프로로 업그레이드
사이트 계속하기
We've updated our
Privacy Policy
effective December 15. Please read our updated Privacy Policy and tap
Continue
솔루션
적분 계산기
도함수 계산기
대수 계산기
행렬 계산기
더...
그래프 작성
선 그래프
지수 그래프
이차 그래프
사인 그래프
더...
계산기
BMI 계산기
복리 계산기
백분율 계산기
가속도 계산기
더...
기하학
피타고라스 정리 계산기
원 면적 계산기
이등변삼각형 계산기
삼각형 계산기
더...
도구
메모
무리
치트 시트
워크시트
학습 가이드
실행
솔루션 확인
ko
English
Español
Português
Français
Deutsch
Italiano
Русский
中文(简体)
한국어
日本語
Tiếng Việt
עברית
العربية
개선하다
일반적인 문제
토픽
사전 대수
대수학
단어 문제
Functions & Graphing
기하학
삼각법
프리 미적분학
미적분학
통계
일반적인 Functions & Graphing 문제
critical f(x,y)=5xy+5ln(x)+8y
critical
f
(
x
,
y
)
=
5
xy
+
5
ln
(
x
)
+
8
y
critical f(x)=(x^2-2x+4)/((x-1)^2)
critical
f
(
x
)
=
x
2
−
2
x
+
4
(
x
−
1
)
2
critical sqrt(x)ln(4x)
critical
√
x
ln
(
4
x
)
critical 3x^{1/2}-x^{3/2}
critical
3
x
1
2
−
x
3
2
critical f(x)= 4/3 x^{-2/3}(x-1)
critical
f
(
x
)
=
4
3
x
−
2
3
(
x
−
1
)
critical f(x)=2x^3+3x^2-72x-9
critical
f
(
x
)
=
2
x
3
+
3
x
2
−
7
2
x
−
9
critical x^{2/3}(3-x)
critical
x
2
3
(
3
−
x
)
derivative of (7x^3y/(x-4y))
d
dx
(
7
x
3
y
x
−
4
y
)
critical f(x)=2cos(x)-2sin(x)
critical
f
(
x
)
=
2
cos
(
x
)
−
2
sin
(
x
)
critical f(x)=(x+3)/(x^2-5x+6)
critical
f
(
x
)
=
x
+
3
x
2
−
5
x
+
6
critical f(x)=60x^3-30x
critical
f
(
x
)
=
6
0
x
3
−
3
0
x
critical y=x
critical
y
=
x
critical f(x)=x^2-3x-10
critical
f
(
x
)
=
x
2
−
3
x
−
1
0
critical f(x,y)=x^2y+2xy+3y^3-3y
critical
f
(
x
,
y
)
=
x
2
y
+
2
xy
+
3
y
3
−
3
y
critical f(x)=sin(x)+sqrt(3)cos(x)
critical
f
(
x
)
=
sin
(
x
)
+
√
3
cos
(
x
)
critical f(x)=12x^2+y^3-12xy
critical
f
(
x
)
=
1
2
x
2
+
y
3
−
1
2
xy
critical f(x)=(2x^2)/(1-x^2)
critical
f
(
x
)
=
2
x
2
1
−
x
2
critical f(x)= 3/(x-1)
critical
f
(
x
)
=
3
x
−
1
critical f(x)= 1/(x^3-6x^2+1)
critical
f
(
x
)
=
1
x
3
−
6
x
2
+
1
critical f(x)=x^2+6x
critical
f
(
x
)
=
x
2
+
6
x
critical (x^2-24)/(x-5)
critical
x
2
−
2
4
x
−
5
critical f(x)=-6x^2+9x-2
critical
f
(
x
)
=
−
6
x
2
+
9
x
−
2
critical y=(x^2-3x+2)/(x^2-4x+3)
critical
y
=
x
2
−
3
x
+
2
x
2
−
4
x
+
3
critical f(x)=-7x^3+21x+2
critical
f
(
x
)
=
−
7
x
3
+
2
1
x
+
2
critical f(x)=x^2+18x+81
critical
f
(
x
)
=
x
2
+
1
8
x
+
8
1
critical f(x)=x+(64)/x
critical
f
(
x
)
=
x
+
6
4
x
critical f(x)=x^3+3x^2-9x+7
critical
f
(
x
)
=
x
3
+
3
x
2
−
9
x
+
7
critical 12x^3+12x^2-24x
