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常见 微积分 问题
derivative of sqrt(2x)+1
d
dx
(
√
2
x
+
1
)
derivative f(x)=(cos(x))/(x^7)
derivative
f
(
x
)
=
cos
(
x
)
x
7
integral of (3x^2+2)/(x^3+2x)
∫
3
x
2
+
2
x
3
+
2
x
dx
(dy)/(dx)-3y= y/x
dy
dx
−
3
y
=
y
x
derivative of (x-y^{10})
d
dx
(
(
x
−
y
)
1
0
)
integral of (x^2+5)e^{2x}
∫
(
x
2
+
5
)
e
2
x
dx
limit as x approaches 8-of x^2+5
lim
x
→
8
−
(
x
2
+
5
)
d/(d{x)}({x}^2e^{{y}{z}})
d
d
x
(
x
2
e
y
z
)
derivative f(x)=5x^2+2x-20
derivative
f
(
x
)
=
5
x
2
+
2
x
−
2
0
(dx)/(dt)=2tcos^2(x)
dx
dt
=
2
t
cos
2
(
x
)
derivative of 3x^2+ln(5x-sin(x))
d
dx
(
3
x
2
+
ln
(
5
x
)
−
sin
(
x
)
)
d/(dj)(2i-3j)
d
dj
(
2
i
−
3
j
)
y^'+5/t y=1
y
′
+
5
t
y
=
1
integral of arccot(5y)
∫
arccot
(
5
y
)
dy
tangent f(x)=x^2-6,(4,10)
tangent
f
(
x
)
=
x
2
−
6
,
(
4
,
1
0
)
(d^2)/(dx^2)(xe^{4x})
d
2
dx
2
(
xe
4
x
)
tangent f(x)= 1/(2sqrt(x)),\at x=81
tangent
f
(
x
)
=
1
2
√
x
,
at
x
=
8
1
derivative of {f}(x((x^4)/4-1/4))
d
dx
(
f
(
x
)
(
x
4
4
−
1
4
)
)
derivative log_{3}(x-4x^2)
derivative
log
3
(
x
−
4
x
2
)
derivative of 1/((x^3+4^2))
d
dx
(
1
(
x
3
+
4
)
2
)
limit as x approaches 0-of xln(x)
lim
x
→
0
−
(
x
ln
(
x
)
)
integral from 3 to 8 of (x^3-pix^2)
∫
3
8
(
x
3
−
π
x
2
)
dx
sum from n=0 to infinity of 9((5/12)^n)
∑
n
=
0
∞
9
(
(
5
1
2
)
n
)
integral of (x^6e^x)/x
∫
x
6
e
x
x
dx
(dy)/(dx)+3x^2y=6x^2
dy
dx
+
3
x
2
y
=
6
x
2
斜率intercept (-4,-5),(3,-5)
slopeintercept
(
−
4
,
−
5
)
,
(
3
,
−
5
)
integral of (sin(x))/(4+cos^2(x))
∫
sin
(
x
)
4
+
cos
2
(
x
)
dx
integral of (5+2w^3-w^5)cos(3w)
∫
(
5
+
2
w
3
−
w
5
)
cos
(
3
w
)
dw
面积 x=y^2-y,x=y-y^2
area
x
=
y
2
−
y
,
x
=
y
−
y
2
integral from 2 to 4 of 8x
∫
2
4
8
xdx
integral of (2sin(x)cos(x))
∫
(
2
sin
(
x
)
cos
(
x
)
)
dx
integral of 7tan^5(x)
∫
7
tan
5
(
x
)
dx
奇偶性 f(x)=sqrt(x+sin(x))
parity
f
(
x
)
=
√
x
+
sin
(
x
)
integral of ye^x
∫
ye
x
dx
integral of (e^{8x})/(e^{8x)+9}
∫
e
8
x
e
8
x
+
9
dx
derivative of (8x^2-13xe^x)
d
dx
(
(
8
x
2
−
1
3
x
)
e
x
)
derivative (x^3-2x)(x^{-4}+x^{-2})
derivative
(
x
3
−
2
x
)
(
x
−
4
+
x
−
2
)
泰勒 2/((3x+1)),2
taylor
2
(
3
x
+
1
)
,
2
(-xysin(x)+2ycos(x))dx+2xcos(x)dy=0
(
−
xy
sin
(
x
)
+
2
y
cos
(
x
)
)
dx
+
2
x
cos
(
x
)
dy
=
0
integral of x^8(x^9-7)^4
∫
x
8
(
x
9
−
7
)
4
dx
derivative of 9/2 x^2
d
dx
(
9
2
x
2
)
(\partial)/(\partial y)(6xy)
∂
∂
y
(
6
xy
)
derivative of 73.3\sqrt[4]{x^3}
d
dx
(
7
3
.
