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일반적인 미적분학 문제
x^2*e^x+4*y*e^{(-y)}*y^'=0
x
2
·
e
x
+
4
·
y
·
e
(
−
y
)
·
y
′
=
0
derivative of (x-1ln(x-1))
d
dx
(
(
x
−
1
)
ln
(
x
−
1
)
)
integral from 0 to x^2 of t^2
∫
0
x
2
t
2
dt
derivative y=5x^4-x^2+6
derivative
y
=
5
x
4
−
x
2
+
6
derivative of 2x+9
d
dx
(
2
x
+
9
)
integral of (4x^3+2x^2+1)/(4x^3-x)
∫
4
x
3
+
2
x
2
+
1
4
x
3
−
x
dx
derivative (x^3+6)e^x
derivative
(
x
3
+
6
)
e
x
derivative of log_{3}(4x-3)
d
dx
(
log
3
(
4
x
−
3
)
)
integral of cot^3(x/2)csc^4(x/2)
∫
cot
3
(
x
2
)
csc
4
(
x
2
)
dx
tangent f(x)=5e^x,\at x=4
tangent
f
(
x
)
=
5
e
x
,
at
x
=
4
integral of (sin(2x))^3
∫
(
sin
(
2
x
)
)
3
dx
integral of (1/(x^3+1))
∫
(
1
x
3
+
1
)
dx
derivative x(2x+1)^3
derivative
x
(
2
x
+
1
)
3
derivative of sinh^2(3x+arcsin(2x))
d
dx
(
sinh
2
(
3
x
)
+
arcsin
(
2
x
)
)
integral of (3x^3+(2x-3)^2)
∫
(
3
x
3
+
(
2
x
−
3
)
2
)
dx
derivative of sqrt(tan(x+cot(x)))
d
dx
(
√
tan
(
x
)
+
cot
(
x
)
)
(\partial)/(\partial x)(sqrt(x^2+4xy+y^6))
∂
∂
x
(
√
x
2
+
4
xy
+
y
6
)
derivative of x/(2^x)
d
dx
(
x
2
x
)
integral from 1 to e of x^nln(x^m)
∫
1
e
x
n
ln
(
x
m
)
dx
(d^2)/(dx^2)(e^{6e^x})
d
2
dx
2
(
e
6
e
x
)
f(x)=x^4-4x^3-20x^2+96x+60
f
(
x
)
=
x
4
−
4
x
3
−
2
0
x
2
+
9
6
x
+
6
0
y^{''}+3y^'=0,y(0)=2
y
′
′
+
3
y
′
=
0
,
y
(
0
)
=
2
integral of cos^2(xsi)n^2x
∫
cos
2
(
xsi
)
n
2
xdx
(dx)/(dy)=((x^2y^2))/(1+x)
dx
dy
=
(
x
2
y
2
)
1
+
x
limit as x approaches 0 of (x)^{sin(x)}
lim
x
→
0
(
(
x
)
sin
(
x
)
)
inverse라플라스 (1960)/(s^2+196)
inverselaplace
1
9
6
0
s
2
+
1
9
6
y^'=-3y+2e^{-x}
y
′
=
−
3
y
+
2
e
−
x
경사지intercept (4,-2),(-8,-1)
slopeintercept
(
4
,
−
2
)
,
(
−
8
,
−
1
)
limit as x approaches 3 of sqrt(25-x^2)
lim
x
→
3
(
√
2
5
−
x
2
)
derivative y=sin(tan(6x))
derivative
y
=
sin
(
tan
(
6
x
)
)
(\partial)/(\partial y)(xy+ln(y)+2x^2)
∂
∂
y
(
xy
+
ln
(
y
)
+
2
x
2
)
(\partial)/(\partial x)(cos^3(x)y-1)
∂
∂
x
(
cos
3
(
x
)
y
−
1
)
inverse라플라스 (s^2)/((s^2+4)^2)
inverselaplace
s
2
(
s
2
+
4
)
2
(2y+3x)dx=-xdy
(
2
y
+
3
x
)
dx
=
−
xdy
derivative of (12/(x^2))
d
dx
(
1
2
x
2
)
y^{''}+y^'+3y=3t^2
y
′
′
+
y
′
+
3
y
=
3
t
2
integral of (sqrt(49x^2-1))/x
∫
√
4
9
x
2
−
1
x
dx
integral of \sqrt[8]{x^9}
∫
8
√
x
9
dx
x^2y^{''}+xy^'-y=0
x
2
y
′
′
+
xy
′
−
y
=
0
derivative of (3x+1^2)
d
dx
(
(
3
x
+
1
)
2
)
derivative of (e^{2-3x}/(x^2))
d
dx
(
e
2
−
3
x
x
2
)
derivative ((s^2-4s+20))/((s+2)(s+4))
derivative
(
s
2
−
4
s
+
2
0
)
(
s
+
2
)
(
s
+
4
)
integral of (6e^{-0.1x})
∫
(
6
e
−
0
.
