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일반적인 미적분학 문제
derivative of (x^2+2x-2/((x+1)^2))
d
dx
(
x
2
+
2
x
−
2
(
x
+
1
)
2
)
지역 f(x)= 7/x ,x=1,x=41
area
f
(
x
)
=
7
x
,
x
=
1
,
x
=
4
1
limit as x approaches 3+of (6x)/(x^2-9)
lim
x
→
3
+
(
6
x
x
2
−
9
)
laplace변환 tsin(t)
laplacetransform
t
sin
(
t
)
derivative of (sqrt(2)^x)
d
dx
(
(
√
2
)
x
)
integral from 0 to infinity of x^2
∫
0
∞
x
2
dx
integral of 1/(x^2+7)
∫
1
x
2
+
7
dx
derivative of arctan(x+x/(1+x^2))
d
dx
(
arctan
(
x
)
+
x
1
+
x
2
)
derivative (tan(x))(sqrt(x))
derivative
(
tan
(
x
)
)
(
√
x
)
(\partial)/(\partial x)(ln(2x+5y))
∂
∂
x
(
ln
(
2
x
+
5
y
)
)
y^{''}+2y^'+3/4 y=0
y
′
′
+
2
y
′
+
3
4
y
=
0
integral of 3-1/(x^4)
∫
3
−
1
x
4
dx
(ln(1))^'
(
ln
(
1
)
)
′
derivative of (sqrt(x)-7/(sqrt(x)+1))
d
dx
(
√
x
−
7
√
x
+
1
)
integral of 8cos^3(x)
∫
8
cos
3
(
x
)
dx
(\partial)/(\partial x)(p(x))
∂
∂
x
(
p
(
x
)
)
derivative of x^2sin^4(x+xcos^{-2}(x))
d
dx
(
x
2
sin
4
(
x
)
+
x
cos
−
2
(
x
)
)
y^'-6y=2e^t
y
′
−
6
y
=
2
e
t
y^{''}-4y^'+4y=0,y(0)=-4,y^'(0)=-6
y
′
′
−
4
y
′
+
4
y
=
0
,
y
(
0
)
=
−
4
,
y
′
(
0
)
=
−
6
limit as x approaches+2 of [7f(x)+g(x)]
lim
x
→
+
2
(
[
7
f
(
x
)
+
g
(
x
)
]
)
y^'+e^ty=-17e^t
y
′
+
e
t
y
=
−
1
7
e
t
integral from 0 to pi/4 of 5sec^2(x)
∫
0
π
4
5
sec
2
(
x
)
dx
integral of 1/(x^2sqrt(x^2+4))
∫
1
x
2
√
x
2
+
4
dx
y^'+4x^3y^2=0
y
′
+
4
x
3
y
2
=
0
(\partial)/(\partial x)(x^2-5x^2y-6xy^2)
∂
∂
x
(
x
2
−
5
x
2
y
−
6
xy
2
)
integral of (x^2-x)/(1+3x^2-2x^3)
∫
x
2
−
x
1
+
3
x
2
−
2
x
3
dx
derivative y=(x^2+1)
derivative
y
=
(
x
2
+
1
)
integral of (sqrt(36+(ln(8x))^2))/x
∫
√
3
6
+
(
ln
(
8
x
)
)
2
x
dx
limit as x approaches 0 of (x^2-9)/(x+3)
lim
x
→
0
(
x
2
−
9
x
+
3
)
y^'=((x+y+1))/((2x+2y+3))
y
′
=
(
x
+
y
+
1
)
(
2
x
+
2
y
+
3
)
derivative of (4x-3/(5x^2+3x))
d
dx
(
4
x
−
3
5
x
2
+
3
x
)
integral of sec^5(θ/2)
∫
sec
5
(
θ
2
)
d
θ
limit as t approaches 0 of (3e^t-3)/t
lim
t
→
0
(
3
e
t
−
3
t
)
(\partial)/(\partial x)(sin(5xy+8yz+9xz))
∂
∂
x
(
sin
(
5
xy
+
8
yz
+
9
xz
)
)
integral of 1/(x^2+pi^2)
∫
1
x
2
+
π
2
dx
(\partial)/(\partial x)(3^{sin(3x)})
∂
∂
x
(
3
sin
(
3
x
)
)
derivative of (4x+3^5)
d
dx
(
(
4
x
+
3
)
5
)
inverse라플라스 (2/s+1/(s^3))^2
inverselaplace
(
2
s
+
1
s
3
)
2
integral from 0 to 9 of pi(9-y)
∫
0
9
π
(
9
−
y
)
dy
f(x)=sqrt(49-x^2)
f
(
x
)
=
√
4
9
−
x
2
derivative-x/(4y)
derivative
−
x
4
y
derivative of (x+6(x-2)^2)
d
dx
(
(
x
+
6
)
(
x
−
2
)
2
)
derivative of 1/(sqrt(5-x))
d
dx
(
1
√
5
−
x
)
(\partial)/(\partial x)(x^2y-y^2x)
∂
∂
x
(
x
2
y
−
y
2
x
)
derivative e^{(x-1)^2}
derivative
e
(
x
−
1
)
2
derivative cot(x^8)
derivative
cot
(
x
8
)
derivative y=((8x^2-5)/(2-x))^3
derivative
y
=
(
8
x
2
−
5
2
−
x
)
3
derivative g(x)=log_{7}(8x^3-9x^2)
derivative
g
(
x
)
=
log
7
(
8
x
3
−
9
x
2
)
integral of x(xsin(x)-cos(x))
∫
x
(
x
sin
(
x
)
−
cos
(
x
)
)
dx
integral from 0 to 0.9 of 1/((1-x))
∫
0
0
.
