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常见 微积分 问题
derivative of 1/3 x^3+x^2-x+5
d
dx
(
1
3
x
3
+
x
2
−
x
+
5
)
limit as n approaches infinity of sin((npi)/2)
lim
n
→
∞
(
sin
(
n
π
2
)
)
integral of (e^{2x})/(sqrt(1-e^{2x))}
∫
e
2
x
√
1
−
e
2
x
dx
limit as x approaches 3-of (x^2-9)/(x-3)
lim
x
→
3
−
(
x
2
−
9
x
−
3
)
(\partial)/(\partial y)(cos(nx)e^{ny})
∂
∂
y
(
cos
(
nx
)
e
ny
)
integral of 9/(x^2sqrt(x^2+36))
∫
9
x
2
√
x
2
+
3
6
dx
integral of sin(4x)sin(2x)
∫
sin
(
4
x
)
sin
(
2
x
)
dx
limit as x approaches-1 of x/(x^2-1)
lim
x
→
−
1
(
x
x
2
−
1
)
derivative (x^3+3x)/(x^2-4x+3)
derivative
x
3
+
3
x
x
2
−
4
x
+
3
limit as x approaches 4-of (|x-4|)/(x-4)
lim
x
→
4
−
(
|
x
−
4
|
x
−
4
)
integral of (x^3+x)sqrt(x^4+2x^2)
∫
(
x
3
+
x
)
√
x
4
+
2
x
2
dx
(\partial)/(\partial x)(sin(xz^2)-xy^2)
∂
∂
x
(
sin
(
xz
2
)
−
xy
2
)
integral of xae^{-ax}
∫
xae
−
ax
dx
y^'+3ty=t,y(0)=1
y
′
+
3
ty
=
t
,
y
(
0
)
=
1
integral of 9/(x(ln(x))^2)
∫
9
x
(
ln
(
x
)
)
2
dx
limit as x approaches 0 of x(cot(2x))
lim
x
→
0
(
x
(
cot
(
2
x
)
)
)
面积 sqrt(x),x^2
area
√
x
,
x
2
derivative of 1+x^3
d
dx
(
1
+
x
3
)
tangent f(x)=sqrt(5x+6),\at x=2
tangent
f
(
x
)
=
√
5
x
+
6
,
at
x
=
2
x(dy)/(dx)+2y=8x^2
x
dy
dx
+
2
y
=
8
x
2
sum from n=0 to infinity of 5/(4^n)
∑
n
=
0
∞
5
4
n
integral of ln(6x+7)
∫
ln
(
6
x
+
7
)
dx
(1+cos(t))y^'=(1-e^{-y})sin(t)
(
1
+
cos
(
t
)
)
y
′
=
(
1
−
e
−
y
)
sin
(
t
)
integral of x^2(x^3-4)^3
∫
x
2
(
x
3
−
4
)
3
dx
derivative of (6x/(x^2+3))
d
dx
(
6
x
x
2
+
3
)
derivative of (x-7/((x+5)^{10)})
d
dx
(
x
−
7
(
x
+
5
)
1
0
)
derivative x^2-12x+k
derivative
x
2
−
1
2
x
+
k
limit as x approaches 4 of xsqrt(25-x^2)
lim
x
→
4
(
x
√
2
5
−
x
2
)
y^{''}+4y^'+12y=0
y
′
′
+
4
y
′
+
1
2
y
=
0
integral from 0 to 4 of (13-t)sqrt(t)
∫
0
4
(
1
3
−
t
)
√
t
dt
derivative y=t^2+5cos(t)
derivative
y
=
t
2
+
5
cos
(
t
)
(dy)/(dx)sin(x+y)=0
dy
dx
sin
(
x
+
y
)
=
0
integral of (sec(x)+cos(x))/(4cos(x))
∫
sec
(
x
)
+
cos
(
x
)
4
cos
(
x
)
dx
limit as x approaches 0 of x*log_{2}(x)
lim
x
→
0
(
x
·
log
2
(
x
)
)
integral of (sqrt(x^2+36))/x
∫
√
x
2
+
3
6
x
dx
limit as t approaches 3 of 4t^2-2t+1
lim
t
→
3
(
4
t
2
−
2
t
+
1
)
derivative of f(x)=\sqrt[5]{5+2x+x^3}
d
dx
f
(
x
)
=
5
√
5
+
2
x
+
x
3
(\partial)/(\partial x)(sin(pixy))
∂
∂
x
(
sin
(
π
xy
)
)
面积 2x-1, 1/x ,x=3
area
2
x
−
1
,
1
x
,
x
=
3
(dy)/(dx)= 1/((2x+y+1))
dy
dx
=
1
(
2
x
+
y
+
1
)
(dy)/(dt)= y/t
dy
dt
=
y
t
面积 y=(x^2-4x-4)/(x^2-4x-5),y=0
area
y
=
x
2
−
4
x
−
4
x
2
−
4
x
−
5
,
y
=
0
6t((dy)/(dt))+y=t^3
6
t
(
dy
dt
)
+
y
=
t
3
derivative of 4x^3+x+5sin(x)
d
dx
(
4
x
3
+
x
+
5
sin
(
x
)
)
integral of 2+3x^2-8x^3
∫
2
+
3
x
2
−
8
x
3
dx
tangent f(x)=-4-3x^2,(2,-16)
tangent
f
(
x
)
=
−
4
−
3
x
2
,
(
2
,
−
1
6
)
integral from-45 to 0 of 1/(sqrt(4-x))
∫
−
4
5
0
1
√
4
−
x
dx
sum from n=1 to infinity of 8^{-n}
∑
n
=
1
∞
8
−
n
(\partial)/(\partial x)(1+e^{-xy}cos(y))
∂
∂
x
(
