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일반적인 프리 미적분학 문제
derivative 2e^x
derivative
2
e
x
cartesian (-4,-pi/3)
cartesian
(
−
4
,
−
π
3
)
derivative y= 1/(x^2)
derivative
y
=
1
x
2
경사지 12x+6y=18
slope
1
2
x
+
6
y
=
1
8
경사지 y=3x-4
slope
y
=
3
x
−
4
derivative-x
derivative
−
x
경사지 ln(x+1)+3
slope
ln
(
x
+
1
)
+
3
경사지 y=3x+4
slope
y
=
3
x
+
4
중간점 (-5,-4),(5,-3)
midpoint
(
−
5
,
−
4
)
,
(
5
,
−
3
)
derivative y=(2x)/(1-x^2)
derivative
y
=
2
x
1
−
x
2
derivative 1/8 x^{2/3}(9x^2-8x-16)
derivative
1
8
x
2
3
(
9
x
2
−
8
x
−
1
6
)
derivative-cos(x)
derivative
−
cos
(
x
)
derivative-1/(x^2)
derivative
−
1
x
2
derivative f(x)=sqrt(x^2+1)
derivative
f
(
x
)
=
√
x
2
+
1
derivative x^2-24x-12
derivative
x
2
−
2
4
x
−
1
2
derivative f(x)=x^2+3x
derivative
f
(
x
)
=
x
2
+
3
x
derivative f(x)=(x+1)/(x-1)
derivative
f
(
x
)
=
x
+
1
x
−
1
적분 e^x
integral
e
x
경사지 y=3x+2
slope
y
=
3
x
+
2
derivative y=x^2-5x
derivative
y
=
x
2
−
5
x
경사지 (-5,2),(4,-7)
slope
(
−
5
,
2
)
,
(
4
,
−
7
)
polar (3,3sqrt(3))
polar
(
3
,
3
√
3
)
derivative f(x)=2
derivative
f
(
x
)
=
2
derivative y=xln(x)
derivative
y
=
x
ln
(
x
)
중간점 (2,-6),(-8,5)
midpoint
(
2
,
−
6
)
,
(
−
8
,
5
)
slopeintercept 5x-6y=7
slopeintercept
5
x
−
6
y
=
7
slopeintercept 2x+3y=6
slopeintercept
2
x
+
3
y
=
6
x=5
x
=
5
경사지-2
slope
−
2
θ=(5pi)/6
θ
=
5
π
6
tangent y=3arcsin(x),(1/2 , pi/2)
tangent
y
=
3
arcsin
(
x
)
,
(
1
2
,
π
2
)
경사지 y=6x+3
slope
y
=
6
x
+
3
derivative y=2x+1
derivative
y
=
2
x
+
1
derivative y=x^3e^x
derivative
y
=
x
3
e
x
경사지 3x+4y=12
slope
3
x
+
4
y
=
1
2
derivative f(x)=sin(ln(x))
derivative
f
(
x
)
=
sin
(
ln
(
x
)
)
polar (-3,3sqrt(3))
polar
(
−
3
,
3
√
3
)
단순화 (-1.8)(7.3)
simplify
(
−
1
.
8
)
(
7
.
3
)
거리 (4,0),(-3,4)
distance
(
4
,
0
)
,
(
−
3
,
4
)
polar (4,-4)
polar
(
4
,
−
4
)
derivative f(x)=tan^2(x)
derivative
f
(
x
)
=
tan
2
(
x
)
polar (-9,9)
polar
(
−
9
,
9
)
tangent f(x)=sqrt(x),(1,1)
tangent
f
(
x
)
=
√
x
,
(
1
,
1
)
경사지 5(y+2)=4(x-3)
slope
5
(
y
+
2
)
=
4
(
x
−
3
)
거리 (1+sqrt(24),-3),(1,-2)
distance
(
1
+
√
2
4
,
−
3
)
,
(
1
,
−
2
)
z=4-2i
z
=
4
−
2
i
cartesian (4, pi/6)
cartesian
(
4
,
π
6
)
단순화 (-2.3)(6.5)
simplify
(
−
2
.
3
)
(
6
.
