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الهندسة
علم المثلثات
قبل التفاضل والتكامل
حساب التفاضل والتكامل
إحصائيات
مسائل حساب التفاضل والتكامل مشهورة
derivative of cos(x-x)
d
dx
(
cos
(
x
)
−
x
)
tangent (x-5)^2+(y-3)^2=18,(8,6)
tangent
(
x
−
5
)
2
+
(
y
−
3
)
2
=
1
8
,
(
8
,
6
)
integral from 0 to 4 of pi(3x)^2
∫
0
4
π
(
3
x
)
2
dx
derivative f(x)=cos(tan(x))
derivative
f
(
x
)
=
cos
(
tan
(
x
)
)
y^{''}+ay^'+by=t+e^{3t}
y
′
′
+
ay
′
+
by
=
t
+
e
3
t
limit as x approaches-1 of ln(x+1)
lim
x
→
−
1
(
ln
(
x
+
1
)
)
(\partial)/(\partial x)(1/2 (x^2+4y^2))
∂
∂
x
(
1
2
(
x
2
+
4
y
2
)
)
(\partial)/(\partial x)(1/(sqrt(2x)))
∂
∂
x
(
1
√
2
x
)
2xy(dy)/(dx)=y^2-x^2+1
2
xy
dy
dx
=
y
2
−
x
2
+
1
tangent 100x^2+400x+5000,0.5
tangent
1
0
0
x
2
+
4
0
0
x
+
5
0
0
0
,
0
.
5
integral of e^{y(1-x)}
∫
e
y
(
1
−
x
)
dx
derivative of y=7x^2cos(x)cot(x)
d
dx
y
=
7
x
2
cos
(
x
)
cot
(
x
)
(dy)/(dx)+e^xy=-9e^x
dy
dx
+
e
x
y
=
−
9
e
x
tangent f(x)=(6x)/(x-1),(-1,3)
tangent
f
(
x
)
=
6
x
x
−
1
,
(
−
1
,
3
)
integral of ((2x^3+3x))/(x^4+3x^2+7)
∫
(
2
x
3
+
3
x
)
x
4
+
3
x
2
+
7
dx
(\partial)/(\partial x)(4xcos(4xy))
∂
∂
x
(
4
x
cos
(
4
xy
)
)
limit as x approaches 0 of (sin(20x))/x
lim
x
→
0
(
sin
(
2
0
x
)
x
)
limit as x approaches 2+of-1/(x^2-4)
lim
x
→
2
+
(
−
1
x
2
−
4
)
integral of (tan(θ)sec(θ))
∫
(
tan
(
θ
)
sec
(
θ
)
)
d
θ
integral of (1-cos(x))/(1+cos(x))
∫
1
−
cos
(
x
)
1
+
cos
(
x
)
dx
integral of e^{2x-7}
∫
e
2
x
−
7
dx
derivative of 4arcsin(x^3)
d
dx
(
4
arcsin
(
x
3
)
)
derivative 2/(\sqrt[3]{x^2)}
derivative
2
3
√
x
2
derivative of (4csc(x)/(5^x))
d
dx
(
4
csc
(
x
)
5
x
)
limit as x approaches infinity of n/(n!)
lim
x
→
∞
(
n
n
!
)
derivative ln(49sin^2(x))
derivative
ln
(
4
9
sin
2
(
x
)
)
y^{''}+10y^'+27y=0
y
′
′
+
1
0
y
′
+
2
7
y
=
0
(\partial)/(\partial v)(v^2)
∂
∂
v
(
v
2
)
f(x)=(25)/x
f
(
x
)
=
2
5
x
integral of 5sin(sqrt(x))
∫
5
sin
(
√
x
)
dx
derivative of sqrt(x^2+y)
d
dx
(
√
x
2
+
y
)
d/(dy)(t/(2y^4))
d
dy
(
t
2
y
4
)
integral of 1/(sqrt(64x^2+1))
∫
1
√
6
4
x
2
+
1
dx
6x^2((dy)/(dx))=((dy)/(dx))+9xe^{-y}
6
x
2
(
dy
dx
)
=
(
dy
dx
)
+
9
xe
−
y
integral of 8x^{-3}
∫
8
x
−
3
dx
integral from 0 to 2 of e^{-x}
∫
0
2
e
−
x
dx
integral of sqrt(3+x^2)
∫
√
3
+
x
2
dx
integral of (3x^2-9x+2)
∫
(
3
x
2
−
9
x
+
2
)
dx
derivative of sqrt(3x+9)
d
dx
(
√
3
x
+
9
)
integral of sqrt((1+cos(x))/(1-cos(x)))
∫
√
1
+
cos
(
x
)
1
−
cos
(
x
)
dx
derivative of arcsin(5x)
d
dx
(
arcsin
(
5
x
)
)
derivative 3/5 x^{5/3}-3/4 x^{1/3}+9
derivative
3
5
x
5
3
−
3
4
x
1
3
+
9
limit as x approaches-2+of (1-x)/(x^3+8)
lim
x
→
−
2
+
(
1
−
x
x
3
+
8
)
limit as x approaches 1-of 2/(x-1)
lim
x
→
1
−
(
2
x
−
1
)
(\partial)/(\partial x)((3x^2+y)e^{xy^2})
∂
∂
x
(
(
3
x
2
+
y
)
e
xy
2
)
laplacetransform (e^{2t}-e^t+t)^2
laplacetransform
(
e
2
t
−
e
t
+
t
)
2
derivative 2x^2-7x-195
derivative
2
x
2
−
7
x
−
1
9
5
integral of-cos((pit)/4)
∫
−
cos
(
π
t
4
)
dt
limit as x approaches-2 of-x^2+6x-8
lim
x
→
−
2
(
−
x
2
+
6
x
−
8
)
integral of aarctan(bx)
∫
a
arctan
(
bx
)
dx
limit as x approaches 1 of x^2+4
lim
x
→
1
(
x
2
+
4
)
tangent y=-0.02x^2-0.6x+90
tangent
y
=
−
0
.
