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일반적인 미적분학 문제
derivative of-4e^xsin(x)
d
dx
(
−
4
e
x
sin
(
x
)
)
integral of 1/(x^4sqrt(16-25x^2))
∫
1
x
4
√
1
6
−
2
5
x
2
dx
derivative of (x^2-16/(x+4))
d
dx
(
x
2
−
1
6
x
+
4
)
derivative (x^2+3)(x^2-3)x^2
derivative
(
x
2
+
3
)
(
x
2
−
3
)
x
2
integral of sec^2(x)tan^2(x)
∫
sec
2
(
x
)
tan
2
(
x
)
dx
derivative 5000(1-1/40 t)^2
derivative
5
0
0
0
(
1
−
1
4
0
t
)
2
(\partial)/(\partial x)(-1/(x-y))
∂
∂
x
(
−
1
x
−
y
)
(\partial)/(\partial x)(4x^3y^3+1)
∂
∂
x
(
4
x
3
y
3
+
1
)
derivative of 2(x-2-2sin(2)(2x+1))
d
dx
(
2
(
x
−
2
)
−
2
sin
(
2
)
(
2
x
+
1
)
)
integral of 1/3 e^{-3x}
∫
1
3
e
−
3
x
dx
integral of 9sin(t)
∫
9
sin
(
t
)
dt
integral of sin(θ)cos(2θ)
∫
sin
(
θ
)
cos
(
2
θ
)
d
θ
integral from 0 to r of xarcsin((r-x)/r)
∫
0
r
x
arcsin
(
r
−
x
r
)
dx
derivative of 1/(sin(2x))
d
dx
(
1
sin
(
2
x
)
)
inverse라플라스 (e^{-s}-e^{-2s})/(s(s+2)(s+1))
inverselaplace
e
−
s
−
e
−
2
s
s
(
s
+
2
)
(
s
+
1
)
integral from 1 to sqrt(2 of)x8^{x^2}
∫
1
√
2
x
8
x
2
dx
y^'=(y(x-y))/(x^2)
y
′
=
y
(
x
−
y
)
x
2
(dy)/(dx)=2+3y
dy
dx
=
2
+
3
y
limit as x approaches 0 of ln(x^2)(-2)
lim
x
→
0
(
ln
(
x
2
)
(
−
2
)
)
(\partial)/(\partial x)(x^2+3xy^2+2y)
∂
∂
x
(
x
2
+
3
xy
2
+
2
y
)
y^{''}+4y=2cos(2t)
y
′
′
+
4
y
=
2
cos
(
2
t
)
integral from 1 to b of (2x)/(x^2+4)
∫
1
b
2
x
x
2
+
4
dx
x^2y+y^'=-3x^2
x
2
y
+
y
′
=
−
3
x
2
tangent f(x)=sqrt(1+4x),\at x=2
tangent
f
(
x
)
=
√
1
+
4
x
,
at
x
=
2
limit as x approaches c of x^3+4x^2-3
lim
x
→
c
(
x
3
+
4
x
2
−
3
)
integral from 0 to 1 of (3+2x^2)
∫
0
1
(
3
+
2
x
2
)
dx
derivative (-x^2-7)/((x^2-7)^2)
derivative
−
x
2
−
7
(
x
2
−
7
)
2
integral of (3x^2)/((2x^3-4)^2)
∫
3
x
2
(
2
x
3
−
4
)
2
dx
inverse라플라스 (2s-1)/(s^2-6s+18)
inverselaplace
2
s
−
1
s
2
−
6
s
+
1
8
d/(dt)(12t)
d
dt
(
1
2
t
)
integral from 0 to 1 of e^{-st}
∫
0
1
e
−
st
dt
integral of (x^x)
∫
(
x
x
)
dx
(dy)/(dx)=x^5(x-xy)
dy
dx
=
x
5
(
x
−
xy
)
테일러 e^x1
taylor
e
x
1
sum from n=0 to infinity of 1/(sqrt(9))
∑
n
=
0
∞
1
√
9
integral of (5sqrt(x))/(x-1)
∫
5
√
x
x
−
1
dx
경사지 (0,0),(6,4)
slope
(
0
,
0
)
,
(
6
,
4
)
integral from 0 to pi/2 of x^2sin(2x)
∫
0
π
2
x
2
sin
(
2
x
)
dx
limit as x approaches 0 of ((sin(4x)))/(2x)
lim
x
→
0
(
(
sin
(
4
x
)
)
2
x
)
integral of 2sin^3(x)cos^5(x)
∫
2
sin
3
(
x
)
cos
5
(
x
)
dx
(\partial)/(\partial y)(xycos(xy)+sin(xy))
∂
∂
y
(
xy
cos
(
xy
)
+
sin
(
xy
)
)
derivative f(x)=arctan(3x)
derivative
f
(
x
)
=
arctan
(
3
x
)
inverse라플라스 (s+1)/(s^2+4)
inverselaplace
s
+
1
s
2
+
4
derivative ((x^2+2)^{3/2})/3
derivative
(
x
2
+
2
)
3
2
3
f^'(x)=tan(x)+cot(x)
f
′
(
x
)
=
tan
(
x
)
+
cot
(
x
)
integral of sin(at)
∫
sin
(
at
)
dt
(dy)/(dx)+ycos(x)=5cos(x)
dy
dx
+
y
cos
(
x
)
=
5
cos
(
x
)
limit as x approaches 2 of e^{1/x}
lim
x
→
2
(
e
1
x
)
derivative 1-e^{-x}
derivative
1
−
e
−
x
integral of sqrt(1-sin(x))
∫
√
1
−
sin
(
x
)
dx
limit as x approaches 0 of (x7^x)/(7x-1)
lim
x
→
0
(
x
7
x
7
x
−
1
)
지역 y=x^2,y=1
area
y
=
x
2
,
y
=
1
integral of (7x^2+3x)/(x^3+4x^2+3x+12)
∫
7
x
2
+
3
x
x
3
+
4
x
2
+
3
x
+
1
2
dx
derivative of ((x^2+x(x^2-x+1))/(x^4))
d
dx
(
(
x
2
+
x
)
(
x
2
−
x
+
1
)
x
4
)
limit as n approaches infinity of-2^n
lim
n
→
∞
(
−
2
n
)
limit as n approaches infinity of n-3
lim
n
→
∞
(
n
−
3
)
tangent y=3+4x^2-2x^3,\at x=1
tangent
y
=
3
+
4
x
2
−
2
x
3
,
at
x
=
1
sum from n=0 to infinity of (2n)/(n!)
