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人気の高い微分積分問題
integral of ((x+1)(x-1))/(x^2)
∫
(
x
+
1
)
(
x
−
1
)
x
2
dx
derivative log_{9}(ln(x))
derivative
log
9
(
ln
(
x
)
)
limit as x approaches+0 of 8/(6+e^x)
lim
x
→
+
0
(
8
6
+
e
x
)
integral from 1 to infinity of 3/(x^4)
∫
1
∞
3
x
4
dx
derivative ((17-x)sqrt(2x+8))/2
derivative
(
1
7
−
x
)
√
2
x
+
8
2
limit as x approaches-1 of x^4-2x^2-1
lim
x
→
−
1
(
x
4
−
2
x
2
−
1
)
integral from 0 to 0.6 of (600x)
∫
0
0
.
6
(
6
0
0
x
)
dx
(dy)/(dx)=((sec(y)))/((x-1)^2)
dy
dx
=
(
sec
(
y
)
)
(
x
−
1
)
2
integral from 0 to pi of sin^5(x)
∫
0
π
sin
5
(
x
)
dx
integral of \sqrt[3]{x}+1/(\sqrt[3]{x)}
∫
3
√
x
+
1
3
√
x
dx
inverselaplace s/((s+1))
inverselaplace
s
(
s
+
1
)
(\partial)/(\partial z)(x^{yz})
∂
∂
z
(
x
yz
)
derivative of 11arccot(x+11arccot(1/x))
d
dx
(
1
1
arccot
(
x
)
+
1
1
arccot
(
1
x
)
)
derivative (-5)/((2x^3+7)^2)
derivative
−
5
(
2
x
3
+
7
)
2
勾配 (2,7),(-5,2)
slope
(
2
,
7
)
,
(
−
5
,
2
)
y^{''}-9y^'=0
y
′
′
−
9
y
′
=
0
integral of sin(2x)sqrt(1+cos^2(x))
∫
sin
(
2
x
)
√
1
+
cos
2
(
x
)
dx
(dy}{dx}=\frac{x^2-2y)/x
dy
dx
=
x
2
−
2
y
x
limit as x approaches 2 of (2x+1)/(x-2)
lim
x
→
2
(
2
x
+
1
x
−
2
)
derivative of sin(sqrt(3)x)
d
dx
(
sin
(
√
3
x
)
)
sum from n=1 to infinity of (2/3)^{n+2}
∑
n
=
1
∞
(
2
3
)
n
+
2
(\partial)/(\partial x)((-1)/(x^2+y^2))
∂
∂
x
(
−
1
x
2
+
y
2
)
laplacetransform e^{-3t}+3+2t+4t^2+5t^3
laplacetransform
e
−
3
t
+
3
+
2
t
+
4
t
2
+
5
t
3
derivative of sin(2x+cos(x))
d
dx
(
sin
(
2
x
)
+
cos
(
x
)
)
integral of cos(x/(sqrt(2)))
∫
cos
(
x
√
2
)
dx
(1+x)dy-ydx=0
(
1
+
x
)
dy
−
ydx
=
0
limit as x approaches infinity of 6^x
lim
x
→
∞
(
6
x
)
limit as x approaches 0-of f(x)
lim
x
→
0
−
(
f
(
x
)
)
derivative f(x)=-3e^{x+1}
derivative
f
(
x
)
=
−
3
e
x
+
1
tangent f(x)=8x-x^2
tangent
f
(
x
)
=
8
x
−
x
2
limit as x approaches 0+of 1/(x+1)
lim
x
→
0
+
(
1
x
+
1
)
(\partial)/(\partial x)(1-x^2-y^2)
∂
∂
x
(
1
−
x
2
−
y
2
)
limit as x approaches 1 of sqrt(x)-x
lim
x
→
1
(
√
x
−
x
)
(\partial)/(\partial x)(4x^{-1})
∂
∂
x
(
4
x
−
1
)
tangent f(x)=x^2+6x,\at a=3
tangent
f
(
x
)
=
x
2
+
6
x
,
at
a
=
3
limit as x approaches 2 of sqrt(3x-2)
lim
x
→
2
(
√
3
x
−
2
)
derivative (x^2)/(8+x)
derivative
x
2
8
+
x
integral from 0 to 1 of 23cos(x^2)
∫
0
1
2
3
cos
(
x
2
)
dx
derivative of (tan(x)^{1/x})
d
dx
(
(
tan
(
x
)
)
1
x
)
integral of 1/(x^2+5x-6)
∫
1
x
2
+
5
x
−
6
dx
derivative of 2cx
d
dx
(
2
cx
)
integral of 1/(x(ln(x^4))^9)
∫
1
x
(
ln
(
x
4
)
)
9
dx
e^xy(dy)/(dx)=e^{-y}+e^{-2x-y}
e
x
y
dy
dx
=
e
−
y
+
e
−
2
x
−
y
laplacetransform 3sin(sqrt(2)t)
laplacetransform
3
sin
(
√
2
t
)
integral of-2x^{-4}
∫
−
2
x
−
4
dx
derivative f(x)=((5^{3x^7})/(8x^2))^4
derivative
f
(
x
)
=
(
5
3
x
7
8
x
2
)
4
integral of (x-3)/(x^2-12x+36)
∫
x
−
3
x
2
−
1
2
x
+
3
6
dx
sum from n=1 to infinity of n/(n+3)
∑
n
=
1
∞
n
n
+
3