1
+
e
−
xy
cos
(
y
)
)
integral of 2cos(4x)cos(2x)
∫
2
cos
(
4
x
)
cos
(
2
x
)
dx
integral of 4sqrt(1-x^2)
∫
4
√
1
−
x
2
dx
derivative (5x-2x^4)^3
derivative
(
5
x
−
2
x
4
)
3
(x^{-2})^'
(
x
−
2
)
′
integral from 2 to 3 of 1/x
∫
2
3
1
x
dx
integral of (6x^2-3x+3)
∫
(
6
x
2
−
3
x
+
3
)
dx
derivative of cos(2-3x)
d
dx
(
cos
(
2
−
3
x
)
)
(dy)/(dt)+e^ty=e^t
dy
dt
+
e
t
y
=
e
t
(d^2y)/(dx^2)-4(dy)/(dx)+2y=0
d
2
y
dx
2
−
4
dy
dx
+
2
y
=
0
limit as x approaches-(7pi)/2-of sec(x)
lim
x
→
−
7
π
2
−
(
sec
(
x
)
)
(dy)/(dx)=9-y/(6x+250)
dy
dx
=
9
−
y
6
x
+
2
5
0
tangent f(x)=x^4+2x^2-x,\at x=1
tangent
f
(
x
)
=
x
4
+
2
x
2
−
x
,
at
x
=
1
x^2y^'+xy=5
x
2
y
′
+
xy
=
5
derivative of 9x^4+6x^3+1
d
dx
(
9
x
4
+
6
x
3
+
1
)
integral of ln(sqrt(x)+sqrt(1+x))
∫
ln
(
√
x
+
√
1
+
x
)
dx
derivative log_{10}(x^7+5)
derivative
log
1
0
(
x
7
+
5
)
derivative of 1/(3x^{2/3})
d
dx
(
1
3
x
2
3
)
integral of sqrt(x)(x^2-1/x)
∫
√
x
(
x
2
−
1
x
)
dx
(\partial)/(\partial x)(e^x+cos(y))
∂
∂
x
(
e
x
+
cos
(
y
)
)
derivative f(x)=(3x-7)/(5x-2)
derivative
f
(
x
)
=
3
x
−
7
5
x
−
2
derivative of 2/3 x^2-5x+3/x+7
d
dx
(
2
3
x
2
−
5
x
+
3
x
+
7
)
面积 y=20-x,y=sqrt(x),y=1
area
y
=
2
0
−
x
,
y
=
√
x
,
y
=
1
y^'=-ay(1+3y)
y
′
=
−
ay
(
1
+
3
y
)
(\partial)/(\partial y)(100e^{-2x^2-y^2})
∂
∂
y
(
1
0
0
e
−
2
x
2
−
y
2
)
integral of (5sin^3(x))/(cos(x))
∫
5
sin
3
(
x
)
cos
(
x
)
dx
(\partial)/(\partial x)(x^3y)
∂
∂
x
(
x
3
y
)
integral of (x^8+1)e^{x^9+9x}
∫
(
x
8
+
1
)
e
x
9
+
9
x
dx
y^{''}+19y=0
y
′
′
+
1
9
y
=
0
limit as x approaches-5-of (|5-x|)/(5-x)
lim
x
→
−
5
−
(
|
5
−
x
|
5
−
x
)
integral of (x^2+36x-9)/(x^3-9x)
∫
x
2
+
3
6
x
−
9
x
3
−
9
x
dx
integral from 0 to pi/2 of tan^2(x)
∫
0
π
2
tan
2
(
x
)
dx
(\partial)/(\partial y)(1+x^2)
∂
∂
y
(
1
+
x
2
)
derivative arctan(x/4)
derivative
arctan
(
x
4
)
integral of ((4-x)^2)/(sqrt(x))
∫
(
4
−
x
)
2
√
x
dx
derivative (e^x)/(e^x+3)
derivative
e
x
e
x
+
3
(dy)/(dx)=2xe^{-y}
dy
dx
=
2
xe
−
y
integral of (4x)/(sqrt(x^2+1))
∫
4
x
√
x
2
+
1
dx
integral of x^2*2^x
∫
x
2
·
2
x
dx
derivative f(x)=sqrt(x)+x^{2/3}-3x
derivative
f
(
x
)
=
√
x
+
x
2
3
−
3
x
limit as x approaches 0 of 2sin(x)ln(x)
lim
x
→
0
(
2
sin
(
x
)
ln
(
x
)
)
derivative 2e^x-e^{x+1}+e^{2/3}-5pi^2
derivative
2
e
x
−
e
x
+
1
+
e
2
3
−
5
π
2
limit as x approaches 0+of sin^2(x)
lim
x
→
0
+
(
sin
2
(
x
)
)
sum from n=0 to infinity of (3/2)^n
∑
n
=
0
∞
(
3
2
)
n
derivative of (4x+asqrt(1+x)/(x^2-1))
d
dx
(
4
x
+
a
√
1
+
x
x
2
−
1
)
dx+e^{2x}dy=0
dx
+
e
2
x
dy
=
0
derivative A/(y^{14)}+Be^y
derivative
A
y
1
4
+
Be
y
limit as x approaches 2-of-3
lim
x
→
2
−
(
−
3
)
derivative of xsin(tan(x))
d
dx
(
x
sin
(
tan
(
x
)
)
)
tangent y=3x^2+2x^2+1,(-1,0)
tangent
y
=
3
x
2
+
2
x
2
+
1
,
(
−
1
,
0
)
limit as x approaches 2 of x^2+2x+1
lim
x
→
2
(
x
2
+
2
x
+
1
)
limit as x approaches infinity of x+x+x
lim
x
→
∞
(
x
+
x
+
x
)
1
..
1501
1502
1503
1504
1505
..
2459