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人気の高い微分積分問題
derivative f(x)=x^8e^x
derivative
f
(
x
)
=
x
8
e
x
xy^'+y=e^x,y(1)=5
xy
′
+
y
=
e
x
,
y
(
1
)
=
5
integral from 1 to 5 of sqrt(26)
∫
1
5
√
2
6
dx
テイラー x^2e^x
taylor
x
2
e
x
面積 y=4sqrt(x),y=x
area
y
=
4
√
x
,
y
=
x
derivative of 4+sin(7x)
d
dx
(
4
+
sin
(
7
x
)
)
integral of (1+x)^{1/2}
∫
(
1
+
x
)
1
2
dx
integral of ((x^2-4))/x
∫
(
x
2
−
4
)
x
dx
y^'+y=e^xy^{-2}
y
′
+
y
=
e
x
y
−
2
derivative f(x)=e^{6/x}
derivative
f
(
x
)
=
e
6
x
limit as x approaches 0 of x^2*sin(1/x)
lim
x
→
0
(
x
2
·
sin
(
1
x
)
)
integral of xsin(4x)cos(4x)
∫
x
sin
(
4
x
)
cos
(
4
x
)
dx
integral of 1000xe^{-0.5x}
∫
1
0
0
0
xe
−
0
.
5
x
dx
derivative f(x)= 1/(sqrt(x-1))
derivative
f
(
x
)
=
1
√
x
−
1
derivative of x(3x-9^3)
d
dx
(
x
(
3
x
−
9
)
3
)
integral from 0 to 5 of (2x-1)/(x+1)
∫
0
5
2
x
−
1
x
+
1
dx
integral from 0 to sqrt(2 of)xe^{-x^2}
∫
0
√
2
xe
−
x
2
dx
integral of |x|
∫
|
x
|
dx
(\partial)/(\partial x)(a^x-b^x)
∂
∂
x
(
a
x
−
b
x
)
integral of t^2e^{-22t}
∫
t
2
e
−
2
2
t
dt
integral of sqrt(1-7x^2)
∫
√
1
−
7
x
2
dx
sum from n=2 to infinity of 5/(2^n)
∑
n
=
2
∞
5
2
n
laplace変換する te^{-5t}
laplacetransform
te
−
5
t
derivative 5tln(t)
derivative
5
t
ln
(
t
)
integral from 0 to b of 1/(sqrt(16-x^2))
∫
0
b
1
√
1
6
−
x
2
dx
integral of 2/(\sqrt[3]{x^2)}
∫
2
3
√
x
2
dx
inverseラプラス s/(s^2+2s+1)
inverselaplace
s
s
2
+
2
s
+
1
derivative of cotan(x-tan(x))
d
dx
(
co
tan
(
x
)
−
tan
(
x
)
)
integral of (x^2-2sqrt(x))/x
∫
x
2
−
2
√
x
x
dx
d/(dt)((2sqrt(2))/3 t^{3/2})
d
dt
(
2
√
2
3
t
3
2
)
limit as x approaches 0+of x/x
lim
x
→
0
+
(
x
x
)
f(x)=e^{3x+2}
f
(
x
)
=
e
3
x
+
2
integral of 1/(x(ln(x)-1))
∫
1
x
(
ln
(
x
)
−
1
)
dx
integral of (4-3x)^2
∫
(
4
−
3
x
)
2
dx
integral of 2x^2+7+9/(x^2+1)
∫
2
x
2
+
7
+
9
x
2
+
1
dx
derivative of (ln(x)^3)
d
dx
(
(
ln
(
x
)
)
3
)
(\partial)/(\partial x)(1/(x-b))
∂
∂
x
(
1
x
−
b
)
derivative f(x)=((10-3x)+2)/2
derivative
f
(
x
)
=
(
1
0
−
3
x
)
+
2
2
integral of (x^2)/(x^3+3)
∫
x
2
x
3
+
3
dx
integral of (In(3x))/(2x)
∫
In
(
3
x
)
2
x
dx
(\partial)/(\partial x)(x^2*sin^2(yz))
∂
∂
x
(
x
2
·
sin
2
(
yz
)
)
面積 y=sqrt(x),y=sqrt(x+6),0<x<5
area
y
=
√
x
,
y
=
√
x
+
6
,
0
<
x
<
5
integral from-1/3 to 1/3 of 1/((1-x^2))
∫
−
1
3
1
3
1
(
1
−
x
2
)
dx
(\partial)/(\partial y)(-y/x)
∂
∂
y
(
−
y
x
)
integral from 0 to pi/3 of cos((2x)/3)
∫
0
π
3
cos
(
2
x
3
)
dx
面積 x^2+5x+1,x^3+x^2+x+1
area
x
2
+
5
x
+
1
,
x
3
+
x
2
+
x
+
1
integral of 1/((x-2)^3)
∫
1
(
x
−
2
)
3
dx
integral of x^3(x^4+16)^4
∫
x
3
(
x
4
+
1
6
)
4
dx
derivative of-cot(xcsc(x))
d
dx
(
−
cot
(
x
)
csc
(
x
)
)
limit as x approaches 5 of 2x^2-3x+7
lim
x
→
5
(
2
x
2
−
3
x
+
7
)
f(x)=1+cos(x)
f
(
x
)
=
1
+
cos
(
x
)
(xdx+ydy)/((x^2+y^2)^{3/2)}=0
xdx
+
ydy
(
x
2
+
y
2
)
3
2
=
0
