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常见 微积分 问题
y^{''}-4y^'+53y=5e^{2t}cos(7t)
y
′
′
−
4
y
′
+
5
3
y
=
5
e
2
t
cos
(
7
t
)
derivative cos^{10}(sin(7x))
derivative
cos
1
0
(
sin
(
7
x
)
)
y=4x(3x-2)^5
y
=
4
x
(
3
x
−
2
)
5
derivative sin(5xln(x))(sin^2(5x))
derivative
sin
(
5
x
ln
(
x
)
)
(
sin
2
(
5
x
)
)
derivative \sqrt[3]{x^2-3}
derivative
3
√
x
2
−
3
integral from 5 to 7 of x
∫
5
7
xdx
integral from-1 to 1 of 1-|x|
∫
−
1
1
1
−
|
x
|
dx
integral of 2e^{2t}
∫
2
e
2
t
dt
x*y^{''}+y^'=0
x
·
y
′
′
+
y
′
=
0
泰勒 e^x2
taylor
e
x
2
integral of cos(x)e^x
∫
cos
(
x
)
e
x
dx
integral of (4x^2-7x-19)/(x^2-2x-3)
∫
4
x
2
−
7
x
−
1
9
x
2
−
2
x
−
3
dx
derivative-3ae^{-3x}+be^x+c(e^x+e^xx)
derivative
−
3
ae
−
3
x
+
be
x
+
c
(
e
x
+
e
x
x
)
泰勒 1/2 (e^{(1-x)})
taylor
1
2
(
e
(
1
−
x
)
)
斜率 y=-12/7 x=+b
slope
y
=
−
1
2
7
x
=
+
b
derivative of y=tan^2(sqrt(x))
d
dx
y
=
tan
2
(
√
x
)
integral of e^{-x}sin(x)
∫
e
−
x
sin
(
x
)
dx
sum from n=1 to infinity of (5n)/(4n+15)
∑
n
=
1
∞
5
n
4
n
+
1
5
limit as x approaches-1-of (x+1)/(x^4-1)
lim
x
→
−
1
−
(
x
+
1
x
4
−
1
)
sum from n=0 to infinity of 1/(2^{n-1)}
∑
n
=
0
∞
1
2
n
−
1
derivative (x^4)/2-2/(x^4)+6sqrt(x)
derivative
x
4
2
−
2
x
4
+
6
√
x
derivative of arcsin(5x-1)
d
dx
(
arcsin
(
5
x
−
1
)
)
integral from-2 to 0 of 5/(x^2+4x+8)
∫
−
2
0
5
x
2
+
4
x
+
8
dx
limit as x approaches 4 of-x^2+3x-7
lim
x
→
4
(
−
x
2
+
3
x
−
7
)
derivative of pi/5
d
dx
(
π
5
)
integral of x^2+2x-15
∫
x
2
+
2
x
−
1
5
dx
面积 x^2-43,-2x+5,-8,6
area
x
2
−
4
3
,
−
2
x
+
5
,
−
8
,
6
x^{'''}=0
x
′
′
′
=
0
integral of (x-1)^2
∫
(
x
−
1
)
2
dx
limit as x approaches 8 of 7
lim
x
→
8
(
7
)
derivative f(x)=3arccos(x/2)
derivative
f
(
x
)
=
3
arccos
(
x
2
)
derivative 8
derivative
8
y=((x^2+2x)/(x+1))^5
y
=
(
x
2
+
2
x
x
+
1
)
5
integral of 1/2 x+1
∫
1
2
x
+
1
dx
integral of (1-t^2)/(1+t^2)
∫
1
−
t
2
1
+
t
2
dt
integral of 1/((y^2-y))
∫
1
(
y
2
−
y
)
dy
x^2y^{''}=(y^')^2
x
2
y
′
′
=
(
y
′
)
2
(\partial)/(\partial x)(3y^3-4yx^2)
∂
∂
x
(
3
y
3
−
4
yx
2
)
integral from 0 to 7 of f(x)
∫
0
7
f
(
x
)
dx
limit as θ approaches 0 of (sin(4θ))/θ
lim
θ
→
0
(
sin
(
4
θ
)
θ
)
derivative f(x)=8x^2+4e^{-0.5x}
derivative
f
(
x
)
=
8
x
2
+
4
e
−
0
.
