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일반적인 미적분학 문제
d/(dt)(1/6 t^3)
d
dt
(
1
6
t
3
)
integral of (xsqrt(x^2+3))
∫
(
x
√
x
2
+
3
)
dx
y^{''}+36y=-60sec(6t)
y
′
′
+
3
6
y
=
−
6
0
sec
(
6
t
)
integral of 12(y^4+4y^2+8)^2(y^3+2y)
∫
1
2
(
y
4
+
4
y
2
+
8
)
2
(
y
3
+
2
y
)
dy
integral of x-10
∫
x
−
1
0
dx
integral of sec^5(θ)
∫
sec
5
(
θ
)
d
θ
derivative C(x)=-0.01x^2+7.2x-163
derivative
C
(
x
)
=
−
0
.
0
1
x
2
+
7
.
2
x
−
1
6
3
integral of sin(-4x)
∫
sin
(
−
4
x
)
dx
integral of 6x+3
∫
6
x
+
3
dx
integral of 1-x
∫
1
−
xdx
derivative (x-1)^4
derivative
(
x
−
1
)
4
integral of sec^4(xta)n^5x
∫
sec
4
(
xta
)
n
5
xdx
sum from n=1 to infinity of 4/(n(n+7))
∑
n
=
1
∞
4
n
(
n
+
7
)
sum from n=2 to infinity of n/(n+2)
∑
n
=
2
∞
n
n
+
2
derivative f(x)=(x^2+3x-2)/(x^2-5x+6)
derivative
f
(
x
)
=
x
2
+
3
x
−
2
x
2
−
5
x
+
6
derivative f(x)=e^x-x^3
derivative
f
(
x
)
=
e
x
−
x
3
y^{''}+12y^'+36y=0,y(1)=0,y^'(1)=-1
y
′
′
+
1
2
y
′
+
3
6
y
=
0
,
y
(
1
)
=
0
,
y
′
(
1
)
=
−
1
y^'=((x-y))/((x+2y)),y(0)=1
y
′
=
(
x
−
y
)
(
x
+
2
y
)
,
y
(
0
)
=
1
derivative of log_{e}(cos(4x))
d
dx
(
log
e
(
cos
(
4
x
)
)
)
integral of xln(x^5)
∫
x
ln
(
x
5
)
dx
integral from 0 to pi/4 of xsin(2x)
∫
0
π
4
x
sin
(
2
x
)
dx
integral from 0 to 9 of (sqrt(x)-1/3 x)
∫
0
9
(
√
x
−
1
3
x
)
dx
integral of e^{2x}cos(7x)
∫
e
2
x
cos
(
7
x
)
dx
limit as z approaches 1-i of x+i(2x+y)
lim
z
→
1
−
i
(
x
+
i
(
2
x
+
y
)
)
(\partial)/(\partial x)(sin(pi(2x-y)))
∂
∂
x
(
sin
(
π
(
2
x
−
y
)
)
)
integral of sqrt(x^7)
∫
√
x
7
dx
derivative of (1-cos(x)/(1+cos(x)))
d
dx
(
1
−
cos
(
x
)
1
+
cos
(
x
)
)
integral of 1/(sqrt((25-y^2)-x^2))
∫
1
√
(
2
5
−
y
2
)
−
x
2
dx
laplacetransform sin(2t)+2cos(2t)+e^{-t}sin(2t)
laplacetransform
sin
(
2
t
)
+
2
cos
(
2
t
)
+
e
−
t
sin
(
2
t
)
y^'=3y^2
y
′
=
3
y
2
sum from n=1 to infinity of 8^nx^nn!
∑
n
=
1
∞
8
n
x
n
n
!
(\partial)/(\partial x)((x^2+y^2)^{-1})
∂
∂
x
(
(
x
2
+
y
2
)
−
1
)
x*(dy)/(dx)=xtan(y/x)+y
x
·
dy
dx
=
x
tan
(
y
x
)
+
y
integral of x(x+8)^5
∫
x
(
x
+
8
)
5
dx
derivative of-3cos^2(x)
d
dx
(
−
3
cos
2
(
x
)
)
derivative y=x^3+1
derivative
y
=
x
3
+
1
derivative (6x+8x^2)/((3+8x)^2)
derivative
6
x
+
8
x
2
(
3
+
8
x
)
2
(dx)/(dt)=-2x+t
dx
dt
=
−
2
x
+
t
테일러 sqrt(x),\at 4
taylor
√
x
,
at
4
limit as x approaches 0 of (1-5x)^{3/x}
lim
x
→
0
(
(
1
−
5
x
)
3
x
)
derivative x^3csc(x)
derivative
x
3
csc
(
x
)
derivative of ln((ln(x)^2))
d
dx
(
ln
(
(
ln
(
x
)
)
2
)
)
integral of (1-sin^3(x))/(sin^2(x))
∫
1
−
sin
3
(
x
)
sin
2
(
x
)
dx
derivative of (2x^2-3x+1/x)
d
dx
(
2
x
2
−
3
x
+
1
x
)
경사지 x^2+xy+2y^2=28,(2,3)
slope
x
2
+
xy
+
2
y
2
=
2
8
,
(
2
,
3
)
t^2y^{''}+7ty^'+10y=0
t
2
y
′
′
+
7
ty
′
+
1
0
y
=
0
integral of tan(4x)sec^5(4x)
∫
tan
(
4
x
)
sec
5
(
4
x
)
dx
limit as x approaches 7-of 1/(x-7)
lim
x
→
7
−
(
1
x
−
7
)
derivative sqrt(x^2+6)
derivative