3
4
√
x
3
)
d/(dt)(t^3-12t^2+45t)
d
dt
(
t
3
−
1
2
t
2
+
4
5
t
)
laplace变换 3t
laplacetransform
3
t
integral of e-x
∫
e
−
xdx
integral of sin(6θ)cos(2θ)
∫
sin
(
6
θ
)
cos
(
2
θ
)
d
θ
tangent f(x)=((2x)/(x^2+1)),\at x=1
tangent
f
(
x
)
=
(
2
x
x
2
+
1
)
,
at
x
=
1
y^{''}=-3y
y
′
′
=
−
3
y
(\partial)/(\partial x)(sec(xy)+tan(xy))
∂
∂
x
(
sec
(
xy
)
+
tan
(
xy
)
)
limit as x approaches 4+of 2/(sqrt(x-4))
lim
x
→
4
+
(
2
√
x
−
4
)
integral of 3x^{-5}
∫
3
x
−
5
dx
integral of (e^x+2)
∫
(
e
x
+
2
)
dx
derivative f(x)=((8x+x^2))/((4+x)^2)
derivative
f
(
x
)
=
(
8
x
+
x
2
)
(
4
+
x
)
2
integral of (3x)/(3x+2)
∫
3
x
3
x
+
2
dx
limit as x approaches 3 of (x^2-25)/(sqrt(x^2+11))
lim
x
→
3
(
x
2
−
2
5
√
x
2
+
1
1
)
integral from 0 to 2 of 2e^{-3x}
∫
0
2
2
e
−
3
x
dx
derivative of (x^{1/3}-1^3)
d
dx
(
(
x
1
3
−
1
)
3
)
xy^'=y+3x^2sin(x),y(pi)=0
xy
′
=
y
+
3
x
2
sin
(
x
)
,
y
(
π
)
=
0
integral from 2 to 4 of 1/(x^2-25)
∫
2
4
1
x
2
−
2
5
dx
limit as x approaches 0 of (4x)^{7x}
lim
x
→
0
(
(
4
x
)
7
x
)
面积-2x^2+x,-2,1
area
−
2
x
2
+
x
,
−
2
,
1
sum from n=0 to infinity of 1/2
∑
n
=
0
∞
1
2
(\partial)/(\partial x)(asin(2x))
∂
∂
x
(
a
sin
(
2
x
)
)
integral of (e^{sqrt(7x)})/(sqrt(7x))
∫
e
√
7
x
√
7
x
dx
sum from n=0 to infinity of cn(x-4)^n
∑
n
=
0
∞
cn
(
x
−
4
)
n
limit as x approaches 0 of (sin(8x))/x
lim
x
→
0
(
sin
(
8
x
)
x
)
derivative (8x^2-14x)e^x
derivative
(
8
x
2
−
1
4
x
)
e
x
integral of 1+1/(x^2)
∫
1
+
1
x
2
dx
integral of-4x^2-12x+16
∫
−
4
x
2
−
1
2
x
+
1
6
dx
derivative of (0.14x/(0.015+x))
d
dx
(
0
.
1
4
x
0
.
0
1
5
+
x
)
integral of y-e^{cos(x)}sin(x)
∫
y
−
e
cos
(
x
)
sin
(
x
)
dx
integral of ((3x-5))/(x^3-5x^2-14x)
∫
(
3
x
−
5
)
x
3
−
5
x
2
−
1
4
x
dx
derivative of \sqrt[3]{x^3+y^3}
d
dx
(
3
√
x
3
+
y
3
)
(sqrt(x)cos(sqrt(x)))^'
(
√
x
cos
(
√
x
)
)
′
integral of cos(x)sec^2(x)
∫
cos
(
x
)
sec
2
(
x
)
dx
f(x)=-sec^2(x)
f
(
x
)
=
−
sec
2
(
x
)
integral from 0 to pi/4 of 4sec^3(x)
∫
0
π
4
4
sec
3
(
x
)
dx
limit as x approaches 4 of 1/((x-4)^2)
lim
x
→
4
(
1
(
x
−
4
)
2
)
integral of 10-1/16 x
∫
1
0
−
1
1
6
xdx
integral of 1/(2sin^2(x/5))
∫
1
2
sin
2
(
x
5
)
dx
tangent x=ln(xy),\at x=1
tangent
x
=
ln
(
xy
)
,
at
x
=
1
derivative sqrt(2x+1)
derivative
√
2
x
+
1
integral of 2/(cos^2(x))
∫
2
cos
2
(
x
)
dx
y^{''}+y^'-6y=0,y(0)=5,y^'(0)=2
y
′
′
+
y
′
−
6
y
=
0
,
y
(
0
)
=
5
,
y
′
(
0
)
=
2
integral of 5x^2+3x+2
∫
5
x
2
+
3
x
+
2
dx
integral from 0 to 5 of (1+2x^3)
∫
0
5
(
1
+
2
x
3
)
dx
derivative of ((x^2+2/(x^2-2))^3)
d
dx
(
(
x
2
+
2
x
2
−
2
)
3
)
(\partial)/(\partial x)(xarctan(x+2y))
∂
∂
x
(
x
arctan
(
x
+
2
y
)
)
derivative of (2cos(sqrt(x))/(x+1))
d
dx
(
2
cos
(
√
x
)
x
+
1
)
integral of ((x-2))/2
∫
(
x
−
2
)
2
dx
derivative of (10x/(x^2-6))
d
dx
(
1
0
x
x
2
−
6
)
tangent f(x)=x^2-5,(-3,4)
tangent
f
(
x
)
=
x
2
−
5
,
(
−
3
,
4
)
integral of (x-3)^2*e^{-x}
∫
(
x
−
3
)
2
·
e
−
x
dx
integral of 1/((x-2)(x+2)^2)
∫
1
(
x
−
2
)
(
x
+
2
)
2
dx
integral of 1/(x^2)sqrt(1-1/x)
∫
1
x
2
√
1
−
1
x
dx
(dy)/(dx)=ycos(3x+2)
dy
dx
=
y
cos
(
3
x
+
2
)
(dy)/(dt)+7y=e^{5t}
dy
dt
+
7
y
=
e
5
t
derivative of-2x^2+x-1
d
dx
(
−
2
x
2
+
x
−
1
)
x^{''}+3x^'+2x=1
x
′
′
+
3
x
′
+
2
x
=
1
1
..
1391
1392
1393
1394
1395
..
2459