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الهندسة
علم المثلثات
قبل التفاضل والتكامل
حساب التفاضل والتكامل
إحصائيات
مسائل حساب التفاضل والتكامل مشهورة
derivative of sin(xcos^2(x))
d
dx
(
sin
(
x
)
cos
2
(
x
)
)
integral of 1/(4-4sin(x))
∫
1
4
−
4
sin
(
x
)
dx
integral of 8x^7e^{7x^8}
∫
8
x
7
e
7
x
8
dx
integral of (-6x^3+8x^2-30x+10)/(x^3+5x)
∫
−
6
x
3
+
8
x
2
−
3
0
x
+
1
0
x
3
+
5
x
dx
integral of x^2+6
∫
x
2
+
6
dx
derivative xsqrt(ln(x))
derivative
x
√
ln
(
x
)
integral of (e^{-x})/(e^{-x)+1}
∫
e
−
x
e
−
x
+
1
dx
derivative 6e^{-2x}cos(4x)
derivative
6
e
−
2
x
cos
(
4
x
)
derivative f(x)=5x^2-2x-7
derivative
f
(
x
)
=
5
x
2
−
2
x
−
7
y^'=0.04y-2000,y(0)=25000
y
′
=
0
.
0
4
y
−
2
0
0
0
,
y
(
0
)
=
2
5
0
0
0
laplacetransform e^{3(t-2)}
laplacetransform
e
3
(
t
−
2
)
derivative of (2x/(3+x^2))
d
dx
(
2
x
3
+
x
2
)
integral of x*sqrt(1-x^2)
∫
x
·
√
1
−
x
2
dx
derivative f(x)=2x^2-3x+6
derivative
f
(
x
)
=
2
x
2
−
3
x
+
6
derivative f(x)=log_{2}(x^2+1)-2^3
derivative
f
(
x
)
=
log
2
(
x
2
+
1
)
−
2
3
(\partial)/(\partial x)(y+3)
∂
∂
x
(
y
+
3
)
integral of p(p+6)^8
∫
p
(
p
+
6
)
8
dp
derivative of (0.2x/(x^2+9))
d
dx
(
0
.
2
x
x
2
+
9
)
integral of 1-x^9
∫
1
−
x
9
dx
(\partial)/(\partial x)(-1/x)
∂
∂
x
(
−
1
x
)
integral of e^xcos(3x)
∫
e
x
cos
(
3
x
)
dx
sum from n=1 to infinity of 5^nx^nn!
∑
n
=
1
∞
5
n
x
n
n
!
derivative of 7e^{2x^4-3x}
d
dx
(
7
e
2
x
4
−
3
x
)
integral of 4t^5
∫
4
t
5
dt
inverselaplace 8/((9s^2+9s+4)(s))
inverselaplace
8
(
9
s
2
+
9
s
+
4
)
(
s
)
(\partial)/(\partial x)(sqrt(x))
∂
∂
x
(
√
x
)
derivative ((t-4)^3)/6+t^2
derivative
(
t
−
4
)
3
6
+
t
2
limit as x approaches 0 of 9sin(x)ln(x)
lim
x
→
0
(
9
sin
(
x
)
ln
(
x
)
)
integral of xln(y)
∫
x
ln
(
y
)
dy
limit as x approaches 1/2 of x/(2x-1)
lim
x
→
1
2
(
x
2
x
−
1
)
f(x)=(x^3+3x)(2x+4)
f
(
x
)
=
(
x
3
+
3
x
)
(
2
x
+
4
)
integral of (e^x)*cos(nx)
∫
(
e
x
)
·
cos
(
nx
)
dx
integral of xsqrt(x-10)
∫
x
√
x
−
1
0
dx
inverselaplace 3/s+(16)/(s(s+1))
inverselaplace
3
s
+
1
6
s
(
s
+
1
)
integral from 1 to e^2 of (ln(x))/(x^2)
∫
1
e
2
ln
(
x
)
x
2
dx
(\partial)/(\partial x)((a-b^2)/(x-c^2))
∂
∂
x
(
a
−
b
2
x
−
c
2
)
derivative of 5-4/x
d
dx
(
5
−
4
x
)
derivative (-u^2+7)/((u^2+7)^2)
derivative
−
u
2
+
7
(
u
2
+
7
)
2
derivative of sec(x^5+x)
d
dx
(
sec
(
x
5
+
x
)
)
slopeintercept (1.1)(0.5)
slopeintercept
(
1
.
