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常见 微积分 问题
derivative f(x)= 4/x
derivative
f
(
x
)
=
4
x
integral of (3x^4-x^3+6x^2)/(x^4)
∫
3
x
4
−
x
3
+
6
x
2
x
4
dx
面积 y=12-x^2,y=x^2-6
area
y
=
1
2
−
x
2
,
y
=
x
2
−
6
derivative of (cos(7x)^x)
d
dx
(
(
cos
(
7
x
)
)
x
)
面积 sqrt(x), 1/2 x,0,25
area
√
x
,
1
2
x
,
0
,
2
5
(\partial)/(\partial x)((3x-y)/(3x+y))
∂
∂
x
(
3
x
−
y
3
x
+
y
)
integral of x(2x-1)^9
∫
x
(
2
x
−
1
)
9
dx
derivative of \sqrt[8]{x}-8e^x
d
dx
(
8
√
x
−
8
e
x
)
tangent f(x)=x^2-9,(4,7)
tangent
f
(
x
)
=
x
2
−
9
,
(
4
,
7
)
(\partial)/(\partial y)(ln(x^3+y^3))
∂
∂
y
(
ln
(
x
3
+
y
3
)
)
6x+10,4x+44,x=15,x=19
6
x
+
1
0
,
4
x
+
4
4
,
x
=
1
5
,
x
=
1
9
integral from 3.5 to 7 of 274000-39200x
∫
3
.
5
7
2
7
4
0
0
0
−
3
9
2
0
0
xdx
derivative of tan(4x+4)
d
dx
(
tan
(
4
x
+
4
)
)
integral of cos^2(x/3)
∫
cos
2
(
x
3
)
dx
integral from-infinity to-1 of e^{-38t}
∫
−
∞
−
1
e
−
3
8
t
dt
sum from n=1 to infinity of 5/(n^2+16)
∑
n
=
1
∞
5
n
2
+
1
6
inverselaplace s^2+6s+7
inverselaplace
s
2
+
6
s
+
7
limit as x approaches pi/2 of x
lim
x
→
π
2
(
x
)
derivative y=(7ln(x))/(3x+4)
derivative
y
=
7
ln
(
x
)
3
x
+
4
limit as x approaches 1/3 of 3x^3+2x^2
lim
x
→
1
3
(
3
x
3
+
2
x
2
)
normal y= x/(x^2+1),\at x=-1
normal
y
=
x
x
2
+
1
,
at
x
=
−
1
(\partial)/(\partial x)(2sqrt(x*y)-1/2 x^2)
∂
∂
x
(
2
√
x
·
y
−
1
2
x
2
)
f(t)=6sin(t)
f
(
t
)
=
6
sin
(
t
)
integral from-1 to 3 of x/(x^2+4)
∫
−
1
3
x
x
2
+
4
dx
derivative of x^2+7x+12
d
dx
(
x
2
+
7
x
+
1
2
)
integral of 1/(cos(x)sin(x)+cos^2(x))
∫
1
cos
(
x
)
sin
(
x
)
+
cos
2
(
x
)
dx
integral of 8xln(7x)
∫
8
x
ln
(
7
x
)
dx
derivative of (sin(x)/(x^2))
d
dx
(
sin
(
x
)
x
2
)
integral from y to x of (e^t)/t
∫
y
x
e
t
t
dt
斜率 (32)(41.5)
slope
(
3
2
)
(
4
1
.
5
)
(\partial)/(\partial x)(x/(x^4-y^6))
∂
∂
x
(
x
x
4
−
y
6
)
integral of cos^2(x)tan^3(x)
∫
cos
2
(
x
)
tan
3
(
x
)
dx
f(x)=(e^x)/(x^2)
f
(
x
)
=
e
x
x
2
limit as x approaches 1/4 of 8x(x-1/5)
lim
x
→
1
4
(
8
x
(
x
−
1
5
)
)
limit as x approaches 0 of 1/(1-x)
lim
x
→
0
(
1
1
−
x
)
y^'=0.5(3-y)
y
′
=
0
.
5
(
3
−
y
)
y^{''}-21y^'+108y=0
y
′
′
−
2
1
y
′
+
1
0
8
y
=
0
(dy)/(dx)+8y=x^2y^2
dy
dx
+
8
y
=
x
2
y
2
(\partial)/(\partial x)(3xcos(5xy))
∂
∂
x
(
3
x
cos
(
5
xy
)
)
derivative 1/2 (x^4+7)
derivative
1
2
(
x
4
+
7
)
integral of e^x0.2
∫
e
x
0
.