√
x
2
+
6
tangent arcsin(x/7)
tangent
arcsin
(
x
7
)
y^'=(x^2+2*y^2)/(x*y)
y
′
=
x
2
+
2
·
y
2
x
·
y
derivative of 10xsin(x)
d
dx
(
1
0
x
sin
(
x
)
)
9x^2y^2+x^{3/2}y^'=y^2
9
x
2
y
2
+
x
3
2
y
′
=
y
2
derivative (x^2-18)(2x+3)
derivative
(
x
2
−
1
8
)
(
2
x
+
3
)
integral of x+1/(x^2)
∫
x
+
1
x
2
dx
(\partial)/(\partial x)(xy-1)
∂
∂
x
(
xy
−
1
)
(\partial)/(\partial y)((x^2-1)(y+2))
∂
∂
y
(
(
x
2
−
1
)
(
y
+
2
)
)
tangent f(x)= 3/(x^2),\at x=1
tangent
f
(
x
)
=
3
x
2
,
at
x
=
1
integral from 0 to pi/4 of 4sin^2(x)
∫
0
π
4
4
sin
2
(
x
)
dx
limit as h approaches 0 of (1+5h)^{1/h}
lim
h
→
0
(
(
1
+
5
h
)
1
h
)
derivative of sqrt(y^2-x^2)
d
dx
(
√
y
2
−
x
2
)
integral of e^{5x+e^{5x}}
∫
e
5
x
+
e
5
x
dx
inverselaplace s/(2s^2+4s+3)
inverselaplace
s
2
s
2
+
4
s
+
3
(dy)/(dx)=(xsqrt(1-y^2))/(ysqrt(1-x^2))
dy
dx
=
x
√
1
−
y
2
y
√
1
−
x
2
integral of x^3-2x^{-2}+6x
∫
x
3
−
2
x
−
2
+
6
xdx
테일러 sqrt(9+x^2)
taylor
√
9
+
x
2
derivative ln(4x^3)
derivative
ln
(
4
x
3
)
integral of (sqrt(x^5-1))/x
∫
√
x
5
−
1
x
dx
integral of 1/(sqrt(x^2-4x+8))
∫
1
√
x
2
−
4
x
+
8
dx
derivative of 2x^{sqrt(x)}
d
dx
(
2
x
√
x
)
integral of (sqrt(2x-3))/(2x+1)
∫
√
2
x
−
3
2
x
+
1
dx
integral of-4sin(5x)sin(x)
∫
−
4
sin
(
5
x
)
sin
(
x
)
dx
derivative of 1/(1+sin(x))
d
dx
(
1
1
+
sin
(
x
)
)
integral of 3/4 t+6
∫
3
4
t
+
6
dt
limit as x approaches 3-of sqrt(9-x^2)
lim
x
→
3
−
(
√
9
−
x
2
)
tangent f(x)=(x+2)/(x^2-9),\at x=1
tangent
f
(
x
)
=
x
+
2
x
2
−
9
,
at
x
=
1
integral of sqrt(3x-12)
∫
√
3
x
−
1
2
dx
derivative of 3/(2x+(4x)/5)
d
dx
(
3
2
x
+
4
x
5
)
derivative y=(3x+4)/(sqrt(2x-1))
derivative
y
=
3
x
+
4
√
2
x
−
1
derivative f(x)=(x^6-4x^2+2)ln(x)
derivative
f
(
x
)
=
(
x
6
−
4
x
2
+
2
)
ln
(
x
)
integral of 2/3 t^{3/2}-8sin(t)+C
∫
2
3
t
3
2
−
8
sin
(
t
)
+
Cdt
(\partial)/(\partial x)(e^{x^2+y}-2xy)
∂
∂
x
(
e
x
2
+
y
−
2
xy
)
y^'=xy(y+2)
y
′
=
xy
(
y
+
2
)
sum from n=1 to infinity of 9/(n^3)
∑
n
=
1
∞
9
n
3
sum from n=0 to infinity of 4(3/4)^n
∑
n
=
0
∞
4
(
3
4
)
n
derivative of (ln(x+2)/(4x^{-2)})
d
dx
(
ln
(
x
+
2
)
4
x
−
2
)
inverselaplace (2s+1)/(s^3)
inverselaplace
2
s
+
1
s
3
derivative h(x)=(x^2+4x+1)/(3x+5)
derivative
h
(
x
)
=
x
2
+
4
x
+
1
3
x
+
5
derivative of 5x^{2x}
d
dx
(
5
x
2
x
)
integral of 2x*e^{2x}
∫
2
x
·
e
2
x
dx
integral of (1+1/u)^{-3}(1/(u^2))
∫
(
1
+
1
u
)
−
3
(
1
u
2
)
du
derivative of 4sqrt(x)+8x^{3/8}
d
dx
(
4
√
x
+
8
x
3
8
)
derivative of sqrt(((x^2-4^3)/(36)))
d
dx
(
√
(
x
2
−
4
)
3
3
6
)
limit as x approaches 1+of 1/(x^3)
lim
x
→
1
+
(
1
x
3
)
slopeintercept (-5,-1),(0,3)
slopeintercept
(
−
5
,
−
1
)
,
(
0
,
3
)
(dy)/(dx)=(y+1)/(x^3)
dy
dx
=
y
+
1
x
3
sum from n=1 to infinity of ((3x)^n)/n
∑
n
=
1
∞
(
3
x
)
n
n
integral of x-sqrt(x)
∫
x
−
√
x
dx
integral of (5x)/(cos^2(x^2))
∫
5
x
cos
2
(
x
2
)
dx
integral of 21
∫
2
1
dx
1
2
3
4
5
6
7
..
1823