5
x
tangent \sqrt[3]{x}
tangent
3
√
x
(x-y)dx+dy=0
(
x
−
y
)
dx
+
dy
=
0
limit as x approaches 0 of (g(x))/(f(x))
lim
x
→
0
(
g
(
x
)
f
(
x
)
)
integral from 0 to 3 of 4
∫
0
3
4
dx
derivative log_{8}(xe^x)
derivative
log
8
(
xe
x
)
derivative of-tan(x-5cot(x))
d
dx
(
−
tan
(
x
)
−
5
cot
(
x
)
)
derivative (-3sin(t))/(sqrt(28))
derivative
−
3
sin
(
t
)
√
2
8
integral from 1 to 2 of e^{1-x}
∫
1
2
e
1
−
x
dx
tangent f(x)=-3x^2
tangent
f
(
x
)
=
−
3
x
2
integral from 0 to 1 of xsqrt(2-x^2)
∫
0
1
x
√
2
−
x
2
dx
integral of (ln(x+5))/(x+5)
∫
ln
(
x
+
5
)
x
+
5
dx
(\partial)/(\partial t)(2)
∂
∂
t
(
2
)
(dy)/(dx)+y^2=0
dy
dx
+
y
2
=
0
limit as x approaches 3 of (2^x-8)/(x-3)
lim
x
→
3
(
2
x
−
8
x
−
3
)
integral of 8/((1-x^2)^{3/2)}
∫
8
(
1
−
x
2
)
3
2
dx
tangent f(x)= 5/(sqrt(x))
tangent
f
(
x
)
=
5
√
x
(d^2x)/(dt^2)+2(dx)/(dt)+x=6e^{-t}
d
2
x
dt
2
+
2
dx
dt
+
x
=
6
e
−
t
derivative ((x+12)/(x-12))^5
derivative
(
x
+
1
2
x
−
1
2
)
5
derivative of 9x(-2^2-3x(-2)1)
d
dx
(
9
x
(
−
2
)
2
−
3
x
(
−
2
)
1
)
sum from n=0 to infinity of (0^n)/(n!)
∑
n
=
0
∞
0
n
n
!
integral of e^{ln(x)} 1/x
∫
e
ln
(
x
)
1
x
dx
(dy)/(dx)=3y,y(0)=2
dy
dx
=
3
y
,
y
(
0
)
=
2
limit as x approaches (5pi)/6 of cos(2x)
lim
x
→
5
π
6
(
cos
(
2
x
)
)
integral of e^tcos(t)
∫
e
t
cos
(
t
)
dt
derivative of ln(xsqrt(x^2-6))
d
dx
(
ln
(
x
√
x
2
−
6
)
)
derivative of sin^2(x+x^2sin(x))
d
dx
(
sin
2
(
x
)
+
x
2
sin
(
x
)
)
integral of x^2-4x+3
∫
x
2
−
4
x
+
3
dx
derivative 1/2 x^2sqrt(49-x^2)
derivative
1
2
x
2
√
4
9
−
x
2
integral of cos^5(x)sin(2x)
∫
cos
5
(
x
)
sin
(
2
x
)
dx
(\partial)/(\partial x)(x^2-2xy+6y^2+x-5y)
∂
∂
x
(
x
2
−
2
xy
+
6
y
2
+
x
−
5
y
)
integral of y^5
∫
y
5
dy
derivative e^{13t}
derivative
e
1
3
t
limit as x approaches 0 of (e^x+1)/x
lim
x
→
0
(
e
x
+
1
x
)
tangent 3x^2-5x
tangent
3
x
2
−
5
x
integral of (e^{4x})/(e^{4x)+3}
∫
e
4
x
e
4
x
+
3
dx
derivative of cos(x^2(2x))
d
dx
(
cos
(
x
2
)
(
2
x
)
)
derivative 5x^2-3x+1
derivative
5
x
2
−
3
x
+
1
derivative of 3*5^x
d
dx
(
3
·
5
x
)
limit as x approaches 3 of 2x^3-10x-8
lim
x
→
3
(
2
x
3
−
1
0
x
−
8
)
limit as x approaches 0 of (x^2-9)/(x-3)
lim
x
→
0
(
x
2
−
9
x
−
3
)
limit as x approaches 0 of ((3+x)^2-9)/x
lim
x
→
0
(
(
3
+
x
)
2
−
9
x
)
4x^2y^{''}+17y=0
4
x
2
y
′
′
+
1
7
y
=
0
laplace变换 f(,\at)
laplacetransform
f
(
,
at
)
y^'+xy=-5xy^4
y
′
+
xy
=
−
5
xy
4
integral of (x^3+2x)sin(x)
∫
(
x
3
+
2
x
)
sin
(
x
)
dx
limit as x approaches 3 of 7+6(-7)
lim
x
→
3
(
7
+
6
(
−
7
)
)
integral of 2x+9
∫
2
x
+
9
dx
(\partial)/(\partial z)(xy)
∂
∂
z
(
xy
)
integral from 0 to infinity of e^{-xy}
∫
0
∞
e
−
xy
dy
integral of 2z^5e^{1-z}
∫
2
z
5
e
1
−
z
dz
derivative of sqrt(x+e^x)
d
dx
(
√
x
+
e
x
)
derivative tan^3(1+2x^2)
derivative
tan
3
(
1
+
2
x
2
)
derivative x(3x-9)^3
derivative
x
(
3
x
−
9
)
3
integral of (x^2)/(sqrt(a^2+x^2))
∫
x
2
√
a
2
+
x
2
dx
integral of (sin(x^3))
∫
(
sin
(
x
3
)
)
dx
y^'(x)=((1+3x^2))/(3y^2-6y),y(0)=1
y
′
(
x
)
=
(
1
+
3
x
2
)
3
y
2
−
6
y
,
y
(
0
)
=
1
derivative of axcos(2x+bxsin(2x))
d
dx
(
ax
cos
(
2
x
)
+
bx
sin
(
2
x
)
)
(\partial)/(\partial x)(cos(x)*sin(x))
∂
∂
x
(
cos
(
x
)
·
sin
(
x
)
)
derivative of 1+e^{x^2}
d
dx
(
1
+
e
x
2
)
1
..
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1162
1163
1164
1165
..
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