
(
3
x
)
y^'=(6x^4e^{y/x}+x^2y^2)/(x^3y)
y
′
=
6
x
4
e
y
x
+
x
2
y
2
x
3
y
derivative 2x^3+2x-1
derivative
2
x
3
+
2
x
−
1
limit as z approaches-1+2i of z/(z+1+2i)
lim
z
→
−
1
+
2
i
(
z
z
+
1
+
2
i
)
derivative of-(x^2/(y^2))
d
dx
(
−
x
2
y
2
)
limit as m approaches 0 of m/(m^2+4m)
lim
m
→
0
(
m
m
2
+
4
m
)
integral of e^{4x-3}
∫
e
4
x
−
3
dx
integral of ((x-1))/((x-2)(x-3))
∫
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
dx
limit as x approaches 2 of |x|
lim
x
→
2
(
|
x
|
)
limit as x approaches 0 of x+5
lim
x
→
0
(
x
+
5
)
derivative of ln(sqrt(3x^5+2))
d
dx
(
ln
(
√
3
x
5
+
2
)
)
sum from n=3 to infinity of (3^n)/(10^n)
∑
n
=
3
∞
3
n
1
0
n
(dy)/(dx)=9xsqrt(3y+7)
dy
dx
=
9
x
√
3
y
+
7
(2xy^2+3x^2)dx+2x^2ydy=0
(
2
xy
2
+
3
x
2
)
dx
+
2
x
2
ydy
=
0
(\partial)/(\partial x)(1/(ln(2/x)))
∂
∂
x
(
1
ln
(
2
x
)
)
tangent f(x)=3x^2-1
tangent
f
(
x
)
=
3
x
2
−
1
tangent f(x)=12sqrt(x),(4,24)
tangent
f
(
x
)
=
1
2
√
x
,
(
4
,
2
4
)
y^{''}+6y^'+8y=e^{2x}
y
′
′
+
6
y
′
+
8
y
=
e
2
x
y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4
y
′
′
−
y
′
−
6
y
=
0
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
4
integral of e^{2-5x}
∫
e
2
−
5
x
dx
limit as x approaches 2+of 1/(x^2-5x+6)
lim
x
→
2
+
(
1
x
2
−
5
x
+
6
)
2y^{''}+(a+1)y=0
2
y
′
′
+
(
a
+
1
)
y
=
0
integral of {(3-x)/(x^2+1)+xln(x^2)}
∫
{
3
−
x
x
2
+
1
+
x
ln
(
x
2
)
}
dx
derivative y=sqrt(1+3x^2)(ln(x^2))
derivative
y
=
√
1
+
3
x
2
(
ln
(
x
2
)
)
derivative f(x)=(x^3+4)e^x
derivative
f
(
x
)
=
(
x
3
+
4
)
e
x
integral of (x^2+4)/(x+1)
∫
x
2
+
4
x
+
1
dx
sum from n=0 to infinity of 3(x/4)^n
∑
n
=
0
∞
3
(
x
4
)
n
tangent f(x)= 1/(x-5),\at x=10
tangent
f
(
x
)
=
1
x
−
5
,
at
x
=
1
0
derivative g(x)=x^2(1-7x)
derivative
g
(
x
)
=
x
2
(
1
−
7
x
)
derivative of ((x+7/(x-7))^5)
d
dx
(
(
x
+
7
x
−
7
)
5
)
derivative of (ln(9)^x)
d
dx
(
(
ln
(
9
)
)
x
)
integral of (ln(y))
∫
(
ln
(
y
)
)
dy
integral of ((5x+7))/((x^2+4x+4))
∫
(
5
x
+
7
)
(
x
2
+
4
x
+
4
)
dx
derivative sqrt((x+3))
derivative
√
(
x
+
3
)
integral of 1/(sin(x/a))
∫
1
sin
(
x
a
)
dx
limit as x approaches 0+of (-1)/(14x)
lim
x
→
0
+
(
−
1
1
4
x
)
integral of x^2-7x+4
∫
x
2
−
7
x
+
4
dx
integral of (sec(x/(24)))^2tan(x/(24))
