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일반적인 미적분학 문제
derivative of |x^3+3x^2-24x-80|
d
dx
(
|
x
3
+
3
x
2
−
2
4
x
−
8
0
|
)
tangent f(x)=x^3,\at x=0
tangent
f
(
x
)
=
x
3
,
at
x
=
0
derivative f(x)=(3x^2-18x+15)/5
derivative
f
(
x
)
=
3
x
2
−
1
8
x
+
1
5
5
derivative of (3sin(x)/(3+cos(x)))
d
dx
(
3
sin
(
x
)
3
+
cos
(
x
)
)
(\partial)/(\partial y)(2x^3y+4)
∂
∂
y
(
2
x
3
y
+
4
)
integral of (x^{3/2}+1)^2
∫
(
x
3
2
+
1
)
2
dx
f(x)=sin(sin(sin(x)))
f
(
x
)
=
sin
(
sin
(
sin
(
x
)
)
)
implicit (dy)/(dx),e^{xy}+x^2-y^2=12
implicit
dy
dx
,
e
xy
+
x
2
−
y
2
=
1
2
(\partial)/(\partial θ)(sin(θ))
∂
∂
θ
(
sin
(
θ
)
)
integral of e^{-x}+4^x
∫
e
−
x
+
4
x
dx
derivative of a*ln(x)
d
dx
(
a
·
ln
(
x
)
)
limit as x approaches 5 of 5sqrt(x-5)
lim
x
→
5
(
5
√
x
−
5
)
integral of x^3sqrt(5x^4+20)
∫
x
3
√
5
x
4
+
2
0
dx
sum from n=0 to infinity of (1/17)^n
∑
n
=
0
∞
(
1
1
7
)
n
tangent f(x)=(4x+5)/(x-1),\at x=2
tangent
f
(
x
)
=
4
x
+
5
x
−
1
,
at
x
=
2
limit as x approaches 0 of (sin(5x))/(6x)
lim
x
→
0
(
sin
(
5
x
)
6
x
)
derivative f(x)=3sec(5x)
derivative
f
(
x
)
=
3
sec
(
5
x
)
(\partial)/(\partial x)(17/2 x^4y)
∂
∂
x
(
1
7
2
x
4
y
)
tangent f(x)=x^2+sqrt(x),\at x=1
tangent
f
(
x
)
=
x
2
+
√
x
,
at
x
=
1
derivative (1-6t)/(5+t)
derivative
1
−
6
t
5
+
t
integral of 11tan^4(xse)c^6x
∫
1
1
tan
4
(
xse
)
c
6
xdx
지역 x,x^2
area
x
,
x
2
derivative of 1-e^{3x}
d
dx
(
1
−
e
3
x
)
integral from 0 to 2 of x^2(1-0.5x)
∫
0
2
x
2
(
1
−
0
.
5
x
)
dx
integral from 1 to 2 of (sqrt(x^2-1))/x
∫
1
2
√
x
2
−
1
x
dx
sum from n=1 to infinity of 1/(3^n+2)
∑
n
=
1
∞
1
3
n
+
2
laplace변환 tcos(2t)
laplacetransform
t
cos
(
2
t
)
sum from k=0 to infinity of (e/(10))^k
∑
k
=
0
∞
(
e
1
0
)
k
limit as x approaches 1-of-x^2+3x-4
lim
x
→
1
−
(
−
x
2
+
3
x
−
4
)
laplace변환 f(t)=4e^{-7t}cos(9t)
laplacetransform
f
(
t
)
=
4
e
−
7
t
cos
(
9
t
)
derivative of e^x(cos(x))
d
dx
(
e
x
(
cos
(
x
)
)
)
(\partial)/(\partial y)(4x^2y^3+4)
∂
∂
y
(
4
x
2
y
3
+
4
)
d/(dt)(t^2sin(wt))
d
dt
(
t
2
sin
(
wt
)
)
integral of 1/((x^2+3)^{3/2)}
∫
1
(
x
2
+
3
)
3
2
dx
integral of 1/(sqrt(9x^2+36x+35))
∫
1
√
9
x
2
+
3
6
x
+
3
5
dx
tangent y=(8x)/(x^2-1),(3,3)
tangent
y
=
8
x
x
2
−
1
,
(
3
,
3
)
y^{''}+625y=sec(25x)
y
′
′
+
6
2
5
y
=
sec
(
2
5
x
)
테일러 e^{5x}
taylor
e
5
x
integral of e^{-1+x}
∫
e
−
1
+
x
dx
(\partial)/(\partial r)(e^rsin(st))
∂
∂
r
(
e
r
sin
(
st
)
)
테일러 1/((1-3x^2)),x=0.577
taylor
1
(
1
−
3
x
2
)
,
x
=
0
.
