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일반적인 미적분학 문제
derivative cos(x)-sin(x)
derivative
cos
(
x
)
−
sin
(
x
)
derivative of (x^2-1^{1/2})
d
dx
(
(
x
2
−
1
)
1
2
)
integral of 3(1+x^2)^{-1}
∫
3
(
1
+
x
2
)
−
1
dx
integral of e^{z+e^z}
∫
e
z
+
e
z
dz
derivative of e^{15x}
d
dx
(
e
1
5
x
)
(d^2)/(dx^2)((2x^2)/(x^2-1))
d
2
dx
2
(
2
x
2
x
2
−
1
)
derivative x^4+2x
derivative
x
4
+
2
x
integral from 4 to 6 of x^3
∫
4
6
x
3
dx
derivative y=(k(x)^2+x^2)^4(x+k(x))
derivative
y
=
(
k
(
x
)
2
+
x
2
)
4
(
x
+
k
(
x
)
)
(\partial)/(\partial x)(x^2y+yln(xz^3))
∂
∂
x
(
x
2
y
+
y
ln
(
xz
3
)
)
integral of 3x^4+7/4 x^5
∫
3
x
4
+
7
4
x
5
dx
y^'+y+4cos(x)=0
y
′
+
y
+
4
cos
(
x
)
=
0
derivative of ((x+1)/((x-1)))
d
dx
(
(
x
+
1
)
(
x
−
1
)
)
derivative y=2ln(3)+1/2 ln(x^2+1)
derivative
y
=
2
ln
(
3
)
+
1
2
ln
(
x
2
+
1
)
derivative of 2x(4-x^2^{1/2})
d
dx
(
2
x
(
4
−
x
2
)
1
2
)
integral of sex^2x
∫
sex
2
xdx
integral of sec^2(x)+7
∫
sec
2
(
x
)
+
7
dx
integral of ky
∫
kydy
derivative of (3x^7-7x+11/(2x^3))
d
dx
(
3
x
7
−
7
x
+
1
1
2
x
3
)
integral of sqrt(6+10x-x^2)
∫
√
6
+
1
0
x
−
x
2
dx
(\partial)/(\partial y)(xyz+xy^2+yz^2+zx^2)
∂
∂
y
(
xyz
+
xy
2
+
yz
2
+
zx
2
)
integral of (x+3)/(x^2+5x-6)
∫
x
+
3
x
2
+
5
x
−
6
dx
limit as x approaches 1 of-4
lim
x
→
1
(
−
4
)
derivative 2x^0
derivative
2
x
0
(dy)/(dx)=sqrt(y)cos^2(sqrt(y))
dy
dx
=
√
y
cos
2
(
√
y
)
tangent g(x)=sqrt(x)
tangent
g
(
x
)
=
√
x
limit as x approaches 3 of (3x+4)^3
lim
x
→
3
(
(
3
x
+
4
)
3
)
derivative ((5t-3)^7)/(8t^2+7)
derivative
(
5
t
−
3
)
7
8
t
2
+
7
derivative of (2x/(x^2-4))
d
dx
(
2
x
x
2
−
4
)
derivative of 5^{cos(x}+ln(x^2+1))
d
dx
(
5
cos
(
x
)
+
ln
(
x
2
+
1
)
)
integral of 1/(y(100-y))
∫
1
y
(
1
0
0
−
y
)
dy
limit as x approaches 0+of 1/(1-e^x)
lim
x
→
0
+
(
1
1
−
e
x
)
derivative sqrt(((2x-7)/(2+3x)))
derivative
√
(
2
x
−
7
2
+
3
x
)
inverse라플라스 1/(s^2(s-1)^2)
inverselaplace
1
s
2
(
s
−
1
)
2
integral of (x/2)
∫
(
x
2
)
dx
integral of (6x)/((x^2+7)^2)
∫
6
x
(
x
2
+
7
)
2
dx
integral of 6cos(t)
∫
6
cos
(
t
)
dt
integral of y/(sqrt(1+y^2))
∫
y
√
1
+
y
2
dy
integral of 8(x+1)ln(x+1)
∫
8
(
x
+
1
)
ln
(
x
+
1
)
dx
integral of w^2sin(10w)
∫
w
2
sin
(
1
0
w
)
dw
derivative of ((x^2-9x+20)/((x+2)(x-2)))
d
dx
(
(
x
2
−
9
x
+
2
0
)
(
x
+
2
)
(
x
−
2
)
)
integral from 1 to 4 of 6/x
∫
1
4
6
x
dx
integral of (3x-2)/(x^5)
∫
3
x
−
2
x
5
dx
derivative of 2cos(x-xsin(x))
d
dx
(
2
cos
(
x
)
−
x
sin
(
x
)
)
sum from n=0 to infinity of (6/7)^n
∑
n
=
0
∞
(
6
7
)
n
(dy)/(dx)+12y=4
dy
dx
+
1
2
y
=
4
(2xy^2+2y)dx+(2x^2y+2x)dy=0,y(1)=2
(
2
xy
2
+
2
y
)
dx
+
(
2
x
2
y
+
2
x
)
dy
=
0
,
y
(
1
)
=
2
y^{''}-5y^'+6y=-sin(5t)
y
′
′
−
5
y
′
+
6
y
=
−
sin
(
5
t
)
(dy)/(dx)= 1/(e^y-x)
dy
dx
=
1
e
y
−
x
implicit (dy)/(dx),(6x)/(y^7)=4
implicit
dy
dx
,
6
x
y
7
=
4
(\partial)/(\partial t)(e^tcos(x))
∂
∂
t
(
e
t
cos
(
x
)
)
laplace변환 20te^{-2t}*sin(4t)
