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일반적인 미적분학 문제
(dz)/(dx)
dz
dx
derivative of 5x+(900/x)
d
dx
(
5
x
+
9
0
0
x
)
integral of 36
∫
3
6
derivative of 2sin^3(5x)
d
dx
(
2
sin
3
(
5
x
)
)
integral of 1/(x^2-3x+4)
∫
1
x
2
−
3
x
+
4
dx
integral of 3x(ln(x^7))^2
∫
3
x
(
ln
(
x
7
)
)
2
dx
derivative of arctan((3+x/(3-x)))
d
dx
(
arctan
(
3
+
x
3
−
x
)
)
derivative of x+{z}(x)
d
dx
(
x
+
z
(
x
)
)
integral from 0 to 2 of (8ti-t^3j+2t^3k)
∫
0
2
(
8
ti
−
t
3
j
+
2
t
3
k
)
dt
integral from 0 to pi/6 of tan(3x)
∫
0
π
6
tan
(
3
x
)
dx
sum from n=1 to infinity of (ln(n))/(n!)
∑
n
=
1
∞
ln
(
n
)
n
!
derivative of (sqrt(x)/(1+sqrt(x)))
d
dx
(
√
x
1
+
√
x
)
integral of 4e^{-x/4}
∫
4
e
−
x
4
dx
derivative f(x)=-2sin(x)
derivative
f
(
x
)
=
−
2
sin
(
x
)
maclaurin (5+sqrt(5^2+4x^2))/2
maclaurin
5
+
√
5
2
+
4
x
2
2
derivative sqrt(e^x+17)
derivative
√
e
x
+
1
7
derivative of ln((cos(x)/(sin(x))))
d
dx
(
ln
(
cos
(
x
)
sin
(
x
)
)
)
laplace변환-e^t+1/2 sin(t)+1/2 cos(t)
laplacetransform
−
e
t
+
1
2
sin
(
t
)
+
1
2
cos
(
t
)
integral of cos(ax+b)
∫
cos
(
ax
+
b
)
dx
integral from-1 to 3 of 6x(x-1)
∫
−
1
3
6
x
(
x
−
1
)
dx
integral of csch^2(x)
∫
csch
2
(
x
)
dx
limit as x approaches-3 of 3x
lim
x
→
−
3
(
3
x
)
integral of 5x+3
∫
5
x
+
3
dx
(\partial)/(\partial x)(dy)
∂
∂
x
(
dy
)
tangent 128t-16t^2,\at [4,5]
tangent
1
2
8
t
−
1
6
t
2
,
at
[
4
,
5
]
limit as x approaches 1-of (1-x)^{ln(x)}
lim
x
→
1
−
(
(
1
−
x
)
ln
(
x
)
)
테일러 sqrt((1+x)/(1-x))
taylor
√
1
+
x
1
−
x
(dy)/(dx)+5y=9
dy
dx
+
5
y
=
9
integral of arccot(14y)
∫
arccot
(
1
4
y
)
dy
(2x+1)y^'=4x+2y
(
2
x
+
1
)
y
′
=
4
x
+
2
y
integral of (sin^3(5x))/(cos^4(5x))
∫
sin
3
(
5
x
)
cos
4
(
5
x
)
dx
limit as x approaches 0-of 1/(x^{2/3)}
lim
x
→
0
−
(
1
x
2
3
)
derivative of 3^3
d
dx
(
3
3
)
integral of e^xsqrt(4+e^x)
∫
e
x
√
4
+
e
x
dx
(\partial)/(\partial x)(2ye^x)
∂
∂
x
(
2
ye
x
)
tangent 6+5x^2-2x^3
tangent
6
+
5
x
2
−
2
x
3
integral of (x^2-5x-6)/(x^2-4)
∫
x
2
−
5
x
−
6
x
2
−
4
dx
integral of 8e^{9x}
∫
8
e
9
x
dx
y^{'''}-5y^{''}+6y^'=0
y
′
′
′
−
5
y
′
′
+
6
y
′
=
0
limit as x approaches 3-of-2/(sqrt(3-x))
lim
x
→
3
−
(
−
2
√
3
−
x
)
(\partial)/(\partial x)(3xe^{2xy})
∂
∂
x
(
3
xe
2
xy
)
integral of ((8x^2+3x+8))/((x^2+1)^2)
∫
(
8
x
2
+
3
x
+
8
)
(
x
2
+
1
)
2
dx
y^'=xe^x
y
′
=
xe
x
integral from 0 to ln(4) of pi(e^{-x})^2
∫
0
ln
(
4
)
π
(
e
−
x
)
2
dx
(\partial)/(\partial x)((1+x^2)^{zsin(y)})
∂
∂
x
(
(
1
+
x
2
)
z
sin
(
y
)
)
(\partial)/(\partial y)(y^2ln(1+x^2+y^2))
∂
∂
y
(
y
2
ln
(
1
+
x
2
+
y
2
)
)
derivative of ln((xln(x-1)/(xln(x)+1)))
d
dx
(
ln
(
x
ln
(
x
)
−
1
x
ln
(
x
)
+
1
)
)
tangent f(x)=((x+1))/((x-1))
tangent
f
(
x
)
=
(
x
+
1
)
(
x
−
1
)
derivative (3t-1)/(sqrt(t)-2)
derivative
3
t
−
1
√
t
−
2
(\partial)/(\partial x)(x/(2sqrt(y)))
∂
∂
x
(
x
2
√
y
)
