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일반적인 미적분학 문제
derivative y^{4/5}
derivative
y
4
5
limit as x approaches 1-of (2x)/(x^3-1)
lim
x
→
1
−
(
2
x
x
3
−
1
)
derivative of (x^4+8^{1/2})
d
dx
(
(
x
4
+
8
)
1
2
)
(\partial)/(\partial x)(y^{1/3})
∂
∂
x
(
y
1
3
)
derivative of (x^2-1^2)
d
dx
(
(
x
2
−
1
)
2
)
derivative y= 5/((4x)^{-2)}
derivative
y
=
5
(
4
x
)
−
2
(\partial)/(\partial x)(sec(y))
∂
∂
x
(
sec
(
y
)
)
integral of e^{2x}cos(x/4)
∫
e
2
x
cos
(
x
4
)
dx
derivative of x/(2+x)
d
dx
(
x
2
+
x
)
1/((y^2-3y+2))y^'= 1/x
1
(
y
2
−
3
y
+
2
)
y
′
=
1
x
limit as x approaches 3 of x-10
lim
x
→
3
(
x
−
1
0
)
limit as x approaches-a of f(x)
lim
x
→
−
a
(
f
(
x
)
)
(dy}{dx}+\frac{3y)/x =-1/x
dy
dx
+
3
y
x
=
−
1
x
integral of cos^4(x)sin(x
∫
cos
4
(
x
)
sin
(
d
)
xdx
integral of 1/(x^{3/2)}
∫
1
x
3
2
dx
(d^2y)/(dx^2)+2(dy)/(dx)-3y=0
d
2
y
dx
2
+
2
dy
dx
−
3
y
=
0
inverse라플라스 (5(s+2)^2)/(s(s+1)^3)
inverselaplace
5
(
s
+
2
)
2
s
(
s
+
1
)
3
integral of (-25sin(5x-pi/2))
∫
(
−
2
5
sin
(
5
x
−
π
2
)
)
dx
integral of 4/((1+x^2))
∫
4
(
1
+
x
2
)
dx
tangent f(x)=(x-3)^2-2,\at x=0
tangent
f
(
x
)
=
(
x
−
3
)
2
−
2
,
at
x
=
0
1/x y^'= y/(x^2)-1/y
1
x
y
′
=
y
x
2
−
1
y
(\partial)/(\partial y)(y^3+x^2y-3y)
∂
∂
y
(
y
3
+
x
2
y
−
3
y
)
sum from n=1 to infinity of 1/(nln(n))
∑
n
=
1
∞
1
n
ln
(
n
)
integral of (cos(θ))/(9-sin^2(θ))
∫
cos
(
θ
)
9
−
sin
2
(
θ
)
d
θ
derivative of y/(x^2+y^2)
d
dx
(
y
x
2
+
y
2
)
tangent f(x)=5x^3-5x,\at x=-1
tangent
f
(
x
)
=
5
x
3
−
5
x
,
at
x
=
−
1
derivative of cos^{n-1}(x)
d
dx
(
cos
n
−
1
(
x
)
)
derivative y=x^4-4x^3+10
derivative
y
=
x
4
−
4
x
3
+
1
0
지역 2x,x|x+2|
area
2
x
,
x
|
x
+
2
|
(dy)/(dx)+3y=10,y(0)=20
dy
dx
+
3
y
=
1
0
,
y
(
0
)
=
2
0
지역 xy=24,2x^2-y^2+4=0
area
xy
=
2
4
,
2
x
2
−
y
2
+
4
=
0
(dy)/(dx)=(x^2)/(10y)-(2x)/(5y)
dy
dx
=
x
2
1
0
y
−
2
x
5
y
derivative 4/3 pir^3
derivative
4
3
π
r
3
derivative (s-sqrt(s))/(s^2)
derivative
s
−
√
s
s
2
지역 y=3-x^2,y=-1
area
y
=
3
−
x
2
,
y
=
−
1
integral from a to b of 1/(r^2)
∫
a
b
1
r
2
dr
(\partial)/(\partial x)(e^xsin(2y))
∂
∂
x
(
e
x
sin
(
2
y
)
)
integral of (2x+4)/(sqrt(x))
∫
2
x
+
4
√
x
dx
limit as x approaches-3 of ((x+3))/(x-3)
lim
x
→
−
3
(
(
x
+
3
)
x
−
3
)
integral of \sqrt[5]{(3-4x)^3}
∫
5
√
(
3
−
4
x
)
3
dx
limit as x approaches 8 of \sqrt[3]{x}-2
lim
x
→
8
(
3
√
x
−
2
)
integral of 3^xcos(x)
∫
3
x
cos
(
x
)
dx
limit as x approaches infinity of xe^{1/x}
lim
x
→
∞
(
xe
1
x
)
integral of cos(y)sin(x)
∫
cos
(
y
)
sin
(
x
)
dx
integral of xsqrt(3x^2+1)
∫
x
√
3
x
2
+
1
dx
limit as x approaches 0 of (sin(9x))/x
lim
x
→
0
(
sin
(
9
x
)
x
)
(2xy+3y^2)dx-(2xy+x^2)dy=0
(
2
xy
+
3
y
2
)
dx
−
(
2
xy
+
x
2
)
dy
=
0
integral of 1/((x^2+z^2)^{3/2)}
∫
1
(
x
2
+
z
2
)
3
2
dx
integral of (10x-17)/(sqrt(x^2-6x-55))
∫
1
0
x
−
1
7
√
x
2
−
6
x
−
5
5
dx
integral of tan^4(4x)