5
)
normal sqrt(1-tanh(5x)),\at x=0
normal
√
1
−
tanh
(
5
x
)
,
at
x
=
0
polar (3,-3)
polar
(
3
,
−
3
)
derivative f(x)=sqrt(5x^6-12)
derivative
f
(
x
)
=
√
5
x
6
−
1
2
derivative y=e^{2x}
derivative
y
=
e
2
x
derivative f(x)=3x+2
derivative
f
(
x
)
=
3
x
+
2
적분 1/(sqrt(x))
integral
1
√
x
f=sin(1)
f
=
sin
(
1
)
polar (sqrt(3),1)
polar
(
√
3
,
1
)
경사지 3/4 x^4-4/3 x^3+5/2
slope
3
4
x
4
−
4
3
x
3
+
5
2
derivative y=sqrt(4-x^2)
derivative
y
=
√
4
−
x
2
polar (1,3)
polar
(
1
,
3
)
derivative-6/(x^4)
derivative
−
6
x
4
derivative (x+1)^2(x-4)^3
derivative
(
x
+
1
)
2
(
x
−
4
)
3
거리 (-2,3),(4,-1)
distance
(
−
2
,
3
)
,
(
4
,
−
1
)
중간점 (-1,-1),(1,2)
midpoint
(
−
1
,
−
1
)
,
(
1
,
2
)
derivative f(x)=cos(80)
derivative
f
(
x
)
=
cos
(
8
0
◦
)
tangent f(x)=sqrt(x^2+18x+86)
tangent
f
(
x
)
=
√
x
2
+
1
8
x
+
8
6
derivative f(x)=-4x^3-cos(x)+2x
derivative
f
(
x
)
=
−
4
x
3
−
cos
(
x
)
+
2
x
tangent y=x^3
tangent
y
=
x
3
derivative e^xsin(x)
derivative
e
x
sin
(
x
)
cartesian (-4,(3pi)/4)
cartesian
(
−
4
,
3
π
4
)
derivative f(x)= 1/(sqrt(x))
derivative
f
(
x
)
=
1
√
x
경사지 y=-1/2 x+3
slope
y
=
−
1
2
x
+
3
경사지 y=5x-1
slope
y
=
5
x
−
1
tangent f(x)=ln(x)log_{2}(x),\at x=2
tangent
f
(
x
)
=
ln
(
x
)
log
2
(
x
)
,
at
x
=
2
tangent f(x)= 1/(x^2)
tangent
f
(
x
)
=
1
x
2
derivative f(x)=x^4
derivative
f
(
x
)
=
x
4
derivative x^{11}arccot(x)
derivative
x
1
1
arccot
(
x
)
중간점 (2,-14),(-3,0)
midpoint
(
2
,
−
1
4
)
,
(
−
3
,
0
)
경사지 y=3x+5
slope
y
=
3
x
+
5
중간점 (2,4),(2,-7)
midpoint
(
2
,
4
)
,
(
2
,
−
7
)
경사지 2x+3y=6
slope
2
x
+
3
y
=
6
단순화 (3.5)(2.2)
simplify
(
3
.
5
)
(
2
.
2
)
직각의 y=2x+3
perpendicular
y
=
2
x
+
3
중간점 (-4,4),(5,-1)
midpoint
(
−
4
,
4
)
,
(
5
,
−
1
)
slopeintercept 3x-2y=-16
slopeintercept
3
x
−
2
y
=
−
1
6
거리 (8,0),(4,-4)
distance
(
8
,
0
)
,
(
4
,
−
4
)
derivative y=ln(ln(x^{32}))
derivative
y
=
ln
(
ln
(
x
3
2
)
)
slopeintercept 4x-3y=9
slopeintercept
4
x
−
3
y
=
9
tangent y=x^2-3x-10,\at x=5.5
tangent
y
=
x
2
−
3
x
−
1
0
,
at
x
=
5
.
5
(
−
1
)
(
0
)
(
4
)
derivative y=e^{x^2}
derivative
y
=
e
x
2
derivative f(x)=-9/x ,\at x=6
derivative
f
(
x
)
=
−
9
x
,
at
x
=
6
중간점 (10,6),(-4,8)
midpoint
(
1
0
,
6
)
,
(
−
4
,
8
)
polar (-3,-3sqrt(3))
polar
(
−
3
,
−
3
√
3
)
derivative f(x)=sqrt(x)
derivative
f
(
x
)
=
√
x
derivative y= 1/x
derivative
y
=
1
x
x^2+y^2=16
x
2
+
y
2
=
1
6
derivative 5x
derivative
5
x
slopeintercept 3x+4y=12
slopeintercept
3
x
+
4
y
=
1
2
직각의 y=-2x+3
perpendicular
y
=
−
2
x
+
3
경사지 8x+2y=6
slope
8
x
+
2
y
=
6
1
..
4
5
6
7
8
..
10
