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일반적인 미적분학 문제
derivative e^{4z}-4e^{-4z}
derivative
e
4
z
−
4
e
−
4
z
(\partial)/(\partial y)(sin(x)sin(y))
∂
∂
y
(
sin
(
x
)
sin
(
y
)
)
(x+y)dx-(x-y)dy=0,y(1)=0
(
x
+
y
)
dx
−
(
x
−
y
)
dy
=
0
,
y
(
1
)
=
0
integral of s/(s^2+6s+11)
∫
s
s
2
+
6
s
+
1
1
ds
derivative f(x)=sqrt(4x-3)
derivative
f
(
x
)
=
√
4
x
−
3
integral of-2cos(2x)
∫
−
2
cos
(
2
x
)
dx
limit as x approaches 4/pi of cos(x)
lim
x
→
4
π
(
cos
(
x
)
)
derivative of \sqrt[3]{x}-6/x
d
dx
(
3
√
x
−
6
x
)
derivative of 1/8 x^8-x^4
d
dx
(
1
8
x
8
−
x
4
)
derivative ln(x^2-4x)
derivative
ln
(
x
2
−
4
x
)
(arcsin((2x)/(1+x^2)))^'
(
arcsin
(
2
x
1
+
x
2
)
)
′
derivative x^4+x^3+2
derivative
x
4
+
x
3
+
2
(\partial)/(\partial x)(sin(y)cos(x))
∂
∂
x
(
sin
(
y
)
cos
(
x
)
)
tangent-8x^2+5
tangent
−
8
x
2
+
5
integral of (4t)/(sqrt(1-16t^4))
∫
4
t
√
1
−
1
6
t
4
dt
integral of sin(t)sec^5(t)
∫
sin
(
t
)
sec
5
(
t
)
dt
limit as x approaches 0 of (x)x
lim
x
→
0
(
(
x
)
x
)
integral of arccos(sqrt((1+x)/2))
∫
arccos
(
√
1
+
x
2
)
dx
integral of 1/(sqrt(1+u^2))
∫
1
√
1
+
u
2
du
지역 y=x^2,y=x+6
area
y
=
x
2
,
y
=
x
+
6
derivative of-ln(-x)
d
dx
(
−
ln
(
−
x
)
)
derivative f(x)=(e^x)/(2x+1)
derivative
f
(
x
)
=
e
x
2
x
+
1
y^{''}+11y^'+30y=0
y
′
′
+
1
1
y
′
+
3
0
y
=
0
extreme f(x,y)=sqrt(x^2+y^2)
extreme
f
(
x
,
y
)
=
√
x
2
+
y
2
derivative ln(16x)
derivative
ln
(
1
6
x
)
derivative y=a^x
derivative
y
=
a
x
tangent f(x)=3-4x^2,(2,-13)
tangent
f
(
x
)
=
3
−
4
x
2
,
(
2
,
−
1
3
)
derivative ln(1/x)
derivative
ln
(
1
x
)
integral of (x+1)/(2+4x^2)
∫
x
+
1
2
+
4
x
2
dx
derivative of x^3cot(x)
d
dx
(
x
3
cot
(
x
)
)
integral of ((sin(sqrt(w))))/(sqrt(w))
∫
(
sin
(
√
w
)
)
√
w
dw
inverselaplace ((s-2))/((s-2)^2-3)
inverselaplace
(
s
−
2
)
(
s
−
2
)
2
−
3
integral of ((e^x))/(1+e^x)
∫
(
e
x
)
1
+
e
x
dx
derivative y=4tsqrt(t+7)
derivative
y
=
4
t
√
t
+
7
integral from-2 to 2 of x^2-1
∫
−
2
2
x
2
−
1
dx
derivative f(x)=2e^{-x}
derivative
f
(
x
)
=
2
e
−
x
integral of 4sin^4(x)cos^2(x)
∫
4
sin
4
(
x
)
cos
2
(
x
)
dx
테일러 1/(2+5x)
taylor
1
2
+
5
x
(dy)/(dx)=y^2-9
dy
dx
=
y
2
−
9
derivative of 5x^3+x^2+1/x
d
dx
(
5
x
3
+
x
2
+
1
x
)
derivative of 2(5-9x^5)
d
dx
(
2
(
5
−
9
x
)
5
)
integral of (1-x)/(1-x^2)
∫
1
−
x
1
−
x
2
dx
integral from 0 to 2 of (x^2-2x)
∫
0
2
(
x
2
−
2
x
)
dx
integral of sin^2(x+4)
∫
sin
2
(
x
+
4
)
dx
integral from 1 to infinity of xe^{-4x}
∫
1
∞
xe
−
4
x
dx
integral of sin^4(4θ)
∫
sin
4
(
4
θ
)
d
θ
integral of ((16)/(1+x^2))
∫
(
1
6
1
+
x
2
)
dx
derivative sin(x^2)
derivative
sin
(
x
2
)
derivative of x*e^{4x}
d
dx
(
x
·
e
4
x
)
integral of ((x+2))/(x^2+3x-4)
∫
(
x
+
2
)
x
2
+
3
x
−
4
dx
integral of ((e^{sqrt(x)}-3))/(sqrt(x))
∫
(
e
√
x
−
3
)
√
x
dx
integral of cos(nt)
∫
cos
(
nt
)
dt
derivative of x^3(x-4)
d
dx
(
x
3
(
x
−
4
)
)
derivative 91-90e^{-0.2t}
derivative
9
1
−
9
0
e
−
0
.