5
7
7
limit as x approaches 10 of+(2x)
lim
x
→
1
0
(
+
(
2
x
)
)
derivative (2x^3+2)(x^4-3x)
derivative
(
2
x
3
+
2
)
(
x
4
−
3
x
)
integral of x/(sqrt(x^2-1))
∫
x
√
x
2
−
1
dx
derivative of a^{sqrt(cos(x)})
d
dx
(
a
√
cos
(
x
)
)
integral of (u+1)/(u^2+1)
∫
u
+
1
u
2
+
1
du
derivative f(x)=cos^4(sin^3(x))
derivative
f
(
x
)
=
cos
4
(
sin
3
(
x
)
)
tangent f(x)=x^4+7x^2-x,\at x=1
tangent
f
(
x
)
=
x
4
+
7
x
2
−
x
,
at
x
=
1
테일러 ((x^2+1))/((x+1)),1
taylor
(
x
2
+
1
)
(
x
+
1
)
,
1
(\partial)/(\partial u)(u-uv)
∂
∂
u
(
u
−
uv
)
derivative 2/(x^4)
derivative
2
x
4
f(y)=yln(1+e^y)
f
(
y
)
=
y
ln
(
1
+
e
y
)
integral of (cos(x))/(sin^3(x)-cos^3(x))
∫
cos
(
x
)
sin
3
(
x
)
−
cos
3
(
x
)
dx
derivative of sin(2x+2xcos(2x))
d
dx
(
sin
(
2
x
)
+
2
x
cos
(
2
x
)
)
derivative f(x)=(e^x)/(1+e^x)
derivative
f
(
x
)
=
e
x
1
+
e
x
integral of (x^2)/((16-x^3)^2)
∫
x
2
(
1
6
−
x
3
)
2
dx
limit as x approaches-4+of (x+3)/(x+4)
lim
x
→
−
4
+
(
x
+
3
x
+
4
)
integral of x^2sec^2(x)tan(x)
∫
x
2
sec
2
(
x
)
tan
(
x
)
dx
지역 y=x^2-4,y=2-5x^2
area
y
=
x
2
−
4
,
y
=
2
−
5
x
2
limit as x approaches 0 of (6sin(2x))/x
lim
x
→
0
(
6
sin
(
2
x
)
x
)
경사지 (2,-14),(1,-11)
slope
(
2
,
−
1
4
)
,
(
1
,
−
1
1
)
integral of 5/(x^3+2x^2-35x)
∫
5
x
3
+
2
x
2
−
3
5
x
dx
derivative u^9
derivative
u
9
derivative of 2xe^x+e^{xx^2}
d
dx
(
2
xe
x
+
e
xx
2
)
integral of 2cos(sqrt(9x))
∫
2
cos
(
√
9
x
)
dx
지역 y=4-x^2,x=0,x=2
area
y
=
4
−
x
2
,
x
=
0
,
x
=
2
derivative of tan(x-0.5x)
d
dx
(
tan
(
x
)
−
0
.
5
x
)
(dy)/(dx)=xy-3x-2y+6
dy
dx
=
xy
−
3
x
−
2
y
+
6
derivative of (sin(x)^x)
d
dx
(
(
sin
(
x
)
)
x
)
integral of 5xln(x)
∫
5
x
ln
(
x
)
dx
limit as x approaches 8+of ln(x-8)
lim
x
→
8
+
(
ln
(
x
−
8
)
)
limit as x approaches 5 of sqrt(4x+5)
lim
x
→
5
(
√
4
x
+
5
)
tangent y=-t^3,(2,-8)
tangent
y
=
−
t
3
,
(
2
,
−
8
)
지역 x^2+x-2,-1,3
area
x
2
+
x
−
2
,
−
1
,
3
tangent f(x)=-1/x ,\at x=3
tangent
f
(
x
)
=
−
1
x
,
at
x
=
3
tangent f(x)=2x^2+3x,\at x=-3
tangent
f
(
x
)
=
2
x
2
+
3
x
,
at
x
=
−
3
(\partial ^2)/(\partial x\partial y)(ln(2+x^2y^2))
∂
2
∂
x
∂
y
(
ln
(
2
+
x
2
y
2
)
)
integral of e^{2x}arcsin(e^x)
∫
e
2
x
arcsin
(
e
x
)
dx
laplace변환 k_{p}*e(t)
laplacetransform
k
p
·
e
(
t
)
limit as x approaches-4 of-x^2+6x-8
lim
x
→
−
4
(
−
x
2
+
6
x
−
8
)
limit as x approaches 1 of (x-1)/x
lim
x
→
1
(
x
−
1
x
)
derivative of x/(sqrt(x-8))
d
dx
(
x
√
x
−
8
)
limit as x approaches 2-of ln(5-2x)
lim
x
→
2
−
(
ln
(
5
−
2
x
)
)
limit as x approaches 0 of (tan(2x))^2
lim
x
→
0
(
(
tan
(
2
x
)
)
2
)
derivative of e^{2x}y
d
dx
(
e
2
x
y
)
integral of-3tan(x)
∫
−
3
tan
(
x
)
dx
y^'=(5x^6e^{y/x}+x^4y^2)/(x^5y)
y
′
=
5
x
6
e
y
x
+
x
4
y
2
x
5
y
확장 (e^x+1)^7
expand
(
e
x
+
1
)
7
8y^'+ty=7
8
y
′
+
ty
=
7
derivative of \sqrt[5]{x^2+ln(x^2})
d
dx
(
5
√
x
2
+
ln
(
x
2
)
)
tangent 1/(x-1)
tangent
1
x
−
1
integral of (8z^2+2)/(2z^3+z)
∫
8
z
2
+
2
2
z
3
+
z
derivative of (e^xcos(x)/(e^x-1))
d
dx
(
e
x
cos
(
x
)
e
x
−
1
)
d/(dt)(4cos(2t))
d
dt
(
4
cos
(
2
t
)
)
(dy)/(dx)=(y/(y-x))
dy
dx
=
(
y
y
−
x
)
derivative of x(x+4^{1/3})
d
dx
(
x
(
x
+
4
)
1
3
)
limit as x approaches 0-of x^3+2x+2
lim
x
→
0
−
(
x
3
+
2
x
+
2
)
y^'= x/y+y/x
y
′
=
x
y
+
y
x
지역 y=6+2sqrt(x),y=(12+x)/2
area
y
=
6
+
2
√
x
,
y
=
1
2
+
x
2
derivative of 2(x^2-1)
d
dx
(
2
(
x
2
−
1
)
)
1
..
647
648
649
650
651
..
2459