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일반적인 미적분학 문제
limit as x approaches 2 of tan((pix)/4)
lim
x
→
2
(
tan
(
π
x
4
)
)
(\partial)/(\partial x)(ln((2xy)/(7z)))
∂
∂
x
(
ln
(
2
xy
7
z
)
)
limit as x approaches infinity of x/5
lim
x
→
∞
(
x
5
)
tangent f(x)=1\sqrt[3]{x},\at x=1
tangent
f
(
x
)
=
1
3
√
x
,
at
x
=
1
integral of (x+2)sin(x)
∫
(
x
+
2
)
sin
(
x
)
dx
integral from-1 to 2 of (20-x^4)
∫
−
1
2
(
2
0
−
x
4
)
dx
derivative of 8x+4
d
dx
(
8
x
+
4
)
y/(1-x^2y^2)dx+x/(1-x^2y^2)dy=0
y
1
−
x
2
y
2
dx
+
x
1
−
x
2
y
2
dy
=
0
integral from 0 to 1 of 2ln(4x)
∫
0
1
2
ln
(
4
x
)
dx
integral of (2-3/(x^{10)})
∫
(
2
−
3
x
1
0
)
dx
integral of-4y^3
∫
−
4
y
3
dy
integral of 1/(sqrt(x^2-4x+3))
∫
1
√
x
2
−
4
x
+
3
dx
d/(dy)((x^3y-xy^3)/(x^2+y^2))
d
dy
(
x
3
y
−
xy
3
x
2
+
y
2
)
integral of e^{x^{-1/2}}
∫
e
x
−
1
2
dx
integral of 1/(2x^2-4x+14)
∫
1
2
x
2
−
4
x
+
1
4
dx
integral of x5^x
∫
x
5
x
dx
derivative of ee^xe^{x^2}
d
dx
(
ee
x
e
x
2
)
integral from 0 to 1 of (8+x)/(1+x^2)
∫
0
1
8
+
x
1
+
x
2
dx
inverse라플라스 (5+s)/(s(s^2-5s+4))
inverselaplace
5
+
s
s
(
s
2
−
5
s
+
4
)
derivative of 3/5
d
dx
(
3
5
)
derivative (1+2x)/(1-2x)
derivative
1
+
2
x
1
−
2
x
sum from n=9 to infinity of e^{3-6n}
∑
n
=
9
∞
e
3
−
6
n
(y^2-1)dx-(2y+xy)dy=0
(
y
2
−
1
)
dx
−
(
2
y
+
xy
)
dy
=
0
tangent y=x^2-3x+1
tangent
y
=
x
2
−
3
x
+
1
(\partial)/(\partial x)(4(x-y)e^{4y+4x^2})
∂
∂
x
(
4
(
x
−
y
)
e
4
y
+
4
x
2
)
x^{''}+3x^'-10x=6e^{4t}
x
′
′
+
3
x
′
−
1
0
x
=
6
e
4
t
(\partial)/(\partial x)(2yx^2-4)
∂
∂
x
(
2
yx
2
−
4
)
integral from 2 to infinity of 1/(3x)
∫
2
∞
1
3
x
dx
derivative sqrt(r^2-13x^2)
derivative
√
r
2
−
1
3
x
2
y^'=3-2x-0.5y,y(0)=1
y
′
=
3
−
2
x
−
0
.
5
y
,
y
(
0
)
=
1
derivative of (ln(x)^{sec(x)})
d
dx
(
(
ln
(
x
)
)
sec
(
x
)
)
(\partial)/(\partial y)(x*y^2*e^z)
∂
∂
y
(
x
·
y
2
·
e
z
)
integral of 8/((x-5)(x+3))
∫
8
(
x
−
5
)
(
x
+
3
)
dx
integral of e^x*ln(x)
∫
e
x
·
ln
(
x
)
dx
sum from n=1 to infinity of n/(e^{n^2)}
∑
n
=
1
∞
n
e
n
2
(\partial)/(\partial y)(e^{xy}-(x+1)cos(y))
∂
∂
y
(
e
xy
−
(
x
+
1
)
cos
(
y
)
)
limit as x approaches 0 of (x^3+7x)/x
lim
x
→
0
(
x
3
+
7
x
x
)
지역 y=x^2-5,y=4
area
y
=
x
2
−
5
,
y
=
4
integral from 6 to 8 of (64)/((x-6)^3)
∫
6
8
6
4
(
x
−
6
)
3
dx
integral of xcos(3x+1)
∫
x
cos
(
3
x
+
1
)
dx
integral of sin^7(3x)
∫
sin
7
(
3
x
)
dx
derivative of \sqrt[5]{ln(6-x^2})
d
dx
(
5
√
ln
(
6
−
x
2
)
)
derivative of 4xdx
d
dx
(
4
xdx
)
derivative of (x^2/(x^2-9))
d
dx
(
x
2
x
2
−
9
)
(\partial)/(\partial x)((y-2)tan(y))
∂
∂
x
(
(
y
−
2
)
tan
(
y
)
)
derivative y=-3sin(4-3x^4)
derivative
y
=
−
3
sin
(
4
−
3
x
4
)
derivative of-0.1x^2+40x
d
dx
(
−
0
.