1
)
(
0
.
5
)
integral of sqrt(1+5x^2)(10x)
∫
√
1
+
5
x
2
(
1
0
x
)
dx
derivative y=3x^2+(10x)/3-2
derivative
y
=
3
x
2
+
1
0
x
3
−
2
derivative of (tan^3(x)/3)
d
dx
(
tan
3
(
x
)
3
)
sum from n=1 to infinity of (2n!)/(n^5)
∑
n
=
1
∞
2
n
!
n
5
(\partial)/(\partial x)(-6e^{-3x^2-y^2}x)
∂
∂
x
(
−
6
e
−
3
x
2
−
y
2
x
)
slope (1-2x)(3x-4),\at x=2
slope
(
1
−
2
x
)
(
3
x
−
4
)
,
at
x
=
2
f(x)=sqrt(2x^2-x+9)
f
(
x
)
=
√
2
x
2
−
x
+
9
derivative f(x)=2-2/3 x
derivative
f
(
x
)
=
2
−
2
3
x
derivative of ln(ln(sec(2x)))
d
dx
(
ln
(
ln
(
sec
(
2
x
)
)
)
)
derivative y=3x+4/x
derivative
y
=
3
x
+
4
x
(du+2dv)/(u+2v)=0
du
+
2
dv
u
+
2
v
=
0
limit as x approaches 2 of 3x^2-2x+1
lim
x
→
2
(
3
x
2
−
2
x
+
1
)
derivative f(x)=(7x^2+7x+7)/(sqrt(x))
derivative
f
(
x
)
=
7
x
2
+
7
x
+
7
√
x
tangent y=(x^{(3)}-4x)^{(12)}(2)
tangent
y
=
(
x
(
3
)
−
4
x
)
(
1
2
)
(
2
)
(\partial)/(\partial y)(sqrt(y+cos^2(x)))
∂
∂
y
(
√
y
+
cos
2
(
x
)
)
integral of 1/(sqrt(x^2-6x))
∫
1
√
x
2
−
6
x
dx
sum from n=1 to infinity of tan(3n)
∑
n
=
1
∞
tan
(
3
n
)
derivative g(x)=(x^2-64)/(x+8)
derivative
g
(
x
)
=
x
2
−
6
4
x
+
8
y^{''}+6y^'+5y=-3te^{(4t)}
y
′
′
+
6
y
′
+
5
y
=
−
3
te
(
4
t
)
integral of 2sqrt(x)-\sqrt[3]{x}-x^4
∫
2
√
x
−
3
√
x
−
x
4
dx
(\partial)/(\partial x)(-x/(x^2+y^2))
∂
∂
x
(
−
x
x
2
+
y
2
)
integral of 5cos(x)-4sin(x)
∫
5
cos
(
x
)
−
4
sin
(
x
)
dx
derivative y=\sqrt[4]{(cos(x))^3}
derivative
y
=
4
√
(
cos
(
x
)
)
3
derivative of (2x+3^2)
d
dx
(
(
2
x
+
3
)
2
)
derivative f(x)=a^4+cos^4(x)
derivative
f
(
x
)
=
a
4
+
cos
4
(
x
)
integral from 0 to 1 of 2pi(2-y)(4y^2)
∫
0
1
2
π
(
2
−
y
)
(
4
y
2
)
dy
integral of-sin(x
∫
−
sin
(
d
)
xdx
integral from 0 to 1 of \sqrt[4]{x}
∫
0
1
4
√
x
dx
integral of (x+1)e^{3x^2+6x}
∫
(
x
+
1
)
e
3
x
2
+
6
x
dx
derivative of Axe^{-2x}
