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Functions & Graphing
גאומטריה
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טרום חשבון אינפיטיסמלי
חשבון אינפיטסימלי
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בעיות חשבון אינפיטסימלי פופולריות
(x+1)y^'=y^2
(
x
+
1
)
y
′
=
y
2
y^'x^2=y
y
′
x
2
=
y
x^'=4x+2e^t*x
x
′
=
4
x
+
2
e
t
·
x
y^'=-4xy^2
y
′
=
−
4
xy
2
(xy+x^3y)y^'=1+y^2
(
xy
+
x
3
y
)
y
′
=
1
+
y
2
y^'+sin(x)y=5sin(x)
y
′
+
sin
(
x
)
y
=
5
sin
(
x
)
y^'=3x+e^x
y
′
=
3
x
+
e
x
y^'ye^{-x}=0
y
′
ye
−
x
=
0
f^{''}(x)=3x+1
f
′
′
(
x
)
=
3
x
+
1
2y^{'''}=e^xy^{'''}
2
y
′
′
′
=
e
x
y
′
′
′
f^'(x)=4x+9
f
′
(
x
)
=
4
x
+
9
2y^'+y^3=0
2
y
′
+
y
3
=
0
2x^2y^'=x^2+y^2
2
x
2
y
′
=
x
2
+
y
2
x^3y^{'''}-x^2y^'=0
x
3
y
′
′
′
−
x
2
y
′
=
0
5x(x+4y)y^'=5y(x-4y)
5
x
(
x
+
4
y
)
y
′
=
5
y
(
x
−
4
y
)
3y^'+7y=x^3-2x^2+1
3
y
′
+
7
y
=
x
3
−
2
x
2
+
1
y^'=x*y-3*x+3*y+3*y-9
y
′
=
x
·
y
−
3
·
x
+
3
·
y
+
3
·
y
−
9
y^'=y+e^x,y(0)=(x+c)e^x,y(0)= 1/2
y
′
=
y
+
e
x
,
y
(
0
)
=
(
x
+
c
)
e
x
,
y
(
0
)
=
1
2
y^'=(x+y)2
y
′
=
(
x
+
y
)
2
y^'=2y+(x^2)+5
y
′
=
2
y
+
(
x
2
)
+
5
(x-1)y^'+xy=sin(x)
(
x
−
1
)
y
′
+
xy
=
sin
(
x
)
y^'-y=2*x*e^{2x}
y
′
−
y
=
2
·
x
·
e
2
x
y^'+y+e^{-x}=0
y
′
+
y
+
e
−
x
=
0
y^'=2xy+1
y
′
=
2
xy
+
1
(y^')/(t+3y)=3
y
′
t
+
3
y
=
3
1+xy=xy^'
1
+
xy
=
xy
′
integral f(x)=5x-6
integral
f
(
x
)
=
5
x
−
6
lhopital limit as x approaches 0 of ((e^{5x}-1-5x))/((x^2))
lhopital
lim
x
→
0
(
(
e
5
x
−
1
−
5
x
)
(
x
2
)
)
derivative of y= 4/x
d
dx
y
=
4
x
derivative derivative of 1/x
derivative
d
dx
(
1
x
)
derivative of y=3x
d
dx
y
=
3
x
slope (2,5),(3,6)
slope
(
2
,
5
)
,
(
3
,
6
)
diffquot f=4x+3
diffquot
f
=
4
x
+
3
integral cos(θ)
integral
cos
(
θ
)
derivative derivative of cos(x)
derivative
d
dx
(
cos
(
x
)
)
integral of (1/((e^x)))
∫
(
1
(
e
x
)
)
dx
derivative of y=sec(x)+tan(x)
d
dx
y
=
sec
(
x
)
+
tan
(
x
)
longdivision limit as x approaches infinity of x/2
longdivision
lim
x
→
∞
(
x
2
)
integral sin(θ)
integral
sin
(
θ
)
derivative derivative of csc(x)
derivative
d
dx
(
csc
(
x
)
)
derivative derivative of 1/((1-x))
derivative
d
dx
(
1
(
1
−
x
)
)
secondderivative y=cos(x)
secondderivative
y
=
cos
(
x
)
derivative of y=sinh(cosh(x))
d
dx
y
=
sinh
(
cosh
(
x
)
)
diffquot f=((f(x+h)-f))/h
diffquot
f
=
(
f
(
x
+
h
)
−
f
)
h
derivative derivative of sec(2x)
derivative
d
dx
(
sec
(
2
x
)
)
derivative of y=xe^x
d
dx
y
=
xe
x
derivative derivative of x/2
derivative
d
dx
(
x
2
)
integral sqrt(X)
integral
√
X
derivative derivative of e^{(-x/2})
derivative
d
dx
(
e
−
x
2
)
integral f(x)=sin(x)
integral
f
(
x
)
=
sin
(
x
)
derivative derivative of cos^2(x)
derivative
d
dx
(
cos
2
(
x
)
)
derivative derivative of ((d^2y(d,x))/((dx^2)))
derivative
d
dx
(
(
d
2
y
(
d
,
x
)
)
(
dx
2
)
)