∑
n
=
0
∞
2
n
n
!
integral of (e^{9x}+7e^{-x})
∫
(
e
9
x
+
7
e
−
x
)
dx
(\partial)/(\partial x)(-2x^4-3y^3)
∂
∂
x
(
−
2
x
4
−
3
y
3
)
integral of (4x-2)/(x(x+1)(x-2))
∫
4
x
−
2
x
(
x
+
1
)
(
x
−
2
)
dx
integral from 4 to infinity of e^{-7x}
∫
4
∞
e
−
7
x
dx
(dy}{4y}=\frac{dx)/x
dy
4
y
=
dx
x
derivative f(x)=6x^2tan(x)
derivative
f
(
x
)
=
6
x
2
tan
(
x
)
derivative of ln|x-3|
d
dx
(
ln
|
x
−
3
|
)
(d^2)/(dx^2)(sqrt(x)+\sqrt[5]{x})
d
2
dx
2
(
√
x
+
5
√
x
)
normal y=2x^2+12x+18,(-2,2)
normal
y
=
2
x
2
+
1
2
x
+
1
8
,
(
−
2
,
2
)
derivative of 2x^2+3x-2
d
dx
(
2
x
2
+
3
x
−
2
)
derivative of 5x^e
d
dx
(
5
x
e
)
integral of 3xe^{5x}
∫
3
xe
5
x
dx
derivative of ((x^2-4x)/(x+1))
d
dx
(
(
x
2
−
4
x
)
x
+
1
)
derivative of (sin(x+cos(x))/(cos(x)))
d
dx
(
sin
(
x
)
+
cos
(
x
)
cos
(
x
)
)
(\partial)/(\partial x)(sin(y^2)+6e^x)
∂
∂
x
(
sin
(
y
2
)
+
6
e
x
)
derivative e^{2y}
derivative
e
2
y
inverse라플라스 (((s+1))/(s^4))^3
inverselaplace
(
(
s
+
1
)
s
4
)
3
integral of x(x+1)^5
∫
x
(
x
+
1
)
5
dx
integral of (3x-4)e^{(-x)}
∫
(
3
x
−
4
)
e
(
−
x
)
dx
derivative of 2x^4+x^2-x^2+4
d
dx
(
2
x
4
+
x
2
−
x
2
+
4
)
(\partial)/(\partial x)(y*e^{xy})
∂
∂
x
(
y
·
e
xy
)
inverse라플라스 (s+1)/(s^2+2)
inverselaplace
s
+
1
s
2
+
2
tangent x^2-9x
tangent
x
2
−
9
x
derivative of-xsin(x-cos(x))
d
dx
(
−
x
sin
(
x
)
−
cos
(
x
)
)
(ye^{4xy}+x)dx+(xe^{4xy})dy=0
(
ye
4
xy
+
x
)
dx
+
(
xe
4
xy
)
dy
=
0
integral of sin(x)cos(5x)
∫
sin
(
x
)
cos
(
5
x
)
dx
limit as x approaches 0 of x^a
lim
x
→
0
(
x
a
)
integral of 1/(6x^3)
∫
1
6
x
3
dx
integral of 18+0.5x
∫
1
8
+
0
.
5
xdx
d/(dt)(cos(at))
d
dt
(
cos
(
at
)
)
derivative of (x-4^8(2x+3)^6)
d
dx
(
(
x
−
4
)
8
(
2
x
+
3
)
6
)
y^{''}-8y^'+17y=0,y(0)=4
y
′
′
−
8
y
′
+
1
7
y
=
0
,
y
(
0
)
=
4
테일러 1-cos(θ)
taylor
1
−
cos
(
θ
)
limit as x approaches-1 of-x^5-3x^4
lim
x
→
−
1
(
−
x
5
−
3
x
4
)
integral of sqrt(16x-x^2)
∫
√
1
6
x
−
x
2
dx
integral from-1 to 3 of x^5
∫
−
1
3
x
5
dx
테일러 1/(x-1),2
taylor
1
x
−
1
,
2
derivative of in(3x+1(x+2)2)
d
dx
(
in
(
3
x
+
1
)
(
x
+
2
)
2
)
요인 ax^n+bx^{n-1}
factor
ax
n
+
bx
n
−
1
integral of 2x^3-6x^2
∫
2
x
3
−
6
x
2
dx
(dy)/(dx)+y=(1-e^{-2x})/(e^x+e^{-x)}
dy
dx
+
y
=
1
−
e
−
2
x
e
x
+
e
−
x
derivative cos(3cos(2sqrt(u)))
derivative
cos
(
3
cos
(
2
√
u
)
)
1
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