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일반적인 미적분학 문제
(\partial)/(\partial x)(e^{2z})
∂
∂
x
(
e
2
z
)
tangent f(x)=3x^2-4,\at x=2
tangent
f
(
x
)
=
3
x
2
−
4
,
at
x
=
2
y^{''}-y=e^{-t},y(0)=1,y^'(0)=0
y
′
′
−
y
=
e
−
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
integral of 8+7^x
∫
8
+
7
x
dx
tangent f(x)=e^{5x}cos(pix),\at x=1
tangent
f
(
x
)
=
e
5
x
cos
(
π
x
)
,
at
x
=
1
integral of-2e^x
∫
−
2
e
x
dx
derivative of-6sin(2x+3cos(3x))
d
dx
(
−
6
sin
(
2
x
)
+
3
cos
(
3
x
)
)
derivative of x(55-0.5x-110)
d
dx
(
x
(
5
5
−
0
.
5
x
)
−
1
1
0
)
d/(dt)(e^{3it})
d
dt
(
e
3
it
)
integral of (x^3)/(x^2-100)
∫
x
3
x
2
−
1
0
0
dx
sum from n=1 to infinity of 2/(n^2+4n+2)
∑
n
=
1
∞
2
n
2
+
4
n
+
2
derivative of (sin(5x)/(cos(6x)))
d
dx
(
sin
(
5
x
)
cos
(
6
x
)
)
derivative of (x^2-4^2(x-1))
d
dx
(
(
x
2
−
4
)
2
(
x
−
1
)
)
derivative ((1-5t))/(2+t)
derivative
(
1
−
5
t
)
2
+
t
(\partial)/(\partial x)(1/(sqrt(2pit))e^{-((x-y)^2)/(2t)})
∂
∂
x
(
1
√
2
π
t
e
−
(
x
−
y
)
2
2
t
)
limit as x approaches 1-of 2x-1
lim
x
→
1
−
(
2
x
−
1
)
derivative f(x)=(4x)/(x^2+4)
derivative
f
(
x
)
=
4
x
x
2
+
4
integral of (28)/(1-cos(4x))
∫
2
8
1
−
cos
(
4
x
)
dx
y^'=y+x,y(0)=1
y
′
=
y
+
x
,
y
(
0
)
=
1
(dy)/(dx)=(y^2-1)/(x^2-1),y(2)=2
dy
dx
=
y
2
−
1
x
2
−
1
,
y
(
2
)
=
2
integral of sin(t)e^{-2/3 t}
∫
sin
(
t
)
e
−
2
3
t
dt
integral from 1 to 2 of x^2e^{x^3-1}
∫
1
2
x
2
e
x
3
−
1
dx
sum from n=1 to infinity of 1/(\sqrt[n]{2)}
∑
n
=
1
∞
1
n
√
2
y^{''}+9y=(sec(3t))^2
y
′
′
+
9
y
=
(
sec
(
3
t
)
)
2
(dy}{dx}+(2y)/x =\frac{sin(x))/(x^2)
dy
dx
+
2
y
x
=
sin
(
x
)
x
2
laplace변환 te^{-t}
laplacetransform
te
−
t
derivative of e^{-2x}-3y
d
dx
(
e
−
2
x
−
3
y
)
derivative of (2x-1/(x+2))
d
dx
(
2
x
−
1
x
+
2
)
integral of ((\sqrt[3]{x}+sqrt(x^5))/x)
∫
(
3
√
x
+
√
x
5
x
)
dx
y^'=e^{8x}-6x
y
′
=
e
8
x
−
6
x
derivative f(x)=(40t)/(t+2)
derivative
f
(
x
)
=
4
0
t
t
+
2
limit as h approaches 0 of (2x+h)-2x
lim
h
→
0
(
(
2
x
+
h
)
−
2
x
)
derivative cos((1-e^{4x})/(1+e^{4x)})
derivative
cos
(
1
−
e
4
x
1
+
e
4
x
)
integral of sin(x^2-5)x
∫
sin
(
x
2
−
5
)
xdx
y^'=x^{2/3}
y
′
=
x
2
3
integral from 1 to e^4 of (ln(x))/(x^2)
∫
1
e
4
ln
(
x
)
x
2
dx
limit as x approaches infinito of 10
lim
x
→
infinito
(
1
0
)
(\partial)/(\partial x)(5(y^2-x^2)ln(x+y))
∂
∂
x
(
5
(
y
2
−
x
2
)
ln
(
x
+
y
)
)
t^2y^{''}-2y=0
t
2
y
′
′
−
2
y
=
0
derivative of sin(xcos(3-x^2))
d
dx
(
sin
(
x
)
cos
(
3
−
x
2
)
)
derivative of e^{ax}a
d
dx
(
e
ax
a
)
(dy)/(dx)=x^3
dy
dx
=
x
3
(x+y-2)dx+(x-y+4)dy=0
(
x
+
y
−
2
)
dx
+
(
x
−
y
+
4
)
dy
=
0
(\partial)/(\partial x)(e^x+cos(xy))
∂
∂
x
(
e
x
+
cos
(
xy
)
)
derivative of-x^2-2
d
dx
(
−
x
2
−
2
)
integral of (2x)/(sqrt(9-x^4))
∫
2
x
√
9
−
x
4
dx
경사지 (-3,1),(-7,-2)
slope
(
−
3
,
1
)
,
(
−
7
,
−
2
)
derivative (sec(x))^3
derivative
(
sec
(
x
)
)
3
integral of (e^x)/((e^x-8)(e^{2x)+1)}