critical
1
2
x
3
+
1
2
x
2
−
2
4
x
critical (x-2)/(x+2)
critical
x
−
2
x
+
2
critical y= 1/x
critical
y
=
1
x
critical sqrt(x)ln(x)
critical
√
x
ln
(
x
)
critical (-4x)/(x-8)
critical
−
4
x
x
−
8
critical f(x)=3x^4-4x^3-12x^2+17
critical
f
(
x
)
=
3
x
4
−
4
x
3
−
1
2
x
2
+
1
7
critical (4x^2)/(x^2+4)
critical
4
x
2
x
2
+
4
critical f(x)=xsqrt(x-x^2)
critical
f
(
x
)
=
x
√
x
−
x
2
critical f(x)=x^4-2x^3+x+1
critical
f
(
x
)
=
x
4
−
2
x
3
+
x
+
1
critical f(x)=x^3-5x^2-8x+2
critical
f
(
x
)
=
x
3
−
5
x
2
−
8
x
+
2
critical f(x)=x^{(4)}-8x^{(2)}+16
critical
f
(
x
)
=
x
(
4
)
−
8
x
(
2
)
+
1
6
critical f(x)=(x+2)^2(1-x)^2
critical
f
(
x
)
=
(
x
+
2
)
2
(
1
−
x
)
2
critical f(x)=-x^3+3x^2-4
critical
f
(
x
)
=
−
x
3
+
3
x
2
−
4
critical f(x)=-x^3+3x^2-5
critical
f
(
x
)
=
−
x
3
+
3
x
2
−
5
critical f(x)= x/(sqrt(x^2+2))
critical
f
(
x
)
=
x
√
x
2
+
2
critical f(x)=(x+1)/(x^2-9)
critical
f
(
x
)
=
x
+
1
x
2
−
9
critical f(x)=4x^3-18x
critical
f
(
x
)
=
4
x
3
−
1
8
x
critical f(x)=x(6-x)^{2/3}
critical
f
(
x
)
=
x
(
6
−
x
)
2
3
critical f(x,y)=x^2+xy+y^2
critical
f
(
x
,
y
)
=
x
2
+
xy
+
y
2
critical f(x)=x^3-75x+150
critical
f
(
x
)
=
x
3
−
7
5
x
+
1
5
0
critical f(x)=x^2+y^3
critical
f
(
x
)
=
x
2
+
y
3
critical f(x)=((x+8))/(x^2)
critical
f
(
x
)
=
(
x
+
8
)
x
2
critical f(x)=x^2-8ln(4x)
critical
f
(
x
)
=
x
2
−
8
ln
(
4
x
)
critical f(x,y)=x^4+4x^2y^2+4y^4+1
critical
f
(
x
,
y
)
=
x
4
+
4
x
2
y
2
+
4
y
4
+
1
critical f(x)=2x^2+5x-1
critical
f
(
x
)
=
2
x
2
+
5
x
−
1
critical f(x)=x^3-5x^2+3x+13
critical
f
(
x
)
=
x
3
−
5
x
2
+
3
x
+
1
3
critical f(x)=(3x-4)/(x^2+1)
critical
f
(
x
)
=
3
x
−
4
x
2
+
1
critical f(x)=x^2-16x+10
critical
f
(
x
)
=
x
2
−
1
6
x
+
1
0
critical f(x)=x^6+2x^3-48
critical
f
(
x
)
=
x
6
+
2
x
3
−
4
8
critical y=(e^x)/x
critical
y
=
e
x
x
critical (-3x^2-2x)/((1-x^2)^{1/2)}
critical
−
3
x
2
−
2
x
(
1
−
x
2
)
1
2
critical f(x)=1+2y
critical
f
(
x
)
=
1
+
2
y
critical e^{3x}(36x^2+4)
critical
e
3
x
(
3
6
x
2
+
4
)
critical-1/((x-2)^2)
critical
−
1
(
x
−
2
)
2
critical 6x^2-18x-24
critical
6
x
2
−
1
8
x
−
2
4
critical \sqrt[3]{x-2}
critical
3
√
x
−
2
critical f(x)=(x^3)/3-5x^2+24x+1
critical
f
(
x
)
=
x
3
3
−
5
x
2
+
2
4
x
+
1
critical e^{2x}(x^2-3x+2)
critical
e
2
x
(
x
2
−
3
x
+
2
)
