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Beliebte Rechnen-Probleme
(dy)/(dt)=e^{-2t+3y}
dy
dt
=
e
−
2
t
+
3
y
steigung (-2,-6),(1,6)
slope
(
−
2
,
−
6
)
,
(
1
,
6
)
integral of sqrt(xy-y^2)
∫
√
xy
−
y
2
dx
(dy)/(dx)=0.2y-0.001y^2
dy
dx
=
0
.
2
y
−
0
.
0
0
1
y
2
derivative y=ln(4t)
derivative
y
=
ln
(
4
t
)
tangent y=2x^2-x^4,(1,1)
tangent
y
=
2
x
2
−
x
4
,
(
1
,
1
)
(dy)/(dx)=-2x+3y-5
dy
dx
=
−
2
x
+
3
y
−
5
(\partial)/(\partial z)(x+y+z)
∂
∂
z
(
x
+
y
+
z
)
integral of e^{at}
∫
e
at
dt
(\partial)/(\partial x)(1/4 2^xy^3)
∂
∂
x
(
1
4
2
x
y
3
)
integral of 1/(sqrt(16+x^2))
∫
1
√
1
6
+
x
2
dx
(\partial)/(\partial y)(8xy-1/4 (x+y)^4)
∂
∂
y
(
8
xy
−
1
4
(
x
+
y
)
4
)
limit as x approaches x of sin(x)
lim
x
→
x
(
sin
(
x
)
)
fläche y=x^2,y=9x,y=-1
area
y
=
x
2
,
y
=
9
x
,
y
=
−
1
derivative of-xe^{-x}-e^{-x}+1
d
dx
(
−
xe
−
x
−
e
−
x
+
1
)
integral of (4x^3-2x+1)/x
∫
4
x
3
−
2
x
+
1
x
dx
tangent y=3x^3-x^2+1,(2,21)
tangent
y
=
3
x
3
−
x
2
+
1
,
(
2
,
2
1
)
limit as x approaches infinity of 2x^2+1
lim
x
→
∞
(
2
x
2
+
1
)
derivative of e^x+e
d
dx
(
e
x
+
e
)
integral of (sin^2(x))/(cos^3(x))
∫
sin
2
(
x
)
cos
3
(
x
)
dx
fläche y= 26/5-1/x ,y=x
area
y
=
2
6
5
−
1
x
,
y
=
x
fläche 2x^2,2x+6,-2,-1
area
2
x
2
,
2
x
+
6
,
−
2
,
−
1
limit as x approaches infinity of e^{3x}
lim
x
→
∞
(
e
3
x
)
limit as x approaches 8+of 2/(x-8)
lim
x
→
8
+
(
2
x
−
8
)
taylor (x-1)ln(x-1),2
taylor
(
x
−
1
)
ln
(
x
−
1
)
,
2
y^{''}+16y=40sin(4t)
y
′
′
+
1
6
y
=
4
0
sin
(
4
t
)
(\partial)/(\partial y)(e^x+e^y)
∂
∂
y
(
e
x
+
e
y
)
y^{''}-2y^'-y=0,y(0)=0,y^'(0)=2sqrt(2)
y
′
′
−
2
y
′
−
y
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
2
√
2
derivative sqrt(1)
derivative
√
1
tangent y=e^{4x},\at x= 1/4 ln(5)
tangent
y
=
e
4
x
,
at
x
=
1
4
ln
(
5
)
derivative of (4+8xcosh(2x))
d
dx
(
(
4
+
8
x
)
cosh
(
2
x
)
)
laplacetransformation 5*sin(2*t)
laplacetransform
5
·
sin
(
2
·
t
)
derivative of xye^x
d
dx
(
xye
x
)
derivative of (x^2+2x-5/((x+1)^2))
d
dx
(
x
2
+
2
x
−
5
(
x
+
1
)
2
)
y^{''}+9/t y^'+(15)/(t^2)y=0
y
′
′
+
9
t
y
′
+
1
5
t
2
y
=
0
sum from n=1 to infinity of (3^n)/(2^n)
∑
n
=
1
∞
3
n
2
n
(\partial)/(\partial x)(2x^{0.5}y^{0.5})
∂
∂
x
(
2
x
0
.
5
y
0
.