∫
(
sec
(
x
2
4
)
)
2
tan
(
x
2
4
)
dx
limit as x approaches-infinity of e
lim
x
→
−
∞
(
e
)
(x^2+49)(dy)/(dx)=1,y(7)=0
(
x
2
+
4
9
)
dy
dx
=
1
,
y
(
7
)
=
0
integral of (x+8)/(x(x+6))
∫
x
+
8
x
(
x
+
6
)
dx
limit as h approaches 0 of (sinh(x))/h
lim
h
→
0
(
sinh
(
x
)
h
)
inverse라플라스 (s+2)/(s^2+2s+1)
inverselaplace
s
+
2
s
2
+
2
s
+
1
integral of 2cos(ln(x))
∫
2
cos
(
ln
(
x
)
)
dx
integral of sin(2x^2)
∫
sin
(
2
x
2
)
dx
integral of (cos^4(x)-cos^6(x))
∫
(
cos
4
(
x
)
−
cos
6
(
x
)
)
dx
integral of (2+ln(7x))/(3x)
∫
2
+
ln
(
7
x
)
3
x
dx
y^'+4x^3y=x^3
y
′
+
4
x
3
y
=
x
3
(\partial)/(\partial x)(-5xy+2)
∂
∂
x
(
−
5
xy
+
2
)
derivative of 4x^2-1
d
dx
(
4
x
2
−
1
)
integral of 1/((3n+5)^4)
∫
1
(
3
n
+
5
)
4
integral of (x^2)/((x^2+7)^2)
∫
x
2
(
x
2
+
7
)
2
dx
y^{''}+2y^'+2y=0,y(0)=0,y^'(0)=1
y
′
′
+
2
y
′
+
2
y
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
(\partial)/(\partial y)((x+y)/(y+z))
∂
∂
y
(
x
+
y
y
+
z
)
integral of 2sin(2x)
∫
2
sin
(
2
x
)
dx
integral of (1-x)sqrt(x)
∫
(
1
−
x
)
√
x
dx
테일러 e^{-x/2}e^{-1/4}
taylor
e
−
x
2
e
−
1
4
(\partial)/(\partial x)(6ycos(x))
∂
∂
x
(
6
y
cos
(
x
)
)
limit as x approaches 7 of 1/((x-7))
lim
x
→
7
(
1
(
x
−
7
)
)
integral of sech^2(2x-1/8)
∫
sech
2
(
2
x
−
1
8
)
dx
integral of (1+ln(x))/x
∫
1
+
ln
(
x
)
x
dx
integral of ln(e^{6x-7})
∫
ln
(
e
6
x
−
7
)
dx
(sqrt(2-x))^'
(
√
2
−
x
)
′
derivative of (9x^2-18x+18e^{-6x})
d
dx
(
(
9
x
2
−
1
8
x
+
1
8
)
e
−
6
x
)
derivative of (x^2+4/(x+5))
d
dx
(
x
2
+
4
x
+
5
)
integral from 1 to e^4 of (ln^2(x^2))/x
∫
1
e
4
ln
2
(
x
2
)
x
dx
integral from-1 to 2 of x^3
∫
−
1
2
x
3
dx
limit as x approaches infinity of 0.6^x
lim
x
→
∞
(
0
.
6
x
)
derivative f(x)=ln(sqrt(x))
derivative
f
(
x
)
=
ln
(
√
x
)
derivative of (x+(x+sin^2(x)^7)^3)
d
dx
(
(
x
+
(
x
+
sin
2
(
x
)
)
7
)
3
)
integral of t^2e^{-t^3}
∫
t
2
e
−
t
3
dt
laplace변환 x^4
laplacetransform
x
4
y^{''}+9y=t^3
y
′
′
+
9
y
=
t
3
sum from n=1 to infinity of 6/(n(n+3))
∑
n
=
1
∞
6
n
(
n
+
3
)
derivative of 2x+cos(2x)
d
dx
(
2
x
+
cos
(
2
x
)
)
1
..
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1374
1375
1376
1377
..
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