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일반적인 미적분학 문제
limit as x approaches 4 of-(x/(x-4))
lim
x
→
4
(
−
(
x
x
−
4
)
)
derivative x^4a^5+y^3a+z^6
derivative
x
4
a
5
+
y
3
a
+
z
6
derivative f(x)=e^x-1
derivative
f
(
x
)
=
e
x
−
1
limit as x approaches 1 of 3x^3-5x^2+x+4
lim
x
→
1
(
3
x
3
−
5
x
2
+
x
+
4
)
derivative sin(x^2)+(1-x)/(1+x)
derivative
sin
(
x
2
)
+
1
−
x
1
+
x
integral of 4y
∫
4
ydy
(dy)/(dt)=2y-3e^{-t},y(0)=1
dy
dt
=
2
y
−
3
e
−
t
,
y
(
0
)
=
1
y^{''}+y=xcos^3(x)
y
′
′
+
y
=
x
cos
3
(
x
)
derivative sin^2(7x)
derivative
sin
2
(
7
x
)
integral of cos(x)sqrt(25-sin^2(x))
∫
cos
(
x
)
√
2
5
−
sin
2
(
x
)
dx
derivative f(t)=(9t+2)^{2/3}
derivative
f
(
t
)
=
(
9
t
+
2
)
2
3
integral of 19θsec^2(θ)
∫
1
9
θ
sec
2
(
θ
)
d
θ
limit as x approaches 0+of tan^{x^2}(x)
lim
x
→
0
+
(
tan
x
2
(
x
)
)
derivative tan(6x)
derivative
tan
(
6
x
)
derivative 1/(x+3)
derivative
1
x
+
3
limit as x approaches 0 of (sin(7x))/(tan(x))
lim
x
→
0
(
sin
(
7
x
)
tan
(
x
)
)
integral of (2x^2+x-8)/(x^3-4x)
∫
2
x
2
+
x
−
8
x
3
−
4
x
dx
(2x-1)y^'+y^2=0
(
2
x
−
1
)
y
′
+
y
2
=
0
y^{''}+9y^'+14y=0,y(0)=1,y^'(0)=0
y
′
′
+
9
y
′
+
1
4
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
derivative x^2+5
derivative
x
2
+
5
(d^2y)/(dt^2)+5(dy)/(dt)=e^{-t}
d
2
y
dt
2
+
5
dy
dt
=
e
−
t
5y^{''}+35y=0
5
y
′
′
+
3
5
y
=
0
limit as x approaches 4+of 1
lim
x
→
4
+
(
1
)
integral of (sqrt(1+x))/(x^2)
∫
√
1
+
x
x
2
dx
derivative of \sqrt[3]{9x+1}
d
dx
(
3
√
9
x
+
1
)
-6*x^2*y+(dy)/(dx)=5x^2
−
6
·
x
2
·
y
+
dy
dx
=
5
x
2
(\partial)/(\partial x)(3x^4+5y^4+9xy)
∂
∂
x
(
3
x
4
+
5
y
4
+
9
xy
)
y^{''}-5y^'+6y=e^x
y
′
′
−
5
y
′
+
6
y
=
e
x
integral of ((x^2))/2
∫
(
x
2
)
2
dx
derivative ((x^2+4)/(x^2-4))^3
derivative
(
x
2
+
4
x
2
−
4
)
3
integral of (8x-3)/(sqrt(12x-4x^2-5))
∫
8
x
−
3
√
1
2
x
−
4
x
2
−
5
dx
d/(dX)((8X^2+2X+8)/(sqrt(X)))
d
dX
(
8
X
2
+
2
X
+
8
√
X
)
laplace변환 (t-5)/5
laplacetransform
t
−
5
5
integral of sin^3(11x)
∫
sin
3
(
1
1
x
)
dx
integral from-3 to 3 of (9-x^2)
∫
−
3
3
(
9
−
x
2
)
dx
derivative pi/2
derivative
π
2
integral of (3+4x)/(sqrt(7+3x+2x^2))
∫
3
+
4
x
√
7
+
3
x
+
2
x
2
dx
limit as x approaches-2 of (x+2)/(x^2-4)
lim
x
→
−
2
(
x
+
2
x
2
−
4
)
limit as x approaches 3 of-(3-x)
lim
x
→
3
(
−
(
3
−
x
)
)
derivative f(x)=-2x^2-20x-48
derivative
f
(
x
)
=
−
2
x
2
−
2
0
x
−
4
8
tangent f(x)=-4cos(x),\at x= pi/2
tangent
f
(
x
)
=
−
4
cos
(
x
)
,
at
x
=
π
2
integral of x^2e^2x
∫
x
2
e
2
xdx
integral of (x^2-1)e^x
∫
(
x
2
−
1
)
e
x
dx
(\partial)/(\partial x)(3x^2+9y^2-xy+x)
∂
∂
x
(
3
x
2
+
9
y
2
−
xy
+
x
)
integral of (x^3+5x^4-7x)/(x^2)
∫
x
3
+
5
x
4
−
7
x
x
2
dx
integral from 1 to 2 of sqrt(5x-1)
∫
1
2
√
5
x
−
1
dx
integral from-infinity to 3 of 1/(x^2+9)
∫
−
∞
3
1
x
2
+
9
dx
(\partial)/(\partial y)((6x)/(3x^2-y^3-3))
∂
∂
y
(
6
x
3
x
2
−
y
3
−
3
)
derivative of (x-1^2*(x-2)*(x-4))
d
dx
(
(
x
−
1
)
2
·
(
x
−
2
)
·
(
x
−
4
)
)
tangent x^7-3x^4+7x^3+43,\at x=-2
tangent
x
7
−
