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常见 微积分 问题
derivative f(x)=4x^2+5x+3
derivative
f
(
x
)
=
4
x
2
+
5
x
+
3
integral of (x^3+3x)^{32}(3x^2+3)
∫
(
x
3
+
3
x
)
3
2
(
3
x
2
+
3
)
dx
limit as x approaches infinity of 1+1/x
lim
x
→
∞
(
1
+
1
x
)
derivative xsqrt(x^2+5)
derivative
x
√
x
2
+
5
sum from n=2 to infinity of 1/n
∑
n
=
2
∞
1
n
derivative of x^{-1/5}
d
dx
(
x
−
1
5
)
integral of x/(x^4sqrt(x^4-x^2))
∫
x
x
4
√
x
4
−
x
2
dx
derivative of x^{0.9}
d
dx
(
x
0
.
9
)
derivative f(x)=(x+1)(x+1-1/(x+2))
derivative
f
(
x
)
=
(
x
+
1
)
(
x
+
1
−
1
x
+
2
)
inverse拉普拉斯 (s-1)/(s(s+2.5))
inverselaplace
s
−
1
s
(
s
+
2
.
5
)
(\partial)/(\partial x)(3xze^{4xy})
∂
∂
x
(
3
xze
4
xy
)
limit as x approaches-3 of 3x^2-4x+1
lim
x
→
−
3
(
3
x
2
−
4
x
+
1
)
(x+1)((dy)/(dx))+(2x-1)y=e^{-2x}
(
x
+
1
)
(
dy
dx
)
+
(
2
x
−
1
)
y
=
e
−
2
x
limit as x approaches-1 of (x+2x^3)^5
lim
x
→
−
1
(
(
x
+
2
x
3
)
5
)
tangent f(x)= 1/2-x^2,\at x=-1/2
tangent
f
(
x
)
=
1
2
−
x
2
,
at
x
=
−
1
2
limit as x approaches+(-5) of 3x-|x+5|
lim
x
→
+
(
−
5
)
(
3
x
−
|
x
+
5
|
)
sqrt(1-3x^2)y^'=x
√
1
−
3
x
2
y
′
=
x
(\partial)/(\partial y)(e^{x^2-y^2+4y})
∂
∂
y
(
e
x
2
−
y
2
+
4
y
)
limit as x approaches 1 of (x^3-x)/(1-x)
lim
x
→
1
(
x
3
−
x
1
−
x
)
d/(d{x)}(({x}^2+2{y}^2+3{z}^2)e^{-({x}^2+{y}^2+{z}^2)})
d
d
x
(
(
x
2
+
2
y
2
+
3
z
2
)
e
−
(
x
2
+
y
2
+
z
2
)
)
derivative 6cos(sin(x^2))
derivative
6
cos
(
sin
(
x
2
)
)
derivative of ln(1+0)
d
dx
(
ln
(
1
+
0
)
)
integral of x/(sqrt(4-x))
∫
x
√
4
−
x
dx
derivative of x/(sqrt(x^2-4))
d
dx
(
x
√
x
2
−
4
)
(pi)^'
(
π
)
′
limit as x approaches 0 of 1/x+1
lim
x
→
0
(
1
x
+
1
)
integral of x/(1-x^8)
∫
x
1
−
x
8
dx
derivative f(x)=cos(x^2)2x
derivative
f
(
x
)
=
cos
(
x
2
)
2
x
integral of 8x^{-1}
∫
8
x
−
1
dx
integral of 1/(sqrt(x^2+8))
∫
1
√
x
2
+
8
dx
tangent f(x)=-2x^3
tangent
f
(
x
)
=
−
2
x
3
inverse拉普拉斯 (s-1)/(2s^2+s+6)
inverselaplace
s
−
1
2
s
2
+
s
+
6
integral from 2 to 4 of (2x^2-3x+1)
∫
2
4
(
2
x
2
−
3
x
+
1
)
dx
limit as x approaches-2 of 3/(x+2)
lim
x
→
−
2
(
3
x
+
2
)
integral of sqrt(1-u^2)
∫
√
1
−
u
2
du
y^{''}-8y^'+16y=0,y(0)=4,y^'(0)= 82/5
y
′
′
−
8
y
′
+
1
6
y
=
0
,
y
(
0
)
=
4
,
y
′
(
0
)
=
8
2
5
integral of sqrt(1-81x^2)
∫
√
1
−
8
1
x
2
dx
integral of 7cos^2(x)
∫
7
cos
2
(
x
)
dx
e^xy(dy)/(dx)=e^{-y}e^{-2x-y}
e
x
y
dy
dx
=
e
−
y
e
−
2
x
−
y
integral of (x^2)/(x+3)
∫
x
2
x
+
3
dx
derivative of sinh(x)
d
dx
(
sinh
(
x
)
)
integral of 3x^2+8x+4
∫
3
x
2
+
8
x
+
4
dx
integral of e^{x^5}x^4
∫
e
x
5
x
4
dx
derivative of (x-5/(x^2-3x+15))
d
dx
(
x
−
5
x
2
−
3
x
+
1
5
)
limit as x approaches 2 of (e^x)/(x^3)
lim
x
→
2
(
e
x
x
3
)
sum from n=0 to infinity of | 1/4 |^2
∑
n
=
0
∞
|
1
4
|
2
integral of-x/(1+x^4)
∫
−
x
1
+
x
4
dx
y^'= 3/(3y)
y
′
=
3
3
y
integral of x^3ln(x^2+1)
∫
x
3
ln
(
x
2
+
1
)
dx
integral of 8/(t^9)sin(1/(t^8)-9)
∫
8
t
9
sin
