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일반적인 프리 미적분학 문제
derivative f(x)=ln(sin(x))
derivative
f
(
x
)
=
ln
(
sin
(
x
)
)
경사지 6x+10y=8
slope
6
x
+
1
0
y
=
8
polar (4,4)
polar
(
4
,
4
)
derivative f(x)=cos(x^3)
derivative
f
(
x
)
=
cos
(
x
3
)
경사지 f(x)=-2x+5
slope
f
(
x
)
=
−
2
x
+
5
tangent f(x)=-3x^2-6x,\at x=-1
tangent
f
(
x
)
=
−
3
x
2
−
6
x
,
at
x
=
−
1
derivative 4e^x
derivative
4
e
x
derivative \sqrt[3]{x^2}+sqrt(x)
derivative
3
√
x
2
+
√
x
derivative f(x)=pi
derivative
f
(
x
)
=
π
derivative f(x)= 1/(3x^2)+4x^3
derivative
f
(
x
)
=
1
3
x
2
+
4
x
3
derivative f(x)=-12x^2+9x,\at x=6
derivative
f
(
x
)
=
−
1
2
x
2
+
9
x
,
at
x
=
6
단순화 (1.3)(3.5)
simplify
(
1
.
3
)
(
3
.
5
)
경사지 y=5x+2
slope
y
=
5
x
+
2
cartesian (6,(2pi)/3)
cartesian
(
6
,
2
π
3
)
derivative f(x)=ln(3x)
derivative
f
(
x
)
=
ln
(
3
x
)
derivative e^{x^2}*2x
derivative
e
x
2
·
2
x
cartesian (4,pi)
cartesian
(
4
,
π
)
derivative 4x^2
derivative
4
x
2
tangent y=ln(x)
tangent
y
=
ln
(
x
)
선 (-6,0),(0,1)
line
(
−
6
,
0
)
,
(
0
,
1
)
derivative f(x)=ax^2+bx+c
derivative
f
(
x
)
=
ax
2
+
bx
+
c
derivative f(x)=x+2
derivative
f
(
x
)
=
x
+
2
polar (5,5)
polar
(
5
,
5
)
경사지 y=2
slope
y
=
2
적분 x^2
integral
x
2
중간점 (-3,-8),(-6.5,-4.5)
midpoint
(
−
3
,
−
8
)
,
(
−
6
.
5
,
−
4
.
5
)
경사지-3
slope
−
3
중간점 (-8,-6),(-4,10)
midpoint
(
−
8
,
−
6
)
,
(
−
4
,
1
0
)
derivative f(x)=(3x-x^3+1)^4
derivative
f
(
x
)
=
(
3
x
−
x
3
+
1
)
4
derivative f(x)=xe^x
derivative
f
(
x
)
=
xe
x
derivative 1-e^x
derivative
1
−
e
x
derivative f(x)= x/2
derivative
f
(
x
)
=
x
2
polar (-3,-3)
polar
(
−
3
,
−
3
)
derivative x-1
derivative
x
−
1
derivative f(x)=sin(x)
derivative
f
(
x
)
=
sin
(
x
)
derivative f(x)= 1/9 x^3+1/21 x-19
derivative
f
(
x
)
=
1
9
x
3
+
1
2
1
x
−
1
9
derivative f(x)=sqrt(x+3)
derivative
f
(
x
)
=
√
x
+
3
tangent f(x)=sqrt(x),\at x=9
tangent
f
(
x
)
=
√
x
,
at
x
=
9
derivative x^2-4x+5
derivative
x
2
−
4
x
+
5
derivative y=2x+5
derivative
y
=
2
x
+
5
derivative x(x-4)^3
derivative
x
(
x
−
4
)
3
derivative f(x)= 1/(x^2),\at x=2
derivative
f
(
x
)
=
1
x
2
,
at
x
=
2
중간점 (-7,-7),(-6,-1)
midpoint
(
−
7
,
−
7
)
,
(
−
6
,
−
1
)
중간점 (-4,-3),(7,-5)
midpoint
(
−
4
,
−
3
)
,
(
7
,
−
5
)
derivative f(x)=ln(x-5)
derivative
f
(
x
)
=
ln
(
x
−
5
)
단순화 (-7.5)(7.3)
simplify
(
−
7
.
5
)
(
7
.