integral of 2/(cos(x))e^{2ln(cos(x))}
∫
2
cos
(
x
)
e
2
ln
(
cos
(
x
)
)
dx
integral from 1 to x of 2/(x^3)
∫
1
x
2
x
3
dx
tangent y=(x-1)/(x+1)
tangent
y
=
x
−
1
x
+
1
derivative of 7x^{-6}-5x^{-3}
d
dx
(
7
x
−
6
−
5
x
−
3
)
integral of cot^7(x)csc^2(x)
∫
cot
7
(
x
)
csc
2
(
x
)
dx
derivative y=-10
derivative
y
=
−
1
0
d/(dy)(x^{2y})
d
dy
(
x
2
y
)
integral of 12-(16-2\sqrt[3]{96-8x})
∫
1
2
−
(
1
6
−
2
3
√
9
6
−
8
x
)
dx
36y^{''}+36y^'+11y=0,y(0)=6,y^'(0)=5
3
6
y
′
′
+
3
6
y
′
+
1
1
y
=
0
,
y
(
0
)
=
6
,
y
′
(
0
)
=
5
tangent 6/(3x+1),\at a=-1
tangent
6
3
x
+
1
,
at
a
=
−
1
integral of (cos(x)+1/8 x)
∫
(
cos
(
x
)
+
1
8
x
)
dx
limit as x approaches 3-of e^{2/(3-x)}
lim
x
→
3
−
(
e
2
3
−
x
)
(\partial)/(\partial y)(x^y+y^x)
∂
∂
y
(
x
y
+
y
x
)
(\partial)/(\partial x)(1+cos(y))
∂
∂
x
(
1
+
cos
(
y
)
)
limit as x approaches 0 of 1-cos^3(x)
lim
x
→
0
(
1
−
cos
3
(
x
)
)
(2y-x^3)dx=xdy
(
2
y
−
x
3
)
dx
=
xdy
6y^'+5y=5
6
y
′
+
5
y
=
5
limit as x approaches sqrt(2) of x^2
lim
x
→
√
2
(
x
2
)
integral of e^xsec^3(e^x)
∫
e
x
sec
3
(
e
x
)
dx
integral of (sqrt(x^2-3))/x
∫
√
x
2
−
3
x
dx
integral of (8x+7)ln(x)
∫
(
8
x
+
7
)
ln
(
x
)
dx
integral from 5 to 10 of e^x
∫
5
1
0
e
x
dx
경사지 y= 1/(sqrt(x)),\at ,x=4
slope
y
=
1
√
x
,
at
,
x
=
4
derivative of acos(t)
d
dx
(
a
cos
(
t
)
)
derivative y=x^2+2x-3
derivative
y
=
x
2
+
2
x
−
3
integral of (e^x(x-1))/(x^2)
∫
e
x
(
x
−
1
)
x
2
dx
integral of 1/(3cos(x)-4sin(x))
∫
1
3
cos
(
x
)
−
4
sin
(
x
)
dx
(d^2}{dx^2}(\frac{e^x)/x)
d
2
dx
2
(
e
x
x
)
limit as x approaches-3-of (|x+3|)/(x+3)
lim
x
→
−
3
−
(
|
x
+
3
|
x
+
3
)
limit as x approaches-8-of (x+3)/(x+8)
lim
x
→
−
8
−
(
x
+
3
x
+
8
)
integral from 0 to 1 of 15cos(x^2)
∫
0
1
1
5
cos
(
x
2
)
dx
integral of 9/(x(x^4+1))
∫
9
x
(
x
4
+
1
)
dx
integral of (ln(ln(x)))/(x*ln(x))
∫
ln
(
ln
(
x
)
)
x
·
ln
(
x
)
dx
integral of (5t+1)^{100}
∫
(
5
t
+
1
)
1
0
0
dt
integral of 2x^{25}
∫
2
x
2
5
dx
limit as n approaches infinity of \sqrt[n]{n^3}
lim
n
→
∞
(
n
√
n
3
)
integral of 9xe^{4x}
∫
9
xe
4
x
dx
derivative f(x)=x^4-2x^3-12x^2+4x-3
derivative
f
(
x
)
=
x
4
−
2
x
3
−
1
2
x
2
+
4
x
−
3
integral of 4sin^3(xco)s^7x
∫
4
sin
3
(
xco
)
s
7
xdx
derivative of x^2sqrt(5-2x)
d
dx
(
x
2
√
5
−
2
x
)
(\partial)/(\partial v)(cos(v))
∂
∂
v
(
cos
(
v
)
)
integral of 1/2 e^x
∫
1
2
e
x
dx
y^'-y/3 =0
y
′
−
y
3
=
0
derivative of 4sin^3(2x)
d
dx
(
4
sin
3
(
2
x
)
)
integral of 1/((w^2+5)^{3/2)}
∫
1
(
w
2
+
5
)
3
2
dw
limit as x approaches 1-of x/(x^2+1)
lim
x
→
1
−
(
x
x
2
+
1
)
sum from n=1 to infinity of (n+1)/(2^n)
∑
n
=
1
∞
n
+
1
2
n
integral from 0 to pi of 4sin^4(x)
∫
0
π
4
sin
4
(
x
)
dx
derivative of x^2(x+2^3)
d
dx
(
x
2
(
x
+
2
)
3
)
tangent x^2-8x
tangent
x
2
−
8
x
1
..
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1498
1499
1500
1501
..
2459