(
1
t
8
−
9
)
dt
y^'+tan(x)y=cos^2(x)
y
′
+
tan
(
x
)
y
=
cos
2
(
x
)
(\partial)/(\partial x)(tan(2x-y))
∂
∂
x
(
tan
(
2
x
−
y
)
)
(\partial)/(\partial x)((x^2-2)e^{x^2y})
∂
∂
x
(
(
x
2
−
2
)
e
x
2
y
)
integral of (30)/(30+e^x)
∫
3
0
3
0
+
e
x
dx
derivative y=4(6-x^2)^5
derivative
y
=
4
(
6
−
x
2
)
5
integral of 4m(9m^2-10m)
∫
4
m
(
9
m
2
−
1
0
m
)
dm
derivative ln(15x)
derivative
ln
(
1
5
x
)
derivative f(x)=x^{12}
derivative
f
(
x
)
=
x
1
2
limit as x approaches-3 of (3x+1)/(x-3)
lim
x
→
−
3
(
3
x
+
1
x
−
3
)
(\partial)/(\partial x)((x^5+y^3)^7)
∂
∂
x
(
(
x
5
+
y
3
)
7
)
integral of z/((s^2+z^2)^{3/2)}
∫
z
(
s
2
+
z
2
)
3
2
dz
derivative m(x)=(-x^2+6x-8)/(-x^2+6x-2)
derivative
m
(
x
)
=
−
x
2
+
6
x
−
8
−
x
2
+
6
x
−
2
tangent y=-5-6x^2,(-4,-101)
tangent
y
=
−
5
−
6
x
2
,
(
−
4
,
−
1
0
1
)
derivative p(t)=5e^{0.0278t}
derivative
p
(
t
)
=
5
e
0
.
0
2
7
8
t
derivative of 1/2 x^2+1
d
dx
(
1
2
x
2
+
1
)
derivative of 5xe^{5x}
d
dx
(
5
xe
5
x
)
limit as x approaches-3 of x/(x-4)
lim
x
→
−
3
(
x
x
−
4
)
integral of 2e^x-1
∫
2
e
x
−
1
dx
integral of sqrt(4x+1)
∫
√
4
x
+
1
dx
limit as x approaches 0 of (6x^2)/(2x^2)
lim
x
→
0
(
6
x
2
2
x
2
)
integral of \sqrt[3]{2x^2}
∫
3
√
2
x
2
dx
(dy)/(dx)= 1/2 (kx^{-1}-x)
dy
dx
=
1
2
(
kx
−
1
−
x
)
limit as x approaches-4 of-(2x^2-17)/3
lim
x
→
−
4
(
−
2
x
2
−
1
7
3
)
integral of 5y^2
∫
5
y
2
dy
(\partial)/(\partial x)(2cos(x)cos(y))
∂
∂
x
(
2
cos
(
x
)
cos
(
y
)
)
limit as h approaches 0 of (13h)/h
lim
h
→
0
(
1
3
h
h
)
limit as x approaches 2 of 2x^2-7x-15
lim
x
→
2
(
2
x
2
−
7
x
−
1
5
)
(\partial)/(\partial x)(cos(pixy))
∂
∂
x
(
cos
(
π
xy
)
)
integral of 4e^{-2x}sin(2x)
∫
4
e
−
2
x
sin
(
2
x
)
dx
limit as x approaches 1 of x(3)
lim
x
→
1
(
x
(
3
)
)
面积 4x-20,[4,8]
area
4
x
−
2
0
,
[
4
,
8
]
integral of 8sin^3(xco)s^5x
∫
8
sin
3
(
xco
)
s
5
xdx
sum from n=1 to infinity of e/n
∑
n
=
1
∞
e
n
inverse拉普拉斯 (s-1)/(s^2+2)
inverselaplace
s
−
1
s
2
+
2
derivative f(x)=cos(3x+2)-7x
derivative
f
(
x
)
=
cos
(
3
x
+
2
)
−
7
x
derivative (xsec^2(x)-tan(x))/(4x^2)
derivative
x
sec
2
(
x
)
−
tan
(
x
)
4
x
2
(dy)/(dx)=3x^2+2x-7
dy
dx
=
3
x
2
+
2
x
−
7
(\partial}{\partial x}(\frac{x^2y^2)/2)
∂
∂
x
(
x
2
y
2
2
)
sum from n=1 to infinity of n^{-sin(2)}
∑
n
=
1
∞
n
−
sin
(
2
)
(cos^2(θ))^'
(
cos
2
(
θ
)
)
′
泰勒 1/(sqrt(1-x))
taylor
1
√
1
−
x
derivative of (8x/(3-tan(x)))
d
dx
(
8
x
3
−
tan
(
x
)
)
derivative f(x)=7x+2
derivative
f
(
x
)
=
7
x
+
2
(dy)/(dx)=((x-3))/(2-y)
dy
dx
=
(
x
−
3
)
2
−
y
derivative of-x^2
d
dx
(
−
x
2
)
derivative of sec^2(xtan(x))
d
dx
(
sec
2
(
x
)
tan
(
x
)
)
(\partial)/(\partial x)(ln(x+7y+2z))
∂
∂
x
(
ln
(
x
+
7
y
+
2
z
)
)
integral from 6 to 8 of (72)/((x-6)^3)
∫
6
8
7
2
(
x
−
6
)
3
dx
limit as x approaches 3 of sqrt(f(x))
lim
x
→
3
(
√
f
(
x
)
)
(dy)/(dx)=(x^2y^2)/(1+2)
dy
dx
=
x
2
y
2
1
+
2
1
..
1221
1222
1223
1224
1225
..
2459