∫
tan
4
(
4
x
)
dx
derivative \sqrt[6]{x}^{ln(x)}
derivative
6
√
x
ln
(
x
)
integral from 1 to 9 of pi(x-1)
∫
1
9
π
(
x
−
1
)
dx
derivative of (arccos(x)^2)
d
dx
(
(
arccos
(
x
)
)
2
)
tangent f(x)= 5/x ,(5,1)
tangent
f
(
x
)
=
5
x
,
(
5
,
1
)
derivative ((x-1))/(x^2+3)
derivative
(
x
−
1
)
x
2
+
3
integral of 1/((9-x^2)^{3/2)}
∫
1
(
9
−
x
2
)
3
2
dx
integral from 0 to 2 of xe^{-5x}
∫
0
2
xe
−
5
x
dx
integral of (x+5)/(x^2+11x+18)
∫
x
+
5
x
2
+
1
1
x
+
1
8
dx
integral of xycos(z)
∫
xy
cos
(
z
)
dz
integral from 1 to 2 of ((x-1)^3)/(x^2)
∫
1
2
(
x
−
1
)
3
x
2
dx
(\partial)/(\partial x)(-xy)
∂
∂
x
(
−
xy
)
integral of (2x)/((x^2+4)ln(x^2+4))
∫
2
x
(
x
2
+
4
)
ln
(
x
2
+
4
)
dx
integral of t/(9+t^4)
∫
t
9
+
t
4
dt
(dy)/(dx)=(1-x)y^2,y(0)=-1/12
dy
dx
=
(
1
−
x
)
y
2
,
y
(
0
)
=
−
1
1
2
integral of cos^3(xsi)n^3x
∫
cos
3
(
xsi
)
n
3
xdx
integral of 4x(x^2+27000)^{-2/3}
∫
4
x
(
x
2
+
2
7
0
0
0
)
−
2
3
dx
(dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x}
dy
dx
−
2
e
3
x
−
2
0
e
2
x
=
e
3
x
integral of 1/(xsqrt(1+16x^2))
∫
1
x
√
1
+
1
6
x
2
dx
derivative of e^x(7-sqrt(x))
d
dx
(
e
x
(
7
−
√
x
)
)
integral of 1/((2-5t)^2)
∫
1
(
2
−
5
t
)
2
dt
integral of (ln(y))/(sqrt(y))
∫
ln
(
y
)
√
y
dy
integral of (4t^3+8)t^2
∫
(
4
t
3
+
8
)
t
2
dt
derivative of (2x+1/(4x-1))
d
dx
(
2
x
+
1
4
x
−
1
)
integral of ((2x))/(x^2+1)
∫
(
2
x
)
x
2
+
1
dx
integral of sin(6)
∫
sin
(
6
)
(\partial)/(\partial u)(sin(u)cos(v))
∂
∂
u
(
sin
(
u
)
cos
(
v
)
)
(dy)/(dx)=e^ysin(x)
dy
dx
=
e
y
sin
(
x
)
derivative of (x^2/(6+sqrt(x)))
d
dx
(
x
2
6
+
√
x
)
tangent f(x)= 1/(x+2),\at x=3
tangent
f
(
x
)
=
1
x
+
2
,
at
x
=
3
(\partial)/(\partial x)(1/(1-x^4))
∂
∂
x
(
1
1
−
x
4
)
(3+x)dx=(e^t-e^{-t})dt
(
3
+
x
)
dx
=
(
e
t
−
e
−
t
)
dt
integral of (x^{1.1}+9x^{3.5})
∫
(
x
1
.
1
+
9
x
3
.
5
)
dx
integral of 2x^2cos(x)
∫
2
x
2
cos
(
x
)
dx
derivative of 4arctan(2x)
d
dx
(
4
arctan
(
2
x
)
)
(dy)/(dx)=(x-2)/(y+1)
dy
dx
=
x
−
2
y
+
1
integral of x/(5^{x^2)}
∫
x
5
x
2
dx
integral from 0 to 1 of arctan(1)
∫
0
1
arctan
(
1
)
dx
derivative of e^{sin(x}-1)
d
dx
(
e
sin
(
x
)
−
1
)
integral from 3 to sqrt(13 of)x
∫
3
√
1
3
xdx
integral of sin^5(x)cos^5(x)
∫
sin
5
(
x
)
cos
5
(
x
)
dx
limit as x approaches-9-of sqrt(x^2-81)
lim
x
→
−
9
−
(
√
x
2
−
8
1
)
integral of 2x^2cos(mx)
∫
2
x
2
cos
(
mx
)
dx
limit as x approaches-3 of 4x^2+2x-1
lim
x
→
−
3
(
4
x
2
+
2
x
−
1
)
integral of sin^6(pix)
∫
sin
6
(
π
x
)
dx
sum from n=7 to infinity of 1/(6^n)
∑
n
=
7
∞
1
6
n
limit as x approaches 0 of (1/(x-1)-1)/x
lim
x
→
0
(
1
x
−
1
−
1
x
)
integral from 0 to 20 of xsqrt(20-x)
∫
0
2
0
x
√
2
0
−
x
dx
integral of (e^x)/4
∫
e
x
4
dx
tangent f(x)= 2/x ,(5, 2/5)
tangent
f
(
x
)
=
2
x
,
(
5
,
2
5
)
y^{''}+12y^'+35y=0
y
′
′
+
1
2
y
′
+
3
5
y
=
0
1
..
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