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常见 微积分 问题
derivative (x^2+1)^5
derivative
(
x
2
+
1
)
5
derivative of tan(e^{sin(x}))
d
dx
(
tan
(
e
sin
(
x
)
)
)
integral of t*e^{4t}
∫
t
·
e
4
t
dt
derivative f(x)=(1+x+x^2)/(1-x^2)
derivative
f
(
x
)
=
1
+
x
+
x
2
1
−
x
2
derivative f(x)=(4x+5)/(4x-5)
derivative
f
(
x
)
=
4
x
+
5
4
x
−
5
derivative of ln(sin(x)+cos^2(x))
d
dx
(
ln
(
sin
(
x
)
)
+
cos
2
(
x
)
)
integral of (sqrt(y^2-81))/y
∫
√
y
2
−
8
1
y
dy
sum from n=0 to infinity of 1/(2^n+3^n)
∑
n
=
0
∞
1
2
n
+
3
n
integral of cos(2nx)
∫
cos
(
2
nx
)
dx
9(t+1)(dy)/(dt)-7y=14t
9
(
t
+
1
)
dy
dt
−
7
y
=
1
4
t
(\partial)/(\partial x)(-5x^2+7y^5x)
∂
∂
x
(
−
5
x
2
+
7
y
5
x
)
derivative h(x)=tan(4x^2-3x-4)
derivative
h
(
x
)
=
tan
(
4
x
2
−
3
x
−
4
)
integral of 7cot^4(x)
∫
7
cot
4
(
x
)
dx
2xy-9x^2+(2y+x^2+1)y^'=0
2
xy
−
9
x
2
+
(
2
y
+
x
2
+
1
)
y
′
=
0
derivative of 5tan(2x^3+2/(x^2))
d
dx
(
5
tan
(
2
x
3
)
+
2
x
2
)
y^'=-(1+y)^4,y(1)=2
y
′
=
−
(
1
+
y
)
4
,
y
(
1
)
=
2
derivative of Cxe^{3x}
d
dx
(
Cxe
3
x
)
derivative 8tsin(pit)
derivative
8
t
sin
(
π
t
)
derivative of (2sqrt(x)-1/(5-4sqrt(x)))
d
dx
(
2
√
x
−
1
5
−
4
√
x
)
derivative ((22.2sin(5t))/t)+44
derivative
(
2
2
.
2
sin
(
5
t
)
t
)
+
4
4
integral of 7cos(t)
∫
7
cos
(
t
)
dt
sum from n=3 to infinity of 1/(4^n)
∑
n
=
3
∞
1
4
n
4y^{''}+8y^'+13y=8sin(1.5t)
4
y
′
′
+
8
y
′
+
1
3
y
=
8
sin
(
1
.
5
t
)
integral of 1/(\sqrt[5]{x^3)}
∫
1
5
√
x
3
dx
derivative 1/5 x^{15}
derivative
1
5
x
1
5
integral of (x^2)/((x^2+4)^2)
∫
x
2
(
x
2
+
4
)
2
dx
斜率 (-3,4),(2,-2)
slope
(
−
3
,
4
)
,
(
2
,
−
2
)
(\partial)/(\partial x)(2y+2x^2)
∂
∂
x
(
2
y
+
2
x
2
)
3x^2y^'+x^3y^{''}=x
3
x
2
y
′
+
x
3
y
′
′
=
x
integral of (x^2-3)/(-x^3+9x+1)
∫
x
2
−
3
−
x
3
+
9
x
+
1
dx
integral of (2x-3)(5x+1)
∫
(
2
x
−
3
)
(
5
x
+
1
)
dx
integral from 1 to 5 of 4/x
∫
1
5
4
x
dx
sum from n=1 to infinity of 2/(3^n+1)
∑
n
=
1
∞
2
3
n
+
1
derivative of cot(tan(x))
d
dx
(
cot
(
tan
(
x
)
)
)
y^'=(1-2x)y^2,y(0)=-1/30
y
′
=
(
1
−
2
x
)
y
2
,
y
(
0
)
=
−
1
3
0
integral from 0 to 8 of k(8-x)
∫
0
8
k
(
8
−
x
)
derivative f(x)=-6x^2+7x
derivative
f
(
x
)
=
−
6
x
2
+
7
x
tangent f(x)=-1-4e^{-x/3},\at x=8
tangent
f
(
x
)
=
−
1
−
4
e
−
x
3
,
at
x
=
8
xy^'-y=2x^2-x-1
xy
′
−
y
=
2
x
2
−
x
−
1
integral of sin^2((pix)/l)
∫
sin
2
(
π
x
l
)
dx
derivative of 2(x+2^{3/2})
d
dx
(
2
(
x
+
2
)
3
2
)
integral of 9/(1+x^2)
∫
9
1
+
x
2
dx
integral of (5/x-3/(x^4))
∫
(
5
x
−
3
x
4
)
dx
derivative y=(2x)/(9-tan(x))
derivative
y
=
2
x
9
−
tan
(
x
)
derivative of-pi^2sin(pix)
d
dx
(
−
π
2
sin
(
π
x
)
)
integral from y to 1 of 3x
∫
y
1
3
xdx
derivative f(4k)=x^2-2x
derivative
f
(
4
k
)
=
x
2
−
2
x
integral of (17-17x)/(1-sqrt(x))
∫
1
7
−
1
7
x
1
−
√
x
dx
d/(d{x)}(ln({x}^2+{y}^2+{z}^2))
d
d
x
(
ln
(
x
2
+
y
2
+
z
2
)
)
derivative of log_{10}(x^2+y)
d
dx
(
log
1
0
(
x
2
+
y
)
)