∫
e
x
(
e
x
−
8
)
(
e
2
x
+
1
)
dx
limit as x approaches infinity of 3+5/x
lim
x
→
∞
(
3
+
5
x
)
(\partial)/(\partial x)(d/t)
∂
∂
x
(
d
t
)
integral from 0 to 5 of |5x-10|
∫
0
5
|
5
x
−
1
0
|
dx
y^'=3x(y-1)^{1/3}
y
′
=
3
x
(
y
−
1
)
1
3
지역 10x-5x^2,x=\sqrt[3]{4},x=2
area
1
0
x
−
5
x
2
,
x
=
3
√
4
,
x
=
2
(\partial)/(\partial x)(3x*e^{2x+y^2})
∂
∂
x
(
3
x
·
e
2
x
+
y
2
)
derivative of xsqrt(3-2x^2)
d
dx
(
x
√
3
−
2
x
2
)
integral of u/(sqrt(u^2-1))
∫
u
√
u
2
−
1
du
(dN)/(dt)=(te^t)/(N^2)
dN
dt
=
te
t
N
2
sum from n=0 to infinity of 1/(n^5)
∑
n
=
0
∞
1
n
5
sum from n=8 to infinity of (1/4)^n
∑
n
=
8
∞
(
1
4
)
n
integral of csc^2(kx)
∫
csc
2
(
kx
)
dx
derivative (7x^2)/(sqrt(x))
derivative
7
x
2
√
x
derivative of (x^2/4+2x+3)
d
dx
(
x
2
4
+
2
x
+
3
)
integral of 1/(x^2-7x+10)
∫
1
x
2
−
7
x
+
1
0
dx
d/(dy)(x^2-3y^2)
d
dy
(
x
2
−
3
y
2
)
integral of 4x^2ln(x)
∫
4
x
2
ln
(
x
)
dx
integral of x/((x^2+2x+2)^2)
∫
x
(
x
2
+
2
x
+
2
)
2
dx
derivative (1+7x^2)(x-x^2)
derivative
(
1
+
7
x
2
)
(
x
−
x
2
)
integral of (e^x)/(sqrt(1-16e^{2x))}
∫
e
x
√
1
−
1
6
e
2
x
dx
integral from 9 to 10 of 1/((x-9)^{4/3)}
∫
9
1
0
1
(
x
−
9
)
4
3
dx
integral from 0 to 6.25 of-x^2+5x
∫
0
6
.
2
5
−
x
2
+
5
xdx
integral of 15x^{1/4}
∫
1
5
x
1
4
dx
derivative of arctan(x^5)
d
dx
(
arctan
(
x
5
)
)
지역 \sqrt[3]{x}, 1/x ,x=27
area
3
√
x
,
1
x
,
x
=
2
7
(\partial)/(\partial y)(y^{2x})
∂
∂
y
(
y
2
x
)
limit as x approaches-2 of 4x^3+4x-2
lim
x
→
−
2
(
4
x
3
+
4
x
−
2
)
지역 8-x^2,x^2,(-3,3)
area
8
−
x
2
,
x
2
,
(
−
3
,
3
)
derivative 1/(x+1)
derivative
1
x
+
1
y^{''}+4y^'+5y=10x+5e^{-x}
y
′
′
+
4
y
′
+
5
y
=
1
0
x
+
5
e
−
x
지역 3x^2,-3x+6
area
3
x
2
,
−
3
x
+
6
integral of (sec^2(x)e^{tan(x)})
∫
(
sec
2
(
x
)
e
tan
(
x
)
)
dx
tangent (sqrt(x))/(x+4)
tangent
√
x
x
+
4
derivative log_{8}(2x^3+3x^2+1)
derivative
log
8
(
2
x
3
+
3
x
2
+
1
)
integral of (sqrt(4x^2-9))/(x^3)
∫
√
4
x
2
−
9
x
3
dx
limit as x approaches 0 of sqrt(x)
lim
x
→
0
(
√
x
)
limit as x approaches 1 of 1/(|x-1|)
lim
x
→
1
(
1
|
x
−
1
|
)
(\partial)/(\partial y)(tan(3+2x^2y^3z^2))
∂
∂
y
(
tan
(
3
+
2
x
2
y
3
z
2
)
)
integral of 1/(x^2sqrt(x-1))
∫
1
x
2
√
x
−
1
dx
integral of (4^x-1/(3x))
∫
(
4
x
−
1
3
x
)
dx
derivative f(x)=x^{7x}
derivative
f
(
x
)
=
x
7
x
maclaurin 1/(1+x+x^2)
maclaurin
1
1
+
x
+
x
2
요인 12x^5-8x^4+20x^3
factor
1
2
x
5
−
8
x
4
+
2
0
x
3
경사지 (-1,8),(3,-4)
slope
(
−
1
,
8
)
,
(
3
,
−
4
)
f(x)=(3x^3-4)(-4x-3)
f
(
x
)
=
(
3
x
3
−
4
)
(
−
4
x
−
3
)
지역 y=cos(x),y=0.5
area
y
=
cos
(
x
)
,
y
=
0
.
5
integral from-10 to 10 of xe^{-x^8}
∫
−
1
0
1
0
xe
−
x
8
dx
derivative sin(x/2)
derivative
sin
(
x
2
)
derivative ((x+3))/(x^2-4)
derivative
(
x
+
3
)
x
2
−
4
(9x^2+y-1)dx-(4y-x)dy=0
(
9
x
2
+
y
−
1
)
dx
−
(
4
y
−
x
)
dy
=
0
(\partial)/(\partial x)(1+ln(x)+y/x)
∂
∂
x
(
1
+
ln
(
x
)
+
y
x
)
1
..
1153
1154
1155
1156
1157
..
2459