3
x
4
+
7
x
3
+
4
3
,
at
x
=
−
2
integral of 1/(xsqrt(1+\sqrt{x))}
∫
1
x
√
1
+
√
x
dx
limit as x approaches 0 of 3-4x
lim
x
→
0
(
3
−
4
x
)
integral of sqrt(x^2+81)
∫
√
x
2
+
8
1
dx
limit as x approaches 0 of \sqrt[3]{x}
lim
x
→
0
(
3
√
x
)
경사지 y=2x^2+7x,(-1,-5)
slope
y
=
2
x
2
+
7
x
,
(
−
1
,
−
5
)
(dy)/(dt)=2y+sin(2t)
dy
dt
=
2
y
+
sin
(
2
t
)
(dy}{dx}=\frac{2xsec(y/x)+y)/x
dy
dx
=
2
x
sec
(
y
x
)
+
y
x
derivative of 6\sqrt[3]{x^2}+1
d
dx
(
6
3
√
x
2
+
1
)
(dy)/(dt)+y=cos(t)
dy
dt
+
y
=
cos
(
t
)
limit as x approaches 0 of (x|x|)/x
lim
x
→
0
(
x
|
x
|
x
)
integral of 1/(x^2+7x-6)
∫
1
x
2
+
7
x
−
6
dx
integral of (xcos(x))
∫
(
x
cos
(
x
)
)
dx
integral of (sin(y))/(2-cos(y))
∫
sin
(
y
)
2
−
cos
(
y
)
dy
integral of (x^2)/(sqrt(5+x^2))
∫
x
2
√
5
+
x
2
dx
integral from 0 to 3 of x^3
∫
0
3
x
3
dx
limit as x approaches 2 of sqrt(2-x)-2
lim
x
→
2
(
√
2
−
x
−
2
)
derivative f(x)=0.4x^{1.6}
derivative
f
(
x
)
=
0
.
4
x
1
.
6
((x-2ln(x)-1)/(x-1))^'
(
x
−
2
ln
(
x
)
−
1
x
−
1
)
′
integral of (x^3+e^{3x})
∫
(
x
3
+
e
3
x
)
dx
(\partial)/(\partial x)(4x^3-5xy+y^2)
∂
∂
x
(
4
x
3
−
5
xy
+
y
2
)
derivative y=-1/(x^2)
derivative
y
=
−
1
x
2
derivative of x^7e^{4x}
d
dx
(
x
7
e
4
x
)
integral of x^5sin(x^6)
∫
x
5
sin
(
x
6
)
dx
derivative of 3/(((56(2x-1)^7))-1/(((24)(2x-1)^6))-1/(((40(2x-1)^5))))
d
dx
(
3
(
(
5
6
)
(
2
x
−
1
)
7
)
−
1
(
(
2
4
)
(
2
x
−
1
)
6
)
−
1
(
(
4
0
(
2
x
−
1
)
5
)
)
)
derivative of 1/(x+y^2)
d
dx
(
1
x
+
y
2
)
y^'=2x+3y-1
y
′
=
2
x
+
3
y
−
1
derivative of 1/(sqrt(2x+1))
d
dx
(
1
√
2
x
+
1
)
derivative f(t)=9tsin(pit)
derivative
f
(
t
)
=
9
t
sin
(
π
t
)
(\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2})
∂
∂
x
(
1
0
0
0
e
−
x
2
−
2
y
2
−
z
2
)
integral of (cos(ln(9x)))/x
∫
cos
(
ln
(
9
x
)
)
x
dx
integral of (3x-2)^{-11}
∫
(
3
x
−
2
)
−
1
1
dx
sum from n=1 to infinity of 2/(n(n+3))
∑
n
=
1
∞
2
n
(
n
+
3
)
limit as x approaches 5 of 4x-3x^2
lim
x
→
5
(
4
x
−
3
x
2
)
limit as x approaches 5 of x^2+2x-35
lim
x
→
5
(
x
2
+
2
x
−
3
5
)
derivative y=3csc^2(5x)^3
derivative
y
=
3
csc
2
(
5
x
)
3
tangent f(x)=x^3+3x^2-45x-19
tangent
f
(
x
)
=
x
3
+
3
x
2
−
4
5
x
−
1
9
tangent y=x^3-2x+2(3.23)
tangent
y
=
x
3
−
2
x
+
2
(
3
.
2
3
)
derivative \sqrt[3]{x^2}
derivative
3
√
x
2
derivative of 1/(2sqrt(x)+1/(7x^{6/7)})
d
dx
(
1
2
√
x
+
1
7
x
6
7
)
(\partial)/(\partial x)(ln(4ye^{xy}))
∂
∂
x
(
ln
(
4
ye
xy
)
)
limit as x approaches 3+of (x-3)/(x^2-9)
lim
x
→
3
+
(
x
−
3
x
2
−
9
)
derivative of 4x^3-5x^2+3x-5
d
dx
(
4
x
3
−
5
x
2
+
3
x
−
5
)
derivative 4excos(x)
derivative
4
ex
cos
(
x
)
derivative of arctan(2x-1)
d
dx
(
arctan
(
2
x
−
1
)
)
xy^'+36y= 1/x
xy
′
+
3
6
y
=
1
x
지역 sin(x),cos(x),[0, pi/4 ]
area
sin
(
x
)
,
cos
(
x
)
,
[
0
,
π
4
]
derivative of (2x^2-2^{-1})
d
dx
(
(
2
x
2
−
2
)
−
1
)
derivative of tan(x/3)
d
dx
(
tan
(
x
3
)
)
integral of sqrt(5)
∫
√
5
dx
derivative f(x)=(sqrt(x))/(x+1)
derivative
f
(
x
)
=
√
x
x
+
1
1
..
1412
1413
1414
1415
1416
..
2459