(\partial)/(\partial x)(-2e^{-x^2-y^2}xcos(xy)-e^{-x^2-y^2}ysin(xy))
∂
∂
x
(
−
2
e
−
x
2
−
y
2
x
cos
(
xy
)
−
e
−
x
2
−
y
2
y
sin
(
xy
)
)
(\partial)/(\partial x)(1/(xy)(x^2y^2+y+x))
∂
∂
x
(
1
xy
(
x
2
y
2
+
y
+
x
)
)
(\partial)/(\partial x)(5xy^4+2ycos(x))
∂
∂
x
(
5
xy
4
+
2
y
cos
(
x
)
)
derivative y=x^3e^{4x}
derivative
y
=
x
3
e
4
x
integral of (e^{-2x}+e^{2x})/2
∫
e
−
2
x
+
e
2
x
2
dx
tangent f(x)=(18)/((2x+4)^2),\at x=9
tangent
f
(
x
)
=
1
8
(
2
x
+
4
)
2
,
at
x
=
9
integral of cos(2x)e^{2x}
∫
cos
(
2
x
)
e
2
x
dx
(\partial)/(\partial x)(5^{xy})
∂
∂
x
(
5
xy
)
limit as x approaches 0 of x^2sin(3/x)
lim
x
→
0
(
x
2
sin
(
3
x
)
)
integral from 0 to pi of sin^3(x)
∫
0
π
sin
3
(
x
)
dx
(\partial)/(\partial x)(ln(x-2y)-z)
∂
∂
x
(
ln
(
x
−
2
y
)
−
z
)
limit as x approaches-7+of x^2sqrt(x+7)
lim
x
→
−
7
+
(
x
2
√
x
+
7
)
integral from-7 to 7 of (6-|x|)
∫
−
7
7
(
6
−
|
x
|
)
dx
integral of (3/2 x+5)^{1/3}
∫
(
3
2
x
+
5
)
1
3
dx
integral of x^2e^{-2x}+5e^{-2x}
∫
x
2
e
−
2
x
+
5
e
−
2
x
dx
integral from 1 to 4 of 2/x
∫
1
4
2
x
dx
integral of (x^5)/(1+x^{12)}
∫
x
5
1
+
x
1
2
dx
integral of ((2x-3))/((x^2-3x+6)^2)
∫
(
2
x
−
3
)
(
x
2
−
3
x
+
6
)
2
dx
integral of 6te^t
∫
6
te
t
dt
y^{''}+4y^'+40y=30cos(8t)
y
′
′
+
4
y
′
+
4
0
y
=
3
0
cos
(
8
t
)
integral from-3 to-3 of x^2
∫
−
3
−
3
x
2
dx
integral of (6x^5)/((x^6+1)^2)
∫
6
x
5
(
x
6
+
1
)
2
dx
derivative of (e^x/(x^n))
d
dx
(
e
x
x
n
)
tangent y=arccos(x)+x,\at x=0
tangent
y
=
arccos
(
x
)
+
x
,
at
x
=
0
t(dx)/(dt)=x-2t
t
dx
dt
=
x
−
2
t
sum from n=1 to infinity of 2+n/(3n+2)
∑
n
=
1
∞
2
+
n
3
n
+
2
inverse拉普拉斯 (s^2)/((s+5)(s^2+2^2))
inverselaplace
s
2
(
s
+
5
)
(
s
2
+
2
2
)
integral of ((ln(x))^3)/x
∫
(
ln
(
x
)
)
3
x
dx
integral of sin(2x-pi/4)
∫
sin
(
2
x
−
π
4
)
dx
limit as x approaches 1 of 1
lim
x
→
1
(
1
)
y^'=(x^2+1)/(3y^2)
y
′
=
x
2
+
1
3
y
2
integral of 1/(x^2-7)
∫
1
x
2
−
7
dx
-4y^{''}+16y=0,y(1)=2,y^'(2)=1
−
4
y
′
′
+
1
6
y
=
0
,
y
(
1
)
=
2
,
y
′
(
2
)
=
1
derivative y=x^3(x-1)^2
derivative
y
=
x
3
(
x
−
1
)
2
derivative f(x)=6sin^3(sqrt(x))
derivative
f
(
x
)
=
6
sin
3
(
√
x
)
integral of 8x^2+6+9/(x^2+1)
∫
8
x
2
+
6
+
9
x
2
+
1
dx
y^{''}+16y^'+73y=0
y
′
′
+
1
6
y
′
+
7
3
y
=
0
y^{''}-8y^'+4y=0
y
′
′
−
8
y
′
+
4
y
=
0
(dy)/(dx)=2
dy
dx
=
2
integral of e^{-x^8}(-8x^7)
∫
e
−
x
8
(
−
8
x
7
)
dx
integral of tan^2(θ)cos(θ)
∫
tan
2
(
θ
)
cos
(
θ
)
d
θ
limit as x approaches 16 of (x^2)/2-8/x
lim
x
→
1
6
(
x
2
2
−
8
x
)
derivative of (3x+2^5)
d
dx
(
(
3
x
+
2
)
5
)
derivative f(x)=8pix^2
derivative
f
(
x
)
=
8
π
x
2
(\partial ^2)/(\partial y^2)((xy)/(x-y))
∂
2
∂
y
2
(
xy
x
−
y
)
limit as x approaches 4 of 5
lim
x
→
4
(
5
)
derivative of 9cos(3x)
d
dx
(
9
cos
(
3
x
)
)
derivative of 4ax
d
dx
(
4
ax
)
limit as x approaches 2-of |x|-x^2
lim
x
→
2
−
(
|
x
|
−
x
2
)
derivative of (5x/((x^2-1)))
d
dx
(
5
x
(
x
2
−
1
)
)
1
..
1402
1403
1404
1405
1406
..
2459