9
1
(
1
−
x
)
dx
integral of 6cos(5x)
∫
6
cos
(
5
x
)
dx
y=2(x+y)y^'
y
=
2
(
x
+
y
)
y
′
integral of 3sin^6(x)cos(x)
∫
3
sin
6
(
x
)
cos
(
x
)
dx
limit as x approaches 0 of 10sqrt(0)
lim
x
→
0
(
1
0
√
0
)
derivative of ax^2e^{2x}
d
dx
(
ax
2
e
2
x
)
derivative h(t)=(t^{2/5}+3)(3t^5+5)
derivative
h
(
t
)
=
(
t
2
5
+
3
)
(
3
t
5
+
5
)
limit as x approaches+8-of x/(x-8)
lim
x
→
+
8
−
(
x
x
−
8
)
derivative of (\sqrt[3]{x}/(x^2+x))
d
dx
(
3
√
x
x
2
+
x
)
tangent f(x)= 3/(sqrt(x)),(1,3)
tangent
f
(
x
)
=
3
√
x
,
(
1
,
3
)
limit as y approaches 0 of 8/(y^2+y)-8/y
lim
y
→
0
(
8
y
2
+
y
−
8
y
)
y^{''}+3y^'-10y=x(e^x+1)
y
′
′
+
3
y
′
−
1
0
y
=
x
(
e
x
+
1
)
derivative of 3^{-6x+6}
d
dx
(
3
−
6
x
+
6
)
f^'(x)=3x^2(8-x^{-3})
f
′
(
x
)
=
3
x
2
(
8
−
x
−
3
)
integral from 0 to 1 of 5^{2x}
∫
0
1
5
2
x
dx
integral from 0 to 1 of x^3+x
∫
0
1
x
3
+
xdx
sum from n=0 to infinity of (x^n)/(n^2)
∑
n
=
0
∞
x
n
n
2
(d^2)/(dx^2)(1/(1-x))
d
2
dx
2
(
1
1
−
x
)
tangent f(x)=arcsin(x/2),\at x=1
tangent
f
(
x
)
=
arcsin
(
x
2
)
,
at
x
=
1
y^'+y=-e^x
y
′
+
y
=
−
e
x
integral of (x+1)sqrt(7-x)
∫
(
x
+
1
)
√
7
−
x
dx
integral from 0 to 1 of t^3e^{-2t}
∫
0
1
t
3
e
−
2
t
dt
limit as x approaches 0 of (e^x-1)/(x^2)
lim
x
→
0
(
e
x
−
1
x
2
)
지역 y=x^2-12,y=4x
area
y
=
x
2
−
1
2
,
y
=
4
x
(dy)/(dx)(2+x)=3y
dy
dx
(
2
+
x
)
=
3
y
limit as x approaches 1 of (x-1)/3
lim
x
→
1
(
x
−
1
3
)
derivative f(x)=4x^2tan(x)
derivative
f
(
x
)
=
4
x
2
tan
(
x
)
integral from 0 to 39 of 0.31sqrt(x)
∫
0
3
9
0
.
3
1
√
x
dx
sum from n=1 to infinity of n(-1)^n
∑
n
=
1
∞
n
(
−
1
)
n
derivative sin^3(t)
derivative
sin
3
(
t
)
integral of 1/(8y)
∫
1
8
y
dy
integral of sec^2(x)tan^5(x)
∫
sec
2
(
x
)
tan
5
(
x
)
dx
(dy)/(dx)+2xy=-x
dy
dx
+
2
xy
=
−
x
ty^'+8y=t^2-t+1
ty
′
+
8
y
=
t
2
−
t
+
1
derivative of 1/((25-x^2))
d
dx
(
1
(
2
5
−
x
2
)
)
integral of e^7
∫
e
7
dx
y^{''}-2y^'-3y=3te^{2t},y(0)=1,y^'(0)=0
y
′
′
−
2
y
′
−
3
y
=
3
te
2
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^'=8x+y,y(0)=1
y
′
=
8
x
+
y
,
y
(
0
)
=
1
(dy)/(dx)=(2xy-y^2)/(x^2)
dy
dx
=
2
xy
−
y
2
x
2
(dy)/(dx)=(4x^3)/(cos(y))
dy
dx
=
4
x
3
cos
(
y
)
derivative of (2x-1(3x+5))
d
dx
(
(
2
x
−
1
)
(
3
x
+
5
)
)
limit as x approaches 2-of x^2+2
lim
x
→
2
−
(
x
2
+
2
)
integral of x^3-6x+7
∫
x
3
−
6
x
+
7
dx
derivative of x(x-1^4)
d
dx
(
x
(
x
−
1
)
4
)
(\partial)/(\partial x)(xy+yz+xz)
∂
∂
x
(
xy
+
yz
+
xz
)
y^{''}-4y^'+4y=2+8x-4x^2
y
′
′
−
4
y
′
+
4
y
=
2
+
8
x
−
4
x
2
경사지intercept (-1,-2),(0,5)
slopeintercept
(
−
1
,
−
2
)
,
(
0
,
5
)
derivative of (1-4e^x/(1-5cos(x)))
d
dx
(
1
−
4
e
x
1
−
5
cos
(
x
)
)
derivative f(x)= 1/2 arctan(x/2)
derivative
f
(
x
)
=
1
2
arctan
(
x
2
)
derivative of 6x^2-96x
d
dx
(
6
x
2
−
9
6
x
)
integral of (2x+1)^4
∫
(
2
x
+
1
)
4
dx
1
..
1191
1192
1193
1194
1195
..
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