3
)
polar (3sqrt(3),3)
polar
(
3
√
3
,
3
)
derivative g(x)=((3x-2))/((x^2+2))
derivative
g
(
x
)
=
(
3
x
−
2
)
(
x
2
+
2
)
x=-5
x
=
−
5
polar (-4,4sqrt(3))
polar
(
−
4
,
4
√
3
)
derivative x^3ln(x)
derivative
x
3
ln
(
x
)
거리 (7,-1),(-8,-9)
distance
(
7
,
−
1
)
,
(
−
8
,
−
9
)
경사지 3x+4y=8
slope
3
x
+
4
y
=
8
경사지 x=4.2
slope
x
=
4
.
2
적분 sin(2x)
integral
sin
(
2
x
)
선 (20,10),(2,5)
line
(
2
0
,
1
0
)
,
(
2
,
5
)
선 (-2,0),(0,2)
line
(
−
2
,
0
)
,
(
0
,
2
)
경사지 y= 4/5 x-3
slope
y
=
4
5
x
−
3
derivative e^{3x}cos(2x)
derivative
e
3
x
cos
(
2
x
)
derivative f(x)=x^2+1
derivative
f
(
x
)
=
x
2
+
1
경사지 (2.3)(4.9)
slope
(
2
.
3
)
(
4
.
9
)
중간점 (15,-3),(5,12)
midpoint
(
1
5
,
−
3
)
,
(
5
,
1
2
)
직각의 y= 2/3 x-3,(0,-3)
perpendicular
y
=
2
3
x
−
3
,
(
0
,
−
3
)
polar (2sqrt(2),2sqrt(2))
polar
(
2
√
2
,
2
√
2
)
tangent f(x)=ln(x),\at x=1
tangent
f
(
x
)
=
ln
(
x
)
,
at
x
=
1
polar (4sqrt(3),4)
polar
(
4
√
3
,
4
)
적분 x
integral
x
경사지 y= 2/3 x
slope
y
=
2
3
x
derivative f(x)=5x^2(x+47)
derivative
f
(
x
)
=
5
x
2
(
x
+
4
7
)
derivative y=csc(x)
derivative
y
=
csc
(
x
)
derivative tan(x-y)= y/(1+x^2)
derivative
tan
(
x
−
y
)
=
y
1
+
x
2
tangent e^x
tangent
e
x
derivative f(x)=e^x
derivative
f
(
x
)
=
e
x
y=8x^2
y
=
8
x
2
derivative x^2+x+1
derivative
x
2
+
x
+
1
derivative y=sqrt(1-x^2)
derivative
y
=
√
1
−
x
2
선 (3,0),(0,-2)
line
(
3
,
0
)
,
(
0
,
−
2
)
y=3x^2
y
=
3
x
2
tangent y=(2x-5)/(x+1),\at x=0
tangent
y
=
2
x
−
5
x
+
1
,
at
x
=
0
polar (4,4sqrt(3))
polar
(
4
,
4
√
3
)
polar (-3,4)
polar
(
−
3
,
4
)
cartesian (6,(5pi)/4)
cartesian
(
6
,
5
π
4
)
polar (-sqrt(2),-sqrt(2))
polar
(
−
√
2
,
−
√
2
)
f=1
f
=
1
derivative y=sqrt(x)
derivative
y
=
√
x
cartesian (4,(3pi)/2)
cartesian
(
4
,
3
π
2
)
x^2+y^2-4x=0
x
2
+
y
2
−
4
x
=
0
직각의 4y=5x-8
perpendicular
4
y
=
5
x
−
8
polar (0,-2)
polar
(
0
,
−
2
)
polar (0,2)
polar
(
0
,
2
)
solvefor g,T=2pisqrt(l/g)
solvefor
g
,
T
=
2
π
√
l
g
polar (-2,2sqrt(3))
polar
(
−
2
,
2
√
3
)
경사지 2x-3y=9
slope
2
x
−
3
y
=
9
polar (3,3)
polar
(
3
,
3
)
derivative f(x)=sin(x)cos(x)
derivative
f
(
x
)
=
sin
(
x
)
cos
(
x
)
derivative f(x)=4^x
derivative
f
(
x
)
=
4
x
slopeintercept x-y=-2
slopeintercept
x
−
y
=
−
2
derivative f(x)=x^2+3
derivative
f
(
x
)
=
x
2
+
3
derivative x^2e^{-x}
derivative
x
2
e
−
x
f(m)= 1/(log_{3)(m)}
f
(
m
)
=
1
log
3
(
m
)
1
2
3
4
5
6
7
..
10