(d^2)/(dx^2)(8/(9t^4))
d
2
dx
2
(
8
9
t
4
)
(\partial)/(\partial x)(x^2+x/t+sin(x))
∂
∂
x
(
x
2
+
x
t
+
sin
(
x
)
)
(dy)/(dx)=18x^5e^{3x^6}
dy
dx
=
1
8
x
5
e
3
x
6
integral of (sin(xy))
∫
(
sin
(
xy
)
)
dy
(d^2x)/(dt^2)+6(dx)/(dt)+8x=5sin(3t)
d
2
x
dt
2
+
6
dx
dt
+
8
x
=
5
sin
(
3
t
)
(d^2)/(dx^2)(x^{9/2}e^x)
d
2
dx
2
(
x
9
2
e
x
)
limit as x approaches infinity of-2(x)
lim
x
→
∞
(
−
2
(
x
)
)
sum from n=1 to infinity of (9n)/(10)
∑
n
=
1
∞
9
n
1
0
勾配 (-10,-3),(4,-3)
slope
(
−
1
0
,
−
3
)
,
(
4
,
−
3
)
integral of e^{9x-14}
∫
e
9
x
−
1
4
dx
derivative g(x)=e^3
derivative
g
(
x
)
=
e
3
(\partial)/(\partial x)(3e^xln(7))
∂
∂
x
(
3
e
x
ln
(
7
)
)
derivative f(x)=4t^{-3/8}
derivative
f
(
x
)
=
4
t
−
3
8
derivative (x^6)/(1-x^5)
derivative
x
6
1
−
x
5
integral of sin(2t)+cos(t)
∫
sin
(
2
t
)
+
cos
(
t
)
dt
integral of sqrt((1+4x^2))
∫
√
(
1
+
4
x
2
)
dx
derivative of (11/(ln(x)))
d
dx
(
1
1
ln
(
x
)
)
x(dy)/(dx)+y=sin(x)
x
dy
dx
+
y
=
sin
(
x
)
tangent f(x)=2x^2-6x+6,\at x=7
tangent
f
(
x
)
=
2
x
2
−
6
x
+
6
,
at
x
=
7
(\partial)/(\partial x)(x*y*ln(x^2+y^2))
∂
∂
x
(
x
·
y
·
ln
(
x
2
+
y
2
)
)
derivative ln(1+e^x)
derivative
ln
(
1
+
e
x
)
tangent (5x)/(x+4)
tangent
5
x
x
+
4
integral of 1/(\sqrt[4]{x)+sqrt(x)}
∫
1
4
√
x
+
√
x
dx
derivative of 3/(tan(x))
d
dx
(
3
tan
(
x
)
)
limit as x approaches 1 of (|x+1|)/(x+1)
lim
x
→
1
(
|
x
+
1
|
x
+
1
)
(\partial)/(\partial y)(ln(x)y)
∂
∂
y
(
ln
(
x
)
y
)
integral of y-1/(y^2)
∫
y
−
1
y
2
dy
laplace変換する 2t^4
laplacetransform
2
t
4
derivative of ln((xe^{-2x}^{1/3}))
d
dx
(
ln
(
(
xe
−
2
x
)
1
3
)
)
y=g(3x)h(2x)
y
=
g
(
3
x
)
h
(
2
x
)
integral of sqrt(x^2+a^2)
∫
√
x
2
+
a
2
dx
limit as x approaches 0 of (2(5x+1))/5
lim
x
→
0
(
2
(
5
x
+
1
)
5
)
sum from n=1 to infinity of 4/(3^n)
∑
n
=
1
∞
4
3
n
integral from 6 to 8 of 8/((x-6)^3)
∫
6
8
8
(
x
−
6
)
3
dx
limit as x approaches-7 of 2x^2-6x
lim
x
→
−
7
(
2
x
2
−
6
x
)
derivative (x+9)(7sqrt(x)+2)
derivative
(
x
+
9
)
(
7
√
x
+
2
)
tangent f(x)=sqrt(3x),(3,3)
tangent
f
(
x
)
=
√
3
x
,
(
3
,
3
)
inverseラプラス (2s+2)/(s^2+4s+5)
inverselaplace
2
s
+
2
s
2
+
4
s
+
5
integral of 1/(2+3x^2)
∫
1
2
+
3
x
2
dx
integral of ln(((1+x))/(1-x))
∫
ln
(
(
1
+
x
)
1
−
x
)
dx
(d^2)/(dx^2)(2sec(x))
d
2
dx
2
(
2
sec
(
x
)
)
derivative f(x)=(4x)/(x^2+1)
derivative
f
(
x
)
=
4
x
x
2
+
1
derivative of (3x-5^2)
d
dx
(
(
3
x
−
5
)
2
)
limit as x approaches 0 of 5/(x^2+x)-5/x
lim
x
→
0
(
5
x
2
+
x
−
5
x
)
テイラー 1/(2-x),0
taylor
1
2
−
x
,
0
derivative of (4x^2/(x^2-1))
d
dx
(
4
x
2
x
2
−
1
)
tangent x^3+7x-6
tangent
x
3
+
7
x
−
6
derivative sqrt(3x)
derivative
√
3
x
1
..
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1044
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1046
1047
..
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