1
x
2
+
4
0
x
)
derivative (2x+1)^5
derivative
(
2
x
+
1
)
5
derivative y=x^{2/5}+6x
derivative
y
=
x
2
5
+
6
x
integral of 6e^t
∫
6
e
t
dt
derivative of (2-2x-x^2/(x^2-4))
d
dx
(
2
−
2
x
−
x
2
x
2
−
4
)
단순화 1/2 x^2ln^2(x)-2x^2ln(x)+5/2 x^2
simplify
1
2
x
2
ln
2
(
x
)
−
2
x
2
ln
(
x
)
+
5
2
x
2
derivative of (-7sin(x)/(4cos(x)))
d
dx
(
−
7
sin
(
x
)
4
cos
(
x
)
)
derivative f(x)=3x^4(x^2-4x)
derivative
f
(
x
)
=
3
x
4
(
x
2
−
4
x
)
limit as x approaches 3 of (|3-x|)/(3-x)
lim
x
→
3
(
|
3
−
x
|
3
−
x
)
integral of (x^2)/(x+15)
∫
x
2
x
+
1
5
dx
integral from 1 to 3 of (x^2+1/(4x^2))
∫
1
3
(
x
2
+
1
4
x
2
)
dx
integral of (-4x^6-5x^5-2x^2+5-e^x)
∫
(
−
4
x
6
−
5
x
5
−
2
x
2
+
5
−
e
x
)
dx
integral of (x+3)(x-3)
∫
(
x
+
3
)
(
x
−
3
)
dx
y^{''}-2y^'=x+2e^x,y(0)=17,y^'(0)= 55/4
y
′
′
−
2
y
′
=
x
+
2
e
x
,
y
(
0
)
=
1
7
,
y
′
(
0
)
=
5
5
4
inverse라플라스 1/(s^2-2s+26)
inverselaplace
1
s
2
−
2
s
+
2
6
(\partial)/(\partial y)(ln(1+x^2+e^y+z))
∂
∂
y
(
ln
(
1
+
x
2
+
e
y
+
z
)
)
inverse라플라스 (s^2+6s+2)/(s(s+1)^2)
inverselaplace
s
2
+
6
s
+
2
s
(
s
+
1
)
2
y^'=ty-2t+y-2
y
′
=
ty
−
2
t
+
y
−
2
laplace변환 3t^3-2t^2-7t+2
laplacetransform
3
t
3
−
2
t
2
−
7
t
+
2
(\partial)/(\partial x)(1^x)
∂
∂
x
(
1
x
)
derivative ((x^2+11))/(x^3)
derivative
(
x
2
+
1
1
)
x
3
deg2rad (x''+4x)^'
deg
2
rad
(
x
′
′
+
4
x
)
′
limit as x approaches 0+of (x^2)/2-1/x
lim
x
→
0
+
(
x
2
2
−
1
x
)
derivative f(x)=24sqrt(x)-4x
derivative
f
(
x
)
=
2
4
√
x
−
4
x
derivative of sqrt(4x^2+9)
d
dx
(
√
4
x
2
+
9
)
(ln(tan(x)))^'
(
ln
(
tan
(
x
)
)
)
′
integral of (xsin(pi)x)
∫
(
x
sin
(
π
)
x
)
dx
integral of x^7(4^{-x^8})
∫
x
7
(
4
−
x
8
)
dx
경사지 (-2,4),(3,a)
slope
(
−
2
,
4
)
,
(
3
,
a
)
derivative of 50
d
dx
(
5
0
)
integral of sqrt(-3+r^2)r
∫
√
−
3
+
r
2
rdr
laplace변환 T+2
laplacetransform
T
+
2
y^'=-y+5
y
′
=
−
y
+
5
limit as x approaches 1 of (x-3)/2
lim
x
→
1
(
x
−
3
2
)
derivative of arctan(5cos(x))
d
dx
(
arctan
(
5
cos
(
x
)
)
)
sum from k=1 to infinity of 1/(4^k)
∑
k
=
1
∞
1
4
k
테일러 sqrt(1+x^2)
taylor
√
1
+
x
2
tangent f(x)=5x^2,\at x=-2
tangent
f
(
x
)
=
5
x
2
,
at
x
=
−
2
derivative y=t(ln(4t))^2
derivative
y
=
t
(
ln
(
4
t
)
)
2
limit as h approaches 0 of (2(x+h)-2x)/h
lim
h
→
0
(
2
(
x
+
h
)
−
2
x
h
)
integral of 1/(-y)
∫
1
−
y
dy
integral of (e^yx^2)/y
∫
e
y
x
2
y
integral of (sqrt(x^2+1)+x)^4
∫
(
√
x
2
+
1
+
x
)
4
dx
integral of (cos(x))/(sin(x)(1-sin(x)))
∫
cos
(
x
)
sin
(
x
)
(
1
−
sin
(
x
)
)
dx
d/(dt)(({v}(t))/t)
d
dt
(
v
(
t
)
t
)
derivative cos^3(sin(2x^4-x))
derivative
cos
3
(
sin
(
2
x
4
−
x
)
)
지역 y=x^2-7,y=9
area
y
=
x
2
−
7
,
y
=
9
integral of e^{-inwt}
∫
e
−
inwt
dt
derivative of-3*e^{x^2+x-1}
d
dx
(
−
3
·
e
x
2
+
x
−
1
)
(\partial)/(\partial x)(-ln(1+e^{-x}))
∂
∂
x
(
−
ln
(
1
+
e
−
x
)
)
derivative f(w)=(6x-8)^2
derivative
f
(
w
)
=
(
6
x
−
8
)
2
derivative f(x)=7arctan(x-sqrt(1+x^2))
derivative
f
(
x
)
=
7
arctan
(
x
−
√
1
+
x
2
)
derivative f(x)=x^{x^x}
derivative
f
(
x
)
=
x
x
x
tangent y=5x^{1/2}+x^{3/2},\at x=25
tangent
y
=
5
x
1
2
+
x
3
2
,
at
x
=
2
5
1
..
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