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人気の高い微分積分問題
(\partial)/(\partial x)(7sqrt(x^2+y^2))
∂
∂
x
(
7
√
x
2
+
y
2
)
tangent f(x)=x^4-5x^2+2,\at x=2
tangent
f
(
x
)
=
x
4
−
5
x
2
+
2
,
at
x
=
2
derivative of 5(e^xcos(x-e^xsin(x)))
d
dx
(
5
(
e
x
cos
(
x
)
−
e
x
sin
(
x
)
)
)
integral of xsqrt(6-x)
∫
x
√
6
−
x
dx
limit as x approaches 3 of (x-1)/(x^2-1)
lim
x
→
3
(
x
−
1
x
2
−
1
)
inverselaplace e^{-2s} 1/(s-9)
inverselaplace
e
−
2
s
1
s
−
9
integral of 1/(sqrt(1+\sqrt{x))}
∫
1
√
1
+
√
x
dx
勾配 (0,-6),(3,-5)
slope
(
0
,
−
6
)
,
(
3
,
−
5
)
derivative y= 6/(\sqrt[4]{x)}
derivative
y
=
6
4
√
x
limit as t approaches 0 of (sin(3t)+4t)/(tsec(t))
lim
t
→
0
(
sin
(
3
t
)
+
4
t
t
sec
(
t
)
)
(\partial)/(\partial y)(5xln(xy))
∂
∂
y
(
5
x
ln
(
xy
)
)
(\partial)/(\partial x)(y^2cos(x))
∂
∂
x
(
y
2
cos
(
x
)
)
(\partial)/(\partial x)(sin(9x+yz))
∂
∂
x
(
sin
(
9
x
+
yz
)
)
derivative of (x^3-2x+4/(x^3))
d
dx
(
x
3
−
2
x
+
4
x
3
)
integral of x(5x-3)^2
∫
x
(
5
x
−
3
)
2
dx
integral of e^{3x}+1/x
∫
e
3
x
+
1
x
dx
derivative of x(dy/(dx))
d
dx
(
x
dy
dx
)
y^'+3y=2e^{-3t}
y
′
+
3
y
=
2
e
−
3
t
derivative f(x)=((sqrt(x)-2))/((2x^2+3))
derivative
f
(
x
)
=
(
√
x
−
2
)
(
2
x
2
+
3
)
integral from 2 to 3 of 1/(x^2-4x)
∫
2
3
1
x
2
−
4
x
dx
derivative 3x^4-5x+2\sqrt[3]{x}
derivative
3
x
4
−
5
x
+
2
3
√
x
derivative of ln(1-6x)
d
dx
(
ln
(
1
−
6
x
)
)
tangent-x^2+3x+4,\at x=1
tangent
−
x
2
+
3
x
+
4
,
at
x
=
1
(dy}{dx}=\frac{-e^x)/8
dy
dx
=
−
e
x
8
(\partial)/(\partial y)(xye^z)
∂
∂
y
(
xye
z
)
derivative cos(7x)
derivative
cos
(
7
x
)
limit as x approaches-1-of {2x^2-5x}
lim
x
→
−
1
−
(
{
2
x
2
−
5
x
}
)
derivative of 3sec^2(pix-1)
d
dx
(
3
sec
2
(
π
x
−
1
)
)
tangent f(x)=(x^2)/(x+1),\at x=2
tangent
f
(
x
)
=
x
2
x
+
1
,
at
x
=
2
integral of 20(e^{3/4 x}-e^{2x})
∫
2
0
(
e
3
4
x
−
e
2
x
)
dx
integral from 4 to infinity of 7e^{-y/2}
∫
4
∞
7
e
−
y
2
dy
(\partial)/(\partial y)(xye^{x+y})
∂
∂
y
(
xye
x
+
y
)
integral of (sin(2x)-sin(3x))^2
∫
(
sin
(
2
x
)
−
sin
(
3
x
)
)
2
dx
tangent f(x)= 5/x ,(3, 5/3)
tangent
f
(
x
)
=
5
x
,
(
3
,
5
3
)
(\partial)/(\partial t)(e^{-2x}cos(9pit))
∂
∂
t
(
e
−
2
x
cos
(
9
π
t
)
)
テイラー 1/2 arctan(2x)
taylor
1
2
arctan
(
2
x
)
sum from n=1 to infinity of 3e^{-4n}
∑
n
=
1
∞
3
e
−
4
n
tangent f(x)= 1/(x^2+4),(1, 1/5)
tangent
f
(
x
)
=
1
x
2
+
4
,
(
1
,
1
5
)
integral of 3e^x-3xe^{x^2}
∫
3
e
x
−
3
xe
x
2
dx
integral of ,^2x
∫
,
2
xdx
derivative of kx+d
d
dx
(
kx
+
d
)
derivative of 2(x-2^2+1)
d
dx
(
2
(
x
−
2
)
2
+
1
)
integral of 1/(2x^3-3x^2)
∫
1
2
x
3
−
3
x
2
dx
derivative x^2(3-x)
derivative
x
2
(
3
−
x
)
derivative cy^{-6}
derivative
cy
−
6
limit as x approaches 1 of x^3-2x^2+x-3
lim
x
→
1
(
x
3
−
2
x
2
+
x
−
3
)
derivative x^6
derivative
x
6
derivative of (90/x)
d
dx
(
9
0
x
)