1
x
)
dx
derivative of (x^2+2x-3/((x+1)^2))
d
dx
(
x
2
+
2
x
−
3
(
x
+
1
)
2
)
limit as x approaches-4 of (x^2-6)/(4-x)
lim
x
→
−
4
(
x
2
−
6
4
−
x
)
derivative of (x^3+3x(2x+4))
d
dx
(
(
x
3
+
3
x
)
(
2
x
+
4
)
)
integral of ysqrt(y)
∫
y
√
y
dy
(dy)/(dx)=x(5-y)
dy
dx
=
x
(
5
−
y
)
limit as x approaches infinity of 3/x
lim
x
→
∞
(
3
x
)
sum from n=0 to infinity of 1-(2/3)^n
∑
n
=
0
∞
1
−
(
2
3
)
n
limit as x approaches 4 of x^2+2x+2
lim
x
→
4
(
x
2
+
2
x
+
2
)
derivative of (sqrt(-x+y-2)/(x-2))
d
dx
(
√
−
x
+
y
−
2
x
−
2
)
derivative of log_{2}((x^2/(x-1)))
d
dx
(
log
2
(
x
2
x
−
1
)
)
limit as x approaches+3 of (pi+x)/4
lim
x
→
+
3
(
π
+
x
4
)
d/(dθ)(sin(θ)+csc(θ))
d
d
θ
(
sin
(
θ
)
+
csc
(
θ
)
)
limit as x approaches pi/2 of 5sec(x)
lim
x
→
π
2
(
5
sec
(
x
)
)
derivative of (x^3y-xy^3/(x^2+y^2))
d
dx
(
x
3
y
−
xy
3
x
2
+
y
2
)
(\partial)/(\partial x)(z^3x^2e^{zx}+x^2z)
∂
∂
x
(
z
3
x
2
e
zx
+
x
2
z
)
y^'(y-x)=1
y
′
(
y
−
x
)
=
1
integral of-x*ln(x)
∫
−
x
·
ln
(
x
)
dx
integral of 1/(1+16x^2)
∫
1
1
+
1
6
x
2
dx
integral from-1 to 2 of (-y^2+y+2)
∫
−
1
2
(
−
y
2
+
y
+
2
)
dy
derivative x^3cos(x^2)
derivative
x
3
cos
(
x
2
)
integral of (x^2)/(sqrt(25-9x^2))
∫
x
2
√
2
5
−
9
x
2
dx
2y^{''}-9y^'-5y=0
2
y
′
′
−
9
y
′
−
5
y
=
0
derivative sec^2(pix)
derivative
sec
2
(
π
x
)
derivative of 6/(x+2)
d
dx
(
6
x
+
2
)
tangent f(x)=(2+3x)(6-5x),\at x=1
tangent
f
(
x
)
=
(
2
+
3
x
)
(
6
−
5
x
)
,
at
x
=
1
derivative of e^{(3-x})
d
dx
(
e
(
3
−
x
)
)
derivative of xe^{-3x}
d
dx
(
xe
−
3
x
)
integral of cos(x)(4+4sin^2(x))
∫
cos
(
x
)
(
4
+
4
sin
2
(
x
)
)
dx
limit as x approaches 0 of (x-x)/(x^2)
lim
x
→
0
(
x
−
x
x
2
)