laplacetransform
2
0
te
−
2
t
·
sin
(
4
t
)
derivative ln(ln(x))
derivative
ln
(
ln
(
x
)
)
limit as x approaches 0+of x/(-3x^3-10x)
lim
x
→
0
+
(
x
−
3
x
3
−
1
0
x
)
tangent y= 1/(x^5),(-2,-1/32)
tangent
y
=
1
x
5
,
(
−
2
,
−
1
3
2
)
integral of 2/((x-4)(x^2+2x+6))
∫
2
(
x
−
4
)
(
x
2
+
2
x
+
6
)
dx
derivative y=e^{4x^2+1}
derivative
y
=
e
4
x
2
+
1
derivative (5t)/(1+2t^2)
derivative
5
t
1
+
2
t
2
tangent f(x)=sqrt(7x+1),(9,8)
tangent
f
(
x
)
=
√
7
x
+
1
,
(
9
,
8
)
integral of a/(a^2+x^2)
∫
a
a
2
+
x
2
dx
integral of 1/(sqrt(5x+4))
∫
1
√
5
x
+
4
dx
sum from n=1 to infinity of (8n)/(7-4n)
∑
n
=
1
∞
8
n
7
−
4
n
derivative of \sqrt[3]{tan(2^{-x}})
d
dx
(
3
√
tan
(
2
−
x
)
)
x(1+y^2)dx+y(1+x^2)dy=0
x
(
1
+
y
2
)
dx
+
y
(
1
+
x
2
)
dy
=
0
limit as x approaches 0 of x(1)
lim
x
→
0
(
x
(
1
)
)
derivative of-(cos(3x)/3)
d
dx
(
−
cos
(
3
x
)
3
)
integral of ysqrt(1-y^2)
∫
y
√
1
−
y
2
dy
derivative 3x^{-2}
derivative
3
x
−
2
(2+x)y^'=7y
(
2
+
x
)
y
′
=
7
y
integral of (x+1)sin(3x)
∫
(
x
+
1
)
sin
(
3
x
)
dx
inverse라플라스 (s+5)/(s^2+4s+13)
inverselaplace
s
+
5
s
2
+
4
s
+
1
3
derivative of ((x+3(x+1))/(x^2-49))
d
dx
(
(
x
+
3
)
(
x
+
1
)
x
2
−
4
9
)
integral from 0 to 1 of xcos(pix)
∫
0
1
x
cos
(
π
x
)
dx
integral from 1 to infinity of x^{-3/2}
∫
1
∞
x
−
3
2
dx
y^{''}-2/x y^'+2/(x^2)y=0
y
′
′
−
2
x
y
′
+
2
x
2
y
=
0
(\partial)/(\partial x)(sec^2(x)-1)
∂
∂
x
(
sec
2
(
x
)
−
1
)
integral of (1+sqrt(cos(x)))^2sin(x)
∫
(
1
+
√
cos
(
x
)
)
2
sin
(
x
)
dx
derivative f(x)=7(x^3-x)^4
derivative
f
(
x
)
=
7
(
x
3
−
x
)
4
laplace변환 t^2e^{-2t}sin(3t+30)
laplacetransform
t
2
e
−
2
t
sin
(
3
t
+
3
0
)
tangent f(x)= 4/(x^2),\at x=-1
tangent
f
(
x
)
=
4
x
2
,
at
x
=
−
1
integral of (ln(x))/(x^{-4)}
∫
ln
(
x
)
x
−
4
dx
limit as x approaches 0 of log_{e}(x)
lim
x
→
0
(
log
e
(
x
)
)
derivative (10x+6x^2)/((5+6x)^2)
derivative
1
0
x
+
6
x
2
(
5
+
6
x
)
2
테일러 (e^t)/(1+t)
taylor
e
t
1
+
t
f(x)=e^{sin(3x)}
f
(
x
)
=
e
sin
(
3
x
)
(\partial)/(\partial x)(ysqrt(x^2+y^2))
∂
∂
x
(
y
√
x
2
+
y
2
)
limit as x approaches infinity of 3x^3-1000x^2
lim
x
→
∞
(
3
x
3
−
1
0
0
0
x
2
)
integral of (sin(ln(x^6)))/x
∫
sin
(
ln
(
x
6
)
)
x
dx
integral of 1/(x^2-2x-3)
∫
1
x
2
−
2
x
−
3
dx
derivative f(x)=-1/4 x^2
derivative
f
(
x
)
=
−
1
4
x
2
f^'(x)= x/4
f
′
(
x
)
=
x
4
integral of sqrt(121-t^2)
∫
√
1
2
1
−
t
2
dt
tangent f(x)=x^2-5,\at x=-4
tangent
f
(
x
)
=
x
2
−
5
,
at
x
=
−
4
integral of 2y
∫
2
ydy
integral from 0 to 7 of (9x-x^2)-(2x)
∫
0
7
(
9
x
−
x
2
)
−
(
2
x
)
dx
inverse라플라스 (0.01s)/(7s^2+19980)
inverselaplace
0
.
0
1
s
7
s
2
+
1
9
9
8
0
derivative of (-ln(1-6x)/x)
d
dx
(
−
ln
(
1
−
6
x
)
x
)
derivative of x^e+e^x
d
dx
(
x
e
+
e
x
)
derivative of 7xy
d
dx
(
7
xy
)
derivative of arcsec(2x+1)
d
dx
(
arcsec
(
2
x
+
1
)
)
1
..
1485
1486
1487
1488
1489
..
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