0
2
x
2
−
0
.
6
x
+
9
0
integral of 5ln(x)
∫
5
ln
(
x
)
dx
derivative of 1/((x^2+1^3))
d
dx
(
1
(
x
2
+
1
)
3
)
integral of (e^{3x})/(e^{3x)+9}
∫
e
3
x
e
3
x
+
9
dx
integral from 0 to 1 of pi(6-3/2 x)^2
∫
0
1
π
(
6
−
3
2
x
)
2
dx
inverselaplace 2/(s^2+s)
inverselaplace
2
s
2
+
s
y^{''}+9y=3cos(2x)+3
y
′
′
+
9
y
=
3
cos
(
2
x
)
+
3
integral of sqrt(9-x^2)(-2x)
∫
√
9
−
x
2
(
−
2
x
)
dx
derivative of (x-2^2(x+1))
d
dx
(
(
x
−
2
)
2
(
x
+
1
)
)
(\partial)/(\partial y)(x^2+y^2-9)
∂
∂
y
(
x
2
+
y
2
−
9
)
derivative f(x)=6x^2+x-3
derivative
f
(
x
)
=
6
x
2
+
x
−
3
laplacetransform t/2
laplacetransform
t
2
area y=sqrt(x),x=9,y=0
area
y
=
√
x
,
x
=
9
,
y
=
0
xy^'+2y=8x^2
xy
′
+
2
y
=
8
x
2
3y^{''}+5y^'+2y=0
3
y
′
′
+
5
y
′
+
2
y
=
0
integral of (3+2cos(x))^2
∫
(
3
+
2
cos
(
x
)
)
2
dx
limit as x approaches 2 of (6x)/(x-2)
lim
x
→
2
(
6
x
x
−
2
)
tangent f(x)=11sin(x),\at x=((3pi))/4
tangent
f
(
x
)
=
1
1
sin
(
x
)
,
at
x
=
(
3
π
)
4
integral from 1 to 4 of ((2x+1))/(2x)
∫
1
4
(
2
x
+
1
)
2
x
dx
integral of sin(2x)(3-cos(2x))^2
∫
sin
(
2
x
)
(
3
−
cos
(
2
x
)
)
2
dx
limit as x approaches 2 of 1/(x^2-4x+4)
lim
x
→
2
(
1
x
2
−
4
x
+
4
)
inverselaplace 5/s-5/s e^{-5s}
inverselaplace
5
s
−
5
s
e
−
5
s
sum from n=0 to infinity of-(-1)^{n+1}
∑
n
=
0
∞
−
(
−
1
)
n
+
1
derivative of 3/(4x^2)
d
dx
(
3
4
x
2
)
tangent f(x)=x^4-13x^2+36
tangent
f
(
x
)
=
x
4
−
1
3
x
2
+
3
6
integral from 0 to 1 of (45)/(x^5)
∫
0
1
4
5
x
5
dx
derivative (1+4/x)^x
derivative
(
1
+
4
x
)
x
(\partial)/(\partial x)(2e^{x-2}-y)
∂
∂
x
(
2
e
x
−
2
−
y
)
derivative f(x)=(-x^2-1)/((x^2+1)^2)
derivative
f
(
x
)
=
−
x
2
−
1
(
x
2
+
1
)
2
integral of sin(20x)sin(21x)
∫
sin
(
2
0
x
)
sin
(
2
1
x
)
dx
integral of x(1/x)
∫
x
(
1
x
)
dx
derivative of (4x^2+5/(x^2+7))
d
dx
(
4
x
2
+
5
x
2
+
7
)
(\partial)/(\partial y)(10-6y+e^{-3x})
∂
∂
y
(
1
0
−
6
y
+
e
−
3
x
)
d/(dt)(3e^t)
d
dt
(
3
e
t
)
derivative F(x)=(x^2)/(4+sqrt(x))
derivative
F
(
x
)
=
x
2
4
+
√
x
(dy)/(dx)=y+y^3
dy
dx
=
y
+
y
3
integral from-9 to 4 of |x+5|
∫
−
9
4
|
x
+
5
|
dx
integral of x/(sqrt(x^2-6x+8))
∫
x
√
x
2
−
6
x
+
8
dx
x^'=x^2,x(0)=1
x
′
=
x
2
,
x
(
0
)
=
1
sum from n=0 to infinity of (1/2)^{2n+1}
∑
n
=
0
∞
(
1
2
)
2
n
+
1
derivative 1/(x+1/x)
derivative
1
x
+
1
x
limit as x approaches+(-0) of f(x)
lim
x
→
+
(
−
0
)
(
f
(
x
)
)
derivative of cos(2x-sin(x))
d
dx
(
cos
(
2
x
)
−
sin
(
x
)
)
integral from 1 to 16 of (x-7)/(sqrt(x))
∫
1
1
6
x
−
7
√
x
dx
integral of 4/((1+2x)^3)
∫
4
(
1
+
2
x
)
3
dx
integral from 1 to e^5 of (ln^3(x^2))/x
∫
1
e
5
ln
3
(
x
2
)
x
dx
integral of x^{-1/4}sqrt(1+x^{1/4)}
∫
x
−
1
4
√
1
+
x
1
4
dx
(\partial)/(\partial x)(5xcos(xy))
∂
∂
x
(
5
x
cos
(
xy
)
)
(\partial)/(\partial x)(-hk^2+k^4)
∂
∂
x
(
−
hk
2
+
k
4
)
1
..
480
481
482
483
484
..
2459