tangent f(x)=(2+4x)(5-4x),\at x=1
tangent
f
(
x
)
=
(
2
+
4
x
)
(
5
−
4
x
)
,
at
x
=
1
tangent y=2x^3-2x^2-2x
tangent
y
=
2
x
3
−
2
x
2
−
2
x
(dy)/(dx)+y/x =x^3
dy
dx
+
y
x
=
x
3
derivative of (e^{ax^2+bx+c}/x)
d
dx
(
e
ax
2
+
bx
+
c
x
)
limit as e approaches 1 of 5ln^2(e)
lim
e
→
1
(
5
ln
2
(
e
)
)
limit as x approaches+0 of (1-1/x)x
lim
x
→
+
0
(
(
1
−
1
x
)
x
)
(\partial)/(\partial y)(x+y+1)
∂
∂
y
(
x
+
y
+
1
)
integral of 1/(x^{2022)}
∫
1
x
2
0
2
2
dx
d/(dt)(7t^3)
d
dt
(
7
t
3
)
inverselaplace 1/(s(4s^2-1))
inverselaplace
1
s
(
4
s
2
−
1
)
integral of 1/(x^2-6x)
∫
1
x
2
−
6
x
dx
integral of 1/(4x+xln^2(3x))
∫
1
4
x
+
x
ln
2
(
3
x
)
dx
integral of sec(t)(2sec(t)+7tan(t))
∫
sec
(
t
)
(
2
sec
(
t
)
+
7
tan
(
t
)
)
dt
integral of (6x^3+4x^2-2x)/(2x^2)
∫
6
x
3
+
4
x
2
−
2
x
2
x
2
dx
(\partial)/(\partial x)(x^3-xsin(y))
∂
∂
x
(
x
3
−
x
sin
(
y
)
)
integral from-1 to 0 of x^3-x
∫
−
1
0
x
3
−
xdx
limit as x approaches 2 of (5x)/(x-2)
lim
x
→
2
(
5
x
x
−
2
)
integral of e^{2θ}sin(3θ)
∫
e
2
θ
sin
(
3
θ
)
d
θ
(ln(f(x)))\prime
(
ln
(
f
(
x
)
)
)
′
inverselaplace 10s
inverselaplace
1
0
s
(3^{-x^2})^'
(
3
−
x
2
)
′
derivative 1-(36)/(x^2)
derivative
1
−
3
6
x
2
(dx)/(dt)=ax+b
dx
dt
=
ax
+
b
-2y^{''}+4y^'+3y=1
−
2
y
′
′
+
4
y
′
+
3
y
=
1
f(x)=(x^2+2)(x^4+1)
f
(
x
)
=
(
x
2
+
2
)
(
x
4
+
1
)
cos(t)y^'-sin(t)y=t^2
cos
(
t
)
y
′
−
sin
(
t
)
y
=
t
2
簡約 x/(x+c/x)
simplify
x
x
+
c
x
derivative sqrt(7)x+sqrt(6x)
derivative
√
7
x
+
√
6
x
tangent f(x)=5x^{3/5}-4
tangent
f
(
x
)
=
5
x
3
5
−
4
integral of (Inx)/((x+1)^2)
∫
Inx
(
x
+
1
)
2
dx
limit as x approaches infinity of 4-x^2
lim
x
→
∞
(
4
−
x
2
)
derivative of 2sec(3x^2)
d
dx
(
2
sec
(
3
x
2
)
)
tangent y=(x^3-9x)^{12}
tangent
y
=
(
x
3
−
9
x
)
1
2
integral of csc^4(4x)
∫
csc
4
(
4
x
)
dx
derivative of (4-sqrt(x)^2)
d
dx
(
(
4
−
√
x
)
2
)
integral of (100)/(25+(5y)^2)+e^4
∫
1
0
0
2
5
+
(
5
y
)
2
+
e
4
dy
derivative (y(4x+4y))/((x^2+y^2))
derivative
y
(
4
x
+
4
y
)
(
x
2
+
y
2
)
integral from 1 to 4 of x^2+2
∫
1
4
x
2
+
2
dx
(\partial)/(\partial x)(2x^{3y})
∂
∂
x
(
2
x
3
y
)
(\partial)/(\partial t)(-3st)
∂
∂
t
(
−
3
st
)
tangent (0.1666)(0.998)^x
tangent
(
0
.
1
6
6
6
)
(
0
.
9
9
8
)
x
derivative of (2x^2-5x+4/(sqrt(x)))
d
dx
(
2
x
2
−
5
x
+
4
√
x
)
面積 y=sqrt(x+4),y= x/2+2
area
y
=
√
x
+
4
,
y
=
x
2
+
2
integral of 8tan^4(xse)c^6x
∫
8
tan
4
(
xse
)
c
6
xdx
derivative e^{1/2 x}
derivative
e
1
2
x
面積 4-4cos(7x),4cos(7x),0>= x>= pi/7
area
4
−
4
cos
(
7
x
)
,
4
cos
(
7
x
)
,
0
≥
x
≥
π
7
derivative of 2xsqrt(x)+1/(sqrt(x))
d
dx
(
2
x
√
x
+
1
√
x
)
integral of x^2+7
∫
x
2
+
7
dx
y^{''}=-3y-2y^',y(0)=1,y^'(0)=0
y
′
′
=
−
3
y
−
2
y
′
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
integral of 4/(1+x^2)
∫
4
1
+
x
2
dx
3y^'-2y=e^{-pi/2}
3
y
′
−
2
y
=
e
−
π
2
derivative y=x^{2cos(x)}
derivative
y
=
x
2
cos
(
x
)
1
..
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