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일반적인 미적분학 문제
derivative of (1+cos^2(x)^8)
d
dx
(
(
1
+
cos
2
(
x
)
)
8
)
integral of ((7x+3)/(sqrt(x)))
∫
(
7
x
+
3
√
x
)
dx
(\partial)/(\partial x)(ln(x)-1)
∂
∂
x
(
ln
(
x
)
−
1
)
integral of sec(x)-cos(x)
∫
sec
(
x
)
−
cos
(
x
)
dx
경사지 (4,-7),(8,-7)
slope
(
4
,
−
7
)
,
(
8
,
−
7
)
f(x)=xln(x)-x
f
(
x
)
=
x
ln
(
x
)
−
x
derivative 1/2 ln(x)
derivative
1
2
ln
(
x
)
derivative f(x)= 1/((x+2)^2)
derivative
f
(
x
)
=
1
(
x
+
2
)
2
derivative of x^2-2x-15
d
dx
(
x
2
−
2
x
−
1
5
)
inverse라플라스 (1-e^{-2s})/s
inverselaplace
1
−
e
−
2
s
s
limit as x approaches-infinity of 1-x^3
lim
x
→
−
∞
(
1
−
x
3
)
integral of xln(sqrt(11)x)
∫
x
ln
(
√
1
1
x
)
dx
limit as x approaches (3pi)/2 of sin(x)
lim
x
→
3
π
2
(
sin
(
x
)
)
integral of \sqrt[x]{2}
∫
x
√
2
dx
derivative f(y)=ln(5x^2-x+1)
derivative
f
(
y
)
=
ln
(
5
x
2
−
x
+
1
)
limit as x approaches infinity of 2x^2-x
lim
x
→
∞
(
2
x
2
−
x
)
integral of (7+t+t^2)/(sqrt(t))
∫
7
+
t
+
t
2
√
t
dt
integral of v/(3-0.001v^2)
∫
v
3
−
0
.
0
0
1
v
2
dv
limit as x approaches infinity of ((xe^{2x}))/2
lim
x
→
∞
(
(
xe
2
x
)
2
)
(\partial)/(\partial x)(y+arctan(y/x))
∂
∂
x
(
y
+
arctan
(
y
x
)
)
(\partial)/(\partial y)(x^3-y^2)
∂
∂
y
(
x
3
−
y
2
)
테일러 ln(6x+1)
taylor
ln
(
6
x
+
1
)
limit as x approaches infinity of (e^{5x-3})/(ln(x-2))
lim
x
→
∞
(
e
5
x
−
3
ln
(
x
−
2
)
)
derivative f(x)=cos(a^8+x^8)
derivative
f
(
x
)
=
cos
(
a
8
+
x
8
)
derivative x^3sqrt(x)
derivative
x
3
√
x
integral from 0 to infinity of x^1e^{-x}
∫
0
∞
x
1
e
−
x
dx
(\partial)/(\partial y)(3x^2y+y^2)
∂
∂
y
(
3
x
2
y
+
y
2
)
derivative of ln((5x^2+9^3))
d
dx
(
ln
(
(
5
x
2
+
9
)
3
)
)
integral of (sqrt(sin(2x))-cos(2x))^2
∫
(
√
sin
(
2
x
)
−
cos
(
2
x
)
)
2
dx
4x(dy)/(dx)+y=x^3
4
x
dy
dx
+
y
=
x
3
(\partial)/(\partial x)(e^{6xe^y})
∂
∂
x
(
e
6
xe
y
)
(dy)/(dt)=-2ty^2
dy
dt
=
−
2
ty
2
integral from 0 to 2 of x^2e^{x^3+0}
∫
0
2
x
2
e
x
3
+
0
dx
derivative of (sqrt(3x)/4)
d
dx
(
√
3
x
4
)
derivative 7/(3x^2)
derivative
7
3
x
2
(\partial)/(\partial x)(sin^3(2x))
∂
∂
x
(
sin
3
(
2
x
)
)
derivative h(t)=(7t^2+t)^{-3}
derivative
h
(
t
)
=
(
7
t
2
+
t
)
−
3
y^'=2y+x^2+5
y
′
=
2
y
+
x
2
+
5
integral from 0 to pi of 3xsin(x)
∫
0
π
3
x
sin
(
x
)
dx
derivative of 3sec(6x)
d
dx
(
3
sec
(
6
x
)
)
inverse라플라스 (10)/(s(s+2)^2)
inverselaplace
1
0
s
(
s
+
2
)
2
integral from 0 to pi/2 of 3sin^2(2x)
∫
0
π
2
3
sin
2
(
2
x
)
dx
derivative f(x)=3x^2-x
derivative
f
(
x
)
=
3
x
2
−
x
derivative f(x)=18
derivative
f
(
x
)
=
1
8
y^'=(xy^3)/4 ,y(0)=6
y
′
=
xy
3
4
,
y
(
0
)
=
6
inverse라플라스 s/(s^4+4)
inverselaplace
s
s
4
+
4
integral of (2x^4+4x^3-x)/(x^3)
∫
2
x
4
+
4
x
3
−
x
x
3
dx
integral of 6^xe^x
∫
6
x
e
x
dx
integral of x/((x^2+1)^{17/2)}
∫
x
(
x
2
+
1
)
1
7
2
dx
y^'+y=-4cos(x)
y
′
+
y
=
−
4
cos
(
x
)
limit as x approaches infinity of 1^x
lim
x
→
∞
(
1
x
)
derivative (7x^6+4x^3)^4