d
dx
(
Axe
−
2
x
)
derivative of (2x-x^2/(3x^2+2))
d
dx
(
2
x
−
x
2
3
x
2
+
2
)
(\partial)/(\partial x)(x/(x^7-y^4))
∂
∂
x
(
x
x
7
−
y
4
)
derivative of (7x^2/(x^3))
d
dx
(
7
x
2
x
3
)
limit as x approaches 0 of (1+x)^{7/x}
lim
x
→
0
(
(
1
+
x
)
7
x
)
k((dx)/(dt))=x+15
k
(
dx
dt
)
=
x
+
1
5
integral from 0 to 10 of x
∫
0
1
0
xdx
derivative of ((x^2+1^2)/((x^4+1)^4))
d
dx
(
(
x
2
+
1
)
2
(
x
4
+
1
)
4
)
limit as x approaches 2 of (2x-8)/(x-1)
lim
x
→
2
(
2
x
−
8
x
−
1
)
derivative 4tsin(pit)
derivative
4
t
sin
(
π
t
)
x^3y^{'''}+3x^2y^{''}-2xy^'+2y=0
x
3
y
′
′
′
+
3
x
2
y
′
′
−
2
xy
′
+
2
y
=
0
limit as x approaches 5 of 6/(x-5)
lim
x
→
5
(
6
x
−
5
)
integral of (sin(x))/((cos(x))^3)
∫
sin
(
x
)
(
cos
(
x
)
)
3
dx
(\partial)/(\partial x)((x^4+y^2)/(xy))
∂
∂
x
(
x
4
+
y
2
xy
)
integral of sqrt(9x+5)
∫
√
9
x
+
5
dx
limit as x approaches-6+of (-2x)/(x+6)
lim
x
→
−
6
+
(
−
2
x
x
+
6
)
slopeintercept (0.2)(2)
slopeintercept
(
0
.
2
)
(
2
)
derivative of x^{10}e^{x+1}
d
dx
(
x
1
0
e
x
+
1
)
(dy)/(dt)=y(1-y),y(0)=16
dy
dt
=
y
(
1
−
y
)
,
y
(
0
)
=
1
6
integral of (t^2-1)/(t^4-1)
∫
t
2
−
1
t
4
−
1
dt
y^{''}+4y^'+4y=e^{-2x}*ln(x)
y
′
′
+
4
y
′
+
4
y
=
e
−
2
x
·
ln
(
x
)
derivative of (sin(x)/(bsin(bx)))
d
dx
(
sin
(
x
)
b
sin
(
bx
)
)
y^'-2xy=2xe^{x^2}
y
′
−
2
xy
=
2
xe
x
2
((4x^2+5)^2*(7x)^{2x})^'
(
(
4
x
2
+
5
)
2
·
(
7
x
)
2
x
)
′
-4x^2y+y^'=4x^2
−
4
x
2
y
+
y
′
=
4
x
2
integral of 1/(12sqrt(x)+12x)
∫
1
1
2
√
x
+
1
2
x
dx
integral of x*(7-x)^9
∫
x
·
(
7
−
x
)
9
dx
derivative of 1/(4(1+x^{3/4)})
d
dx
(
1
4
(
1
+
x
)
3
4
)
integral of (sin(x))/(cos^5(x))
∫
sin
(
x
)
cos
5
(
x
)
dx
derivative of 5x^2-1
d
dx
(
5
x
2
−
1
)
(dN)/(dt)+N=Nte^{(t+2)}
dN
dt
+
N
=
Nte
(
t
+
2
)
1
..
4
5
6
7
8
..
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