2
t
inverselaplace 6/s+16*1/(s^2+16)
inverselaplace
6
s
+
1
6
·
1
s
2
+
1
6
tangent f(x)= 2/(4-x),\at x=-1
tangent
f
(
x
)
=
2
4
−
x
,
at
x
=
−
1
(sin^2(x))^'
(
sin
2
(
x
)
)
′
derivative of 4x^{1/3}
d
dx
(
4
x
1
3
)
지역 5x-x^2,0
area
5
x
−
x
2
,
0
limit as h approaches 0 of h
lim
h
→
0
(
h
)
2x^2y+x^3((dy)/(dx))=1
2
x
2
y
+
x
3
(
dy
dx
)
=
1
derivative f(x)=(ln(sqrt(x)))/x
derivative
f
(
x
)
=
ln
(
√
x
)
x
limit as x approaches 0 of (e^{2x}-5x)^2
lim
x
→
0
(
(
e
2
x
−
5
x
)
2
)
integral of 9/(x(x^4+8))
∫
9
x
(
x
4
+
8
)
dx
tangent y=(5x)/(x+4),(1,1)
tangent
y
=
5
x
x
+
4
,
(
1
,
1
)
integral of (cos(x))/(sin(2x))
∫
cos
(
x
)
sin
(
2
x
)
dx
테일러 1/(x^2),2
taylor
1
x
2
,
2
(2x^2y+2sqrt(1+x^4y^2))dx+x^3dy=0
(
2
x
2
y
+
2
√
1
+
x
4
y
2
)
dx
+
x
3
dy
=
0
derivative of (4x+3^4(x+1)^{-3})
d
dx
(
(
4
x
+
3
)
4
(
x
+
1
)
−
3
)
(dq)/(dt)+1/(5*10^{-9)}q= 200/1000
dq
dt
+
1
5
·
1
0
−
9
q
=
2
0
0
1
0
0
0
integral of ((ln^6(x)))/x
∫
(
ln
6
(
x
)
)
x
dx
derivative of e^{(x+y}-1)
d
dx
(
e
(
x
+
y
)
−
1
)
tangent f(x)=(1+5x)^9,(0,1)
tangent
f
(
x
)
=
(
1
+
5
x
)
9
,
(
0
,
1
)
테일러 e^{-x},1
taylor
e
−
x
,
1
(\partial)/(\partial x)((cos(x))^2)
∂
∂
x
(
(
cos
(
x
)
)
2
)
tangent-1/((x-6)^2)
tangent
−
1
(
x
−
6
)
2
integral of csc(4x)
∫
csc
(
4
x
)
dx
derivative of arcsinh(x)
d
dx
(
arcsinh
(
x
)
)
d/(dt)(\sqrt[3]{t}(t^2+4))
d
dt
(
3
√
t
(
t
2
+
4
)
)
integral of-4/(x^2)
∫
−
4
x
2
dx
(dy)/(dx)= y/(y^2),y(0)=2
dy
dx
=
y
y
2
,
y
(
0
)
=
2
sum from n=1 to infinity of 1/(2+sin(n))
∑
n
=
1
∞
1
2
+
sin
(
n
)
derivative of e^{14x}
d
dx
(
e
1
4
x
)
integral of (x^2)/(\sqrt[3]{1+2x)}
∫
x
2
3
√
1
+
2
x
dx
derivative of (x-2^2)
d
dx
(
(
x
−
2
)
2
)
2(sqrt(xy)-y)dx-xdy=0
2
(
√
xy
−
y
)
dx
−
xdy
=
0
integral of 1/(x^{1/2)}
∫
1
x
1
2
dx
integral of x*ln(5+x)
∫
x
·
ln
(
5
+
x
)
dx
integral of pi/2-5x^{-0.5}
∫
π
2
−
5
x
−
0
.
5
dx
(d^3)/(dx^3)(x^4-8x^3)
d
3
dx
3
(
x
4
−
8
x
3
)
derivative of e^{cos(sqrt(x+3)})
d
dx
(
e
cos
(
√
x
+
3
)
)
-8t^2y^{''}-4t(t-4)y^'+4(t-4)y=0
−
8
t
2
y
′
′
−
4
t
(
t
−
4
)
y
′
+
4
(
t
−
4
)
y
=
0
지역 y^2=x,x-2y=3
area
y
2
=
x
,
x
−
2
y
=
3
derivative of 3x(x^2-x+1(5x-3))
d
dx
(
3
x
(
x
2
−
x
+
1
)
(
5
x
−
3
)
)
(dy)/(dt)=-2y,y(0)= 1/10
dy
dt
=
−
2
y
,
y
(
0
)
=
1
1
0
tangent x^2-8
tangent
x
2
−
8
derivative of sin(2xcos(2x))
d
dx
(
sin
(
2
x
)
cos
(
2
x
)
)
tangent f(x)=x^3,\at x=6
tangent
f
(
x
)
=
x
3
,
at
x
=
6
integral of-9x
∫
−
9
xdx
limit as x approaches 2 of sqrt(51-x)-7
lim
x
→
2
(
√
5
1
−
x
−
7
)
1
..
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13
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15
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