derivative
(
7
x
6
+
4
x
3
)
4
integral of (sin(x)cos(x))/(5+sin(x))
∫
sin
(
x
)
cos
(
x
)
5
+
sin
(
x
)
dx
y^{''}+2y^'=e^t,y(0)=1,y^'(0)=2
y
′
′
+
2
y
′
=
e
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
x^2(dy)/(dx)=y(1-x)
x
2
dy
dx
=
y
(
1
−
x
)
integral of (e^{1-x}+1/(x^{2022)})x
∫
(
e
1
−
x
+
1
x
2
0
2
2
)
xdx
derivative of 20cos(x)
d
dx
(
2
0
cos
(
x
)
)
(\partial)/(\partial x)(5x^2+y^2)
∂
∂
x
(
5
x
2
+
y
2
)
tangent-6sqrt(x),\at x=4
tangent
−
6
√
x
,
at
x
=
4
integral of ysin(x)y
∫
y
sin
(
x
)
ydx
integral of (e^x)/(e^{3x)-2e^{2x}+e^x-2}
∫
e
x
e
3
x
−
2
e
2
x
+
e
x
−
2
dx
(\partial)/(\partial y)(6xy^2)
∂
∂
y
(
6
xy
2
)
integral of 4xln(7x)
∫
4
x
ln
(
7
x
)
dx
(\partial)/(\partial x)(ln(2x+y+1))
∂
∂
x
(
ln
(
2
x
+
y
+
1
)
)
y^'+3y=8x,y(0)=4
y
′
+
3
y
=
8
x
,
y
(
0
)
=
4
tangent f(x)=1-9x^2,\at x=3
tangent
f
(
x
)
=
1
−
9
x
2
,
at
x
=
3
sum from n=0 to infinity of (-5/4)^n
∑
n
=
0
∞
(
−
5
4
)
n
(dv)/(dt)=9.8-0.6
dv
dt
=
9
.
8
−
0
.
6
derivative of x-1/2
d
dx
(
x
−
1
2
)
derivative of (2-x^3/(2+x^3))
d
dx
(
2
−
x
3
2
+
x
3
)
integral from 1 to 4 of 2pix(-3/2 x+6)
∫
1
4
2
π
x
(
−
3
2
x
+
6
)
dx
derivative f(x)=x^3(2x-1)
derivative
f
(
x
)
=
x
3
(
2
x
−
1
)
limit as x approaches 0+of (sin(x))/(x^{1/2)}
lim
x
→
0
+
(
sin
(
x
)
x
1
2
)
y^'=y(xy^6+4)
y
′
=
y
(
xy
6
+
4
)
integral from-infinity to 0 of x^2e^{-x}
∫
−
∞
0
x
2
e
−
x
dx
derivative of (1-xe^x)
d
dx
(
(
1
−
x
)
e
x
)
inverse라플라스 3/((s^2+9)(s^2+1))
inverselaplace
3
(
s
2
+
9
)
(
s
2
+
1
)
derivative of sqrt(2-x^2)-x
d
dx
(
√
2
−
x
2
−
x
)
지역 2y=3sqrt(x),2y+3x=6,y=4
area
2
y
=
3
√
x
,
2
y
+
3
x
=
6
,
y
=
4
integral from pi/2 to pi of cos(x)
∫
π
2
π
cos
(
x
)
dx
integral of 1/(e^x+4e^{-x)}
∫
1
e
x
+
4
e
−
x
dx
integral from 1 to 3 of 2pix(-x^2+4x-3)
∫
1
3
2
π
x
(
−
x
2
+
4
x
−
3
)
dx
derivative y=x^{3/2}(x+ce^x)
derivative
y
=
x
3
2
(
x
+
ce
x
)
integral of 10-(14-2(16-2x)^{1/2})
∫
1
0
−
(
1
4
−
2
(
1
6
−
2
x
)
1
2
)
dx
integral of 8x^9e^{-x^5}
∫
8
x
9
e
−
x
5
dx
integral of x^4-8x^2+16
∫
x
4
−
8
x
2
+
1
6
dx
derivative f(x)=sqrt(3)x+sqrt(2x)
derivative
f
(
x
)
=
√
3
x
+
√
2
x
limit as x approaches-3 of x/((x+3)^4)
lim
x
→
−
3
(
x
(
x
+
3
)
4
)
tangent x^4+2/x ,\at x=1
tangent
x
4
+
2
x
,
at
x
=
1
y^{''}-ky=kxe^{-x}
y
′
′
−
ky
=
kxe
−
x
derivative f(x)=(2x-1)/(sqrt(x))
derivative
f
(
x
)
=
2
x
−
1
√
x
derivative of 4sqrt(2)
d
dx
(
4
√
2
)
y^{''}+9y=e^t,y(0)=0,y^'(0)=0
y
′
′
+
9
y
=
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
integral of e^{(3x+1)}
∫
e
(
3
x
+
1
)
dx
limit as x approaches 27 of (x-27)/(sqrt(x+9-6))
lim
x
→
2
7
(
x
−
2
7
√
x
+
9
−
6
)
(\partial)/(\partial x)(3e^{5xy})
∂
∂
x
(
3
e
5
xy
)
inverse라플라스 2/(s(s+1)(s+2)(s+3))
inverselaplace
2
s
(
s
+
1
)
(
s
+
2
)
(
s
+
3
)
limit as x approaches infinity of-2x-1
lim
x
→
∞
(
−
2
x
−
1
)
지역 4x,x^2
area
4
x
,
x
2
integral of (2y+1)
∫
(
2
y
+
1
)
dy
1
..
1378
1379
1380
1381
1382
..
2459