derivative of (x+1ln^2(x+1))
d
dx
(
(
x
+
1
)
ln
2
(
x
+
1
)
)
derivative y=x(x^2+1)
derivative
y
=
x
(
x
2
+
1
)
f(y)=cos^2(y)
f
(
y
)
=
cos
2
(
y
)
integral of sec^4(5x)tan^3(5x)
∫
sec
4
(
5
x
)
tan
3
(
5
x
)
dx
f^'(x)= 1/(1+\frac{1){1+1/(1+x)}}
f
′
(
x
)
=
1
1
+
1
1
+
1
1
+
x
derivative (x^3)/(1-x^2)
derivative
x
3
1
−
x
2
integral of \sqrt[3]{x}(x+1)^2
∫
3
√
x
(
x
+
1
)
2
dx
integral of ((3x^2+2)/(x^2))
∫
(
3
x
2
+
2
x
2
)
dx
지역 f(x)=xsin(x),0,2pi
area
f
(
x
)
=
x
sin
(
x
)
,
0
,
2
π
derivative of (-3x+2^4(-2x+3)^3)
d
dx
(
(
−
3
x
+
2
)
4
(
−
2
x
+
3
)
3
)
derivative f(x)=sqrt(x-5)
derivative
f
(
x
)
=
√
x
−
5
y^{''}+2y^'+y=sin(x)+4cos(2x)
y
′
′
+
2
y
′
+
y
=
sin
(
x
)
+
4
cos
(
2
x
)
(y+4)*(dy)/(dx)=2xy+4y
(
y
+
4
)
·
dy
dx
=
2
xy
+
4
y
limit as x approaches pi of-csc(2x)
lim
x
→
π
(
−
csc
(
2
x
)
)
integral of sec(2x)+tan(2x)
∫
sec
(
2
x
)
+
tan
(
2
x
)
dx
limit as x approaches 1 of ln(2x)+e^x
lim
x
→
1
(
ln
(
2
x
)
+
e
x
)
inverse라플라스 (11)/((s-1)^3)
inverselaplace
1
1
(
s
−
1
)
3
integral from 0 to 2 of 8x-1/8 x
∫
0
2
8
x
−
1
8
xdx
sum from n=0 to infinity of 2x^{2n}
∑
n
=
0
∞
2
x
2
n
integral from 3 to infinity of e^{-x}
∫
3
∞
e
−
x
dx
limit as x approaches 3+of 3/(x^2-9)
lim
x
→
3
+
(
3
x
2
−
9
)
integral from 0 to 0.9 of 1/(1-x)
∫
0
0
.
9
1
1
−
x
dx
8y^{''}+2y^'-y=0
8
y
′
′
+
2
y
′
−
y
=
0
지역 sin(x),cos(x),[0, pi/2 ]
area
sin
(
x
)
,
cos
(
x
)
,
[
0
,
π
2
]
(dy)/(dx)=2xe^{4y}
dy
dx
=
2
xe
4
y
y^{''}-2y^'+y=-6-3x+(2e^x)/x
y
′
′
−
2
y
′
+
y
=
−
6
−
3
x
+
2
e
x
x
derivative of ln(sqrt(x^2e^{x^{2+1)}})
d
dx
(
ln
(
√
x
2
e
x
2
+
1
)
)
integral of cot^5(x)csc^2(x)
∫
cot
5
(
x
)
csc
2
(
x
)
dx
1
..
1494
1495
1496
1497
1498
..
2459