5
)
derivative 3x^2+8x-25
derivative
3
x
2
+
8
x
−
2
5
integral of 4x^2+3
∫
4
x
2
+
3
dx
derivative w(z)=(3z)/(1+2z)
derivative
w
(
z
)
=
3
z
1
+
2
z
limit as x approaches infinity of-8
lim
x
→
∞
(
−
8
)
fläche cos(x),x^2+2,[0,2]
area
cos
(
x
)
,
x
2
+
2
,
[
0
,
2
]
integral of e^{-2x^2}
∫
e
−
2
x
2
dx
integral of 4x^4e^{-x}
∫
4
x
4
e
−
x
dx
integral of (x^6-x^3+49)/(x^4+7x^2)
∫
x
6
−
x
3
+
4
9
x
4
+
7
x
2
dx
integral of (6sqrt(x))/(x-1)
∫
6
√
x
x
−
1
dx
integral from-1 to 5 of-x^2+4x+5
∫
−
1
5
−
x
2
+
4
x
+
5
dx
integral of (x^2)/(sqrt(x^6-7))
∫
x
2
√
x
6
−
7
dx
d/(dy)(2x^3-x^2y)
d
dy
(
2
x
3
−
x
2
y
)
integral of 1/(x^2-12x+35)
∫
1
x
2
−
1
2
x
+
3
5
dx
3x^'-5x=12
3
x
′
−
5
x
=
1
2
(dy)/(dx)= 1/2 x+y-1
dy
dx
=
1
2
x
+
y
−
1
y^{''''}+18y^{''}+81y=0
y
′
′
′
′
+
1
8
y
′
′
+
8
1
y
=
0
limit as x approaches 1 of x^2+2
lim
x
→
1
(
x
2
+
2
)
derivative of (2x/((1+x)^2))
d
dx
(
2
x
(
1
+
x
)
2
)
integral of (ln(sqrt(3x)))/x
∫
ln
(
√
3
x
)
x
dx
derivative-(18)/(t^3)+3/(t^2)
derivative
−
1
8
t
3
+
3
t
2
integral of xsqrt(x+2)
∫
x
√
x
+
2
dx
integral of (x-1)ln(x)
∫
(
x
−
1
)
ln
(
x
)
dx
(\partial)/(\partial x)(-f(r,x)rsin(x)*sin(x))
∂
∂
x
(
−
f
(
r
,
x
)
r
sin
(
x
)
·
sin
(
x
)
)
derivative f(x)=(-2x^2-2)^3
derivative
f
(
x
)
=
(
−
2
x
2
−
2
)
3
derivative of-e^{-x}cos(x-e^{-x}sin(x))
d
dx
(
−
e
−
x
cos
(
x
)
−
e
−
x
sin
(
x
)
)
(\partial)/(\partial x)(xe^{xy}+2y)
∂
∂
x
(
xe
xy
+
2
y
)
integral of e^{1-2t}
∫
e
1
−
2
t
dt
integral of sqrt(2-3x)
∫
√
2
−
3
x
dx
(\partial)/(\partial x)(4y^8+3y^2x^2)
∂
∂
x
(
4
y
8
+
3
y
2
x
2
)
(x^2+y^2)dx=2xydy
(
x
2
+
y
2
)
dx
=
2
xydy
maclaurin ln(1+e^{-x})
maclaurin
ln
(
1
+
e
−
x
)
integral of 1/(x^{2/3)(2+x^{1/3})}
∫
1
x
2
3
(
2
+
x
1
3
)
dx
integral of sin(sqrt(t))
∫
sin
(
√
t
)
dt
derivative of a*x^2+b*x+c
d
dx
(
a
·
x
2
+
b
·
x
+
c
)
integral of (x^3+x+1)/(1+x^2)
∫
x
3
+
x
+
1
1
+
x
2
dx
laplacetransformation (t)e^{4t}
laplacetransform
(
t
)
e
4
t
integral of sin^2(2x)
∫
sin
2
(
2
x
)
dx
integral of 1/(sqrt(9x^2-49))
∫
1
√
9
x
2
−
4
9
dx
derivative of (x^2-1^3)
d
dx
(
(
x
2
−
1
)
3
)
derivative 1/(t^2-1)
derivative
1
t
2
−
1
integral of (7x-1)/(x^2-1)
∫
7
x
−
1
x
2
−
1
dx
derivative f(x)=sqrt(4x+1)
derivative
f
(
x
)
=
√
4
x
+
1
integral of ((x^3+16))/(x^2+16)
∫
(
x
3
+
1
6
)
x
2
+
1
6
dx
integral of-tan(x)+C
∫
−
tan
(
x
)
+
Cdx
integral of x*cos(8x^2+pi)
∫
x
·
cos
(
8
x
2
+
π
)
dx
taylor 9sqrt(1+x)
taylor
9
√
1
+
x
derivative sin^3(4x)
derivative
sin
3
(
4
x
)
integral of 3x^2(x^3-4)^4
∫
3
x
2
(
x
3
−
4
)
4
dx
derivative of (2x/(e^{4x)})
d
dx
(
2
x
e
4
x
)
y^'=x+y
y
′
=
x
+
y
y^{''}+y=sin(6t),y(0)=0,y^'(0)=0
y
′
′
+
y
=
sin
(
6
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
(\partial)/(\partial x)(1+cos^4(x^4))
∂
∂
x
(
1
+
cos
4
(
x
4
)
)
derivative sin(ln(w))
derivative
sin
(
ln
(
w
)
)
(4y+2t-5)dt+(6y+4t-1)dy=0
(
4
y
+
2
t
−
5
)
dt
+
(
6
y
+
4
t
−
1
)
dy
=
0
sum from n=0 to infinity of e^{-an}
∑
n
=
0
∞
e
−
an
(2dy)/(dx)+6y=3
2
dy
dx
+
6
y
=
3
limit as x approaches infinity of-12
lim
x
→
∞
(
−
1
2
)
derivative of-(4x-3/((2x^2-3x+1)^2))
d
dx
(
−
4
x
−
3
(
2
x
2
−
3
x
+
1
)
2
)
integral from-5 to 5 of sqrt(4+|x|)
∫
−
5
5
√
4
+
|
x
|
dx
limit as x approaches 3+of x-1
lim
x
→
3
+
(
x
−
1
)
integral of sin(2x)cos^3(2x)
∫
sin
(
2
x
)
cos
3
(
2
x
)
dx
limit as x approaches 4 of (2x)/(x-4)
lim
x
→
4
(
2
x
x
−
4
)
(\partial)/(\partial x)(sin(xye^{x^2}))
∂
∂
x
(
sin
(
xye
x
2
)
)
1
..
1156
1157
1158
1159
1160
..
2459