integral of (sec(θ))
∫
(
sec
(
θ
)
)
d
θ
derivative of y=csc^2(x)
d
dx
y
=
csc
2
(
x
)
integral 1/((x^{-2))}
integral
1
(
x
−
2
)
derivative derivative of sin(2x)
derivative
d
dx
(
sin
(
2
x
)
)
derivative derivative of 1/((1+x^2))
derivative
d
dx
(
1
(
1
+
x
2
)
)
derivative of y=5x
d
dx
y
=
5
x
slope (-4,2),(4,-4)
slope
(
−
4
,
2
)
,
(
4
,
−
4
)
derivative derivative of sin(x^2)
derivative
d
dx
(
sin
(
x
2
)
)
integral of (e^{xy})
∫
(
e
xy
)
dx
derivative derivative of sec^2(x)
derivative
d
dx
(
sec
2
(
x
)
)
derivative of y=2e^x
d
dx
y
=
2
e
x
derivative derivative of xcos(x)
derivative
d
dx
(
x
cos
(
x
)
)
derivative derivative of cos(xsec(x))
derivative
d
dx
(
cos
(
x
)
sec
(
x
)
)
derivative derivative of e^{3x}
derivative
d
dx
(
e
3
x
)
slope (4,0),(0,3)
slope
(
4
,
0
)
,
(
0
,
3
)
longdivision limit as x approaches infinity of x/4
longdivision
lim
x
→
∞
(
x
4
)
(dy)/(dx)y=cos(x)
dy
dx
y
=
cos
(
x
)
derivative derivative of cos(3x)
derivative
d
dx
(
cos
(
3
x
)
)
secondderivative f(x)=arctan(x)
secondderivative
f
(
x
)
=
arctan
(
x
)
derivative derivative of e^{-2x}
derivative
d
dx
(
e
−
2
x
)
derivative derivative of xy
derivative
d
dx
(
xy
)
volumeabout x,y=0,x=2,y=sqrt(x)
volumeabout
x
,
y
=
0
,
x
=
2
,
y
=
√
x
integral csc(x)cot(x)
integral
csc
(
x
)
cot
(
x
)
derivative derivative of x/((x+1))
derivative
d
dx
(
x
(
x
+
1
)
)
integral (-1)/u
integral
−
1
u
(dy)/(dx)y=2x
dy
dx
y
=
2
x
derivative derivative of x^{1/2}
derivative
d
dx
(
x
1
2
)
derivative of y=sin(x)
d
dx
y
=
sin
(
x
)
secondderivative f(x)=cos(2x)
secondderivative
f
(
x
)
=
cos
(
2
x
)
derivative d/(dy)(-2y)
derivative
d
dy
(
−
2
y
)
derivative derivative of 2x
derivative
d
dx
(
2
x
)
derivative derivative of sin(3x)
derivative
d
dx
(
sin
(
3
x
)
)
derivative derivative of 2cos(x)
derivative
d
dx
(
2
cos
(
x
)
)
derivative derivative of 1/((2x))
derivative
d
dx
(
1
(
2
x
)
)
derivative of y= 5/x
d
dx
y
=
5
x
derivative of y=((sec(x)))/x
d
dx
y
=
(
sec
(
x
)
)
x
derivative derivative of tan(2x)
derivative
d
dx
(
tan
(
2
x
)
)
derivative derivative of 1-sin(x)
derivative
d
dx
(
1
−
sin
(
x
)
)
integral f(x)=cos(2x)
integral
f
(
x
)
=
cos
(
2
x
)
derivative d/(dθ)(sin(θ)cos(θ))
derivative
d
d
θ
(
sin
(
θ
)
cos
(
θ
)
)
slope (4,5),(9,11)
slope
(
4
,
5
)
,
(
9
,
1
1
)
derivative derivative of c/x
derivative
d
dx
(
c
x
)
derivative d/(dt)(e^t)
derivative
d
dt
(
e
t
)
integral of 1/((y^2))
∫
1
(
y
2
)
dy
derivative derivative of ((e^x)/x)
derivative
d
dx
(
(
e
x
)
x
)
limit as x approaches infinity of (x,x,(sqrt(x)+x^2))/((2x-x^2))
lim
x
→
∞
(
x
,
x
,
(
√
x
+
x
2
)
(
2
x
−
x
2
)
)
derivative of y= 7/x
d
dx
y
=
7
x
derivative derivative of 8/x
derivative
d
dx
(
8
x
)
1
..
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