2
dx
tangent f(x)=x^3-2x^2-6x+6,\at x=0
tangent
f
(
x
)
=
x
3
−
2
x
2
−
6
x
+
6
,
at
x
=
0
integral of (3x)^2
∫
(
3
x
)
2
dx
derivative of-xy^3
d
dx
(
−
xy
3
)
斜率 (-2,4),(-1,-1)
slope
(
−
2
,
4
)
,
(
−
1
,
−
1
)
integral from-a to a of (a-|x|)
∫
−
a
a
(
a
−
|
x
|
)
dx
limit as a approaches 0 of x^a
lim
a
→
0
(
x
a
)
tangent (x+7)/(x+1)
tangent
x
+
7
x
+
1
tangent y=4x^3-4x,(1,0)
tangent
y
=
4
x
3
−
4
x
,
(
1
,
0
)
integral of (x+5)(x^3+5x-10)
∫
(
x
+
5
)
(
x
3
+
5
x
−
1
0
)
dx
integral of-x^2ln(x)
∫
−
x
2
ln
(
x
)
dx
integral of 24x^{-3}
∫
2
4
x
−
3
dx
integral from 0 to pi/2 of 8cos^5(x)
∫
0
π
2
8
cos
5
(
x
)
dx
(dy)/(dx)=3x-y
dy
dx
=
3
x
−
y
laplacetransform sin(t+pi/4)
laplacetransform
sin
(
t
+
π
4
)
integral from 0 to 1 of (1-x^2)^2
∫
0
1
(
1
−
x
2
)
2
dx
(2-x)^'
(
2
−
x
)
′
derivative of-7cos(x)
d
dx
(
−
7
cos
(
x
)
)
面积 y=6x,y=3x^2
area
y
=
6
x
,
y
=
3
x
2
integral from 0 to 1 of 9x
∫
0
1
9
xdx
integral of xarcsec(x)
∫
x
arcsec
(
x
)
dx
integral of ((xe^{2x}))/((1+2x)^2)
∫
(
xe
2
x
)
(
1
+
2
x
)
2
dx
tangent f(x)= 1/x ,\at x=-2
tangent
f
(
x
)
=
1
x
,
at
x
=
−
2
derivative of (x^3/3+(x^2)/2-6x)
d
dx
(
x
3
3
+
x
2
2
−
6
x
)
derivative of 2e^{x^2}
d
dx
(
2
e
x
2
)
(\partial)/(\partial x)((x+y)e^x)
∂
∂
x
(
(
x
+
y
)
e
x
)
integral of 1/P
∫
1
P
dP
derivative f(t)=0.1(400-40t+t^2)
derivative
f
(
t
)
=
0
.
1
(
4
0
0
−
4
0
t
+
t
2
)
derivative of sqrt(x)+2sin(x)
d
dx
(
√
x
+
2
sin
(
x
)
)
integral of 1/(cos^2(t)*sqrt(1+tan(t)))
∫
1
cos
2
(
t
)
·
√
1
+
tan
(
t
)
dt
limit as x approaches 7-of (|x-7|)/(x-7)
lim
x
→
7
−
(
|
x
−
7
|
x
−
7
)
derivative f(x)=3x+4
derivative
f
(
x
)
=
3
x
+
4
derivative of cos^9(x^2y^6)
d
dx
(
cos
9
(
x
2
y
6
)
)
derivative sqrt(14x)
derivative
√
1
4
x
tangent xy^3+xy=2,(1,1)
tangent
xy
3
+
xy
=
2
,
(
1
,
1
)
tangent f(x)= 4/(x^2),\at x=1
tangent
f
(
x
)
=
4
x
2
,
at
x
=
1
derivative of (5x^3+7x^2/x)
d
dx
(
5
x
3
+
7
x
2
x
)
derivative of sqrt(x)-1/9 x
d
dx
(
√
x
−
1
9
x
)
limit as x approaches 0 of e
lim
x
→
0
(
e
)
sum from n=1 to infinity of (n-1)/(3n-1)
∑
n
=
1
∞
n
−
1
3
n
−
1
y^{''}+1500y=320
y
′
′
+
1
5
0
0
y
=
3
2
0
derivative f(x)=ln(18)
derivative
f
(
x
)
=
ln
(
1
8
)
integral of cos(x)sin(sin(x))
∫
cos
(
x
)
sin
(
sin
(
x
)
)
dx
面积 y=6cos(pix),y=8x^2-2,-0.5,0.5
area
y
=
6
cos
(
π
x
)
,
y
=
8
x
2
−
2
,
−
0
.
5
,
0
.
5
integral of 1/(2+2x)
∫
1
2
+
2
x
dx
integral of sin(ln(13x))
∫
sin
(
ln
(
1
3
x
)
)
dx
tangent f(x)=2x^2+5x,\at x=-3
tangent
f
(
x
)
=
2
x
2
+
5
x
,
at
x
=
−
3
(d^2h)/(dt^2)=-kh
d
2
h
dt
2
=
−
kh
limit as x approaches 2 of 2x^2-3x+1
lim
x
→
2
(
2
x
2
−
3
x
+
1
)
integral of (x^2)/4-1
∫
x
2
4
−
1
dx
y^{''}+36y=-36sec(6t)
y
′
′
+
3
6
y
=
−
3
6
sec
(
6
t
)
derivative of sqrt(e^x+1)
d
dx
(
√
e
x
+
1
)
derivative (arctan(x))^2
derivative
(
arctan
(
x
)
)
2
(\partial)/(\partial x)(x^6)
∂
∂
x
(
x
6
)
integral of ye^{-y/x}
∫
ye
−
y
x
dy
integral from-infinity to 0 of 1/(6-2x)
∫
−
∞
0
1
6
−
2
x
dx
derivative of 3/(sqrt(1-x^2))
d
dx
(
3
√
1
−
x
2
)
(\partial)/(\partial x)(M/(2px))
∂
∂
x
(
M
2
px
)
limit as x approaches 3 of 3x^4+2x^2-5
lim
x
→
3
(
3
x
4
+
2
x
2
−
5
)
f(x)=(-3x^2+2x+4)^{12}
f
(
x
)
=
(
−
3
x
2
+
2
x
+
4
)
1
2
1
..
7
8
9
10
11
..
1823