critical f(x)=x^3+y^3-3xy+1
critical
f
(
x
)
=
x
3
+
y
3
−
3
xy
+
1
extreme f(x,y)=2x+8x^5+7y+6y^3
extreme
f
(
x
,
y
)
=
2
x
+
8
x
5
+
7
y
+
6
y
3
critical f(x)=3x^2-4x^3
critical
f
(
x
)
=
3
x
2
−
4
x
3
critical y^3+3x^2y-6x^2-6y^2+2
critical
y
3
+
3
x
2
y
−
6
x
2
−
6
y
2
+
2
critical f(x)=(-2(x+1))/((x-2)^4)
critical
f
(
x
)
=
−
2
(
x
+
1
)
(
x
−
2
)
4
critical f(x)=5-2x^2+3x^3-x^4
critical
f
(
x
)
=
5
−
2
x
2
+
3
x
3
−
x
4
critical f(x)=x^2-8ln(7x)
critical
f
(
x
)
=
x
2
−
8
ln
(
7
x
)
critical f(x,y)=x^2-2x+y^2+2y+1
critical
f
(
x
,
y
)
=
x
2
−
2
x
+
y
2
+
2
y
+
1
critical f(x)=((x^4)/4-x^3-2x^2+3)
critical
f
(
x
)
=
(
x
4
4
−
x
3
−
2
x
2
+
3
)
critical f(x)=14sqrt(10pix)+(160)/x
critical
f
(
x
)
=
1
4
√
1
0
π
x
+
1
6
0
x
critical f(x,y)=x+y-1
critical
f
(
x
,
y
)
=
x
+
y
−
1
critical f(x)=In(2x+1)
critical
f
(
x
)
=
In
(
2
x
+
1
)
critical (2x)/(sqrt(x^2+9))-1
critical
2
x
√
x
2
+
9
−
1
critical-3x^4+5x^2+3
critical
−
3
x
4
+
5
x
2
+
3
critical y=-x^3+3x^2
critical
y
=
−
x
3
+
3
x
2
critical f(x)=((x))/((x^2+11x+30))
critical
f
(
x
)
=
(
x
)
(
x
2
+
1
1
x
+
3
0
)
critical 5-sqrt(10-2x)
critical
5
−
√
1
0
−
2
x
critical f(x)=5x-x^2
critical
f
(
x
)
=
5
x
−
x
2
critical y=2x^2-x^4
critical
y
=
2
x
2
−
x
4
critical a^3y=x^3(4a-3x)
critical
a
3
y
=
x
3
(
4
a
−
3
x
)
critical f(x)=3x^2-1
critical
f
(
x
)
=
3
x
2
−
1
critical f(x)=1+12x-x^3
critical
f
(
x
)
=
1
+
1
2
x
−
x
3
critical-x^3
critical
−
x
3
critical f(x)=-7(x+1)^2+3x+7
critical
f
(
x
)
=
−
7
(
x
+
1
)
2
+
3
x
+
7
critical f(x)=(x^2-5/4)e^x
critical
f
(
x
)
=
(
x
2
−
5
4
)
e
x
critical f(x)=x^2-2x+y^2+2y+1
critical
f
(
x
)
=
x
2
−
2
x
+
y
2
+
2
y
+
1
critical (x^4)/4-(9x^2)/2+1
critical
x
4
4
−
9
x
2
2
+
1
critical f(x)=(3x-2)/(-5x^2+2)
critical
f
(
x
)
=
3
x
−
2
−
5
x
2
+
2
critical f(x,y)=x^2+y^2+3xy
critical
f
(
x
,
y
)
=
x
2
+
y
2
+
3
xy
critical f(x)=x-7x^{1/7}
critical
f
(
x
)
=
x
−
7
x
1
7
critical f(x)=4cos(x)+2sin^2(x)
critical
f
(
x
)
=
4
cos
(
x
)
+
2
sin
2
(
x
)
critical x^4+2x^3-3x^2-4x+4
critical
x
4
+
2
x
3
−
3
x
2
−
4
x
+
4
critical f(x)=e^x-3x
critical
f
(
x
)
=
e
x
−
3
x
critical 2x^3-12x^2+18x
critical
2
x
3
−
1
2
x
2
+
1
8
x
critical f(x,y)=3x^2-2x+y^2-4y+1
critical
f
(
x
,
y
)
=
3
x
2
−
2
x
+
y
2
−
4
y
+
1
1
..
845
846
847
848
849
..
1324