limit as x approaches infinity of x^2+1
lim
x
→
∞
(
x
2
+
1
)
derivative of 1/3 pix^2y
d
dx
(
1
3
π
x
2
y
)
integral of tan^4(7x)
∫
tan
4
(
7
x
)
dx
(\partial)/(\partial x)(cos(x)sin(x)-xy)
∂
∂
x
(
cos
(
x
)
sin
(
x
)
−
xy
)
(\partial)/(\partial x)(4)
∂
∂
x
(
4
)
derivative ax+b
derivative
ax
+
b
tangent ((3x))/((1+x^2))
tangent
(
3
x
)
(
1
+
x
2
)
integral of tan(5v)sec(5v)
∫
tan
(
5
v
)
sec
(
5
v
)
dv
(dy)/(dt)=20-y/(230+t)
dy
dt
=
2
0
−
y
2
3
0
+
t
inverselaplace 1/((x+3)^2)
inverselaplace
1
(
x
+
3
)
2
integral of tanh(x)
∫
tanh
(
x
)
dx
(\partial)/(\partial z)(xyz^2)
∂
∂
z
(
xyz
2
)
derivative of sin(3x+cos(3x))
d
dx
(
sin
(
3
x
)
+
cos
(
3
x
)
)
integral of 7arccos(x)
∫
7
arccos
(
x
)
dx
integral of 1/(sqrt(x^2+b^2))
∫
1
√
x
2
+
b
2
dx
integral of sqrt(e^{2x)+x}*(e^{2x}+1/2)
∫
√
e
2
x
+
x
·
(
e
2
x
+
1
2
)
dx
derivative f(x)=x^x(ln(x)+1)
derivative
f
(
x
)
=
x
x
(
ln
(
x
)
+
1
)
derivative f(x)=xe^{4x}
derivative
f
(
x
)
=
xe
4
x
(\partial)/(\partial y)(sin(x^2-y^2))
∂
∂
y
(
sin
(
x
2
−
y
2
)
)
derivative cos(e^x)
derivative
cos
(
e
x
)
integral from 1 to infinity of 3^{-x}
∫
1
∞
3
−
x
dx
integral from 0 to 3 of sqrt(5)
∫
0
3
√
5
dx
integral of-ln(1-x)
∫
−
ln
(
1
−
x
)
dx
tangent sqrt(x)+sqrt(y)=sqrt(2)
tangent
√
x
+
√
y
=
√
2
integral of cos^3(x/(18))
∫
cos
3
(
x
1
8
)
dx
integral of (sqrt(5x+1))
∫
(
√
5
x
+
1
)
dx
tangent y=(5x)/(x+2),(3,3)
tangent
y
=
5
x
x
+
2
,
(
3
,
3
)
(\partial)/(\partial x)(1(x-y)e^{y+2x^2})
∂
∂
x
(
1
(
x
−
y
)
e
y
+
2
x
2
)
y+y^{''}=0
y
+
y
′
′
=
0
limit as x approaches 0+of x/(x+|x|)
lim
x
→
0
+
(
x
x
+
|
x
|
)
(\partial)/(\partial x)(z^3-3xyz)
∂
∂
x
(
z
3
−
3
xyz
)
(\partial)/(\partial x)(e^{9xe^y})
∂
∂
x
(
e
9
xe
y
)
(\partial)/(\partial x)(sin^2(3x))
∂
∂
x
(
sin
2
(
3
x
)
)
integral of csc^9(x)
∫
csc
9
(
x
)
dx
limit as x approaches 0 of x^2-3x+3
lim
x
→
0
(
x
2
−
3
x
+
3
)
derivative of (2x/(sqrt(x)))
d
dx
(
2
x
√
x
)
limit as x approaches 0+of 3/x
lim
x
→
0
+
(
3
x
)
integral of x^{27}e^{x^{28}}
∫
x
2
7
e
x
2
8
dx
integral of cos^4(7x+8)
∫
cos
4
(
7
x
+
8
)
dx
integral of ln(10x)
∫
ln
(
1
0
x
)
dx
y^'-4/x y=(y^3)/(x^4)
y
′
−
4
x
y
=
y
3
x
4
integral of 5xe^{5x}
∫
5
xe
5
x
dx
integral of 1/(x^2-14x+68)
∫
1
x
2
−
1
4
x
+
6
8
dx
(dy)/(dx)+(y/x)=7x^3y^2
dy
dx
+
(
y
x
)
=
7
x
3
y
2
(\partial)/(\partial x)(25x^{3/4}y^{1/4})
∂
∂
x
(
2
5
x
3
4
y
1
4
)
integral of-csc^2(x)
∫
−
csc
2
(
x
)
dx
(dy)/(dt)=y
dy
dt
=
y
derivative y=sqrt(2x-1)
derivative
y
=
√
2
x
−
1
tangent 7+2e^x-4x^4x-y=9
tangent
7
+
2
e
x
−
4
x
4
x
−
y
=
9
(\partial)/(\partial x)(x^{2x})
∂
∂
x
(
x
2
x
)
limit as t approaches 1 of (t^3-1)/(t-1)
lim
t
→
1
(
t
3
−
1
t
−
1
)
limit as x approaches+0-of 6/(5x^{1/3)}
lim
x
→
+
0
−
(
6
5
x
1
3
)
1
2
3
4
5
6
7
..
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