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일반적인 미적분학 문제
경사지 (2,3),(4,5)
slope
(
2
,
3
)
,
(
4
,
5
)
derivative f(x)=sqrt(4x+32)
derivative
f
(
x
)
=
√
4
x
+
3
2
d/(dj)(i+j)
d
dj
(
i
+
j
)
x^2y^'+3xy=((sin(2x)))/x
x
2
y
′
+
3
xy
=
(
sin
(
2
x
)
)
x
limit as x approaches 8 of (x-9)/(x-8)
lim
x
→
8
(
x
−
9
x
−
8
)
지역 f(x)=((25-x^2)^{1/2}), 4/3 x,5
area
f
(
x
)
=
(
(
2
5
−
x
2
)
1
2
)
,
4
3
x
,
5
(\partial)/(\partial x)(ae^{2x})
∂
∂
x
(
ae
2
x
)
integral from 0 to 2 of ((x+2))/(x-4)
∫
0
2
(
x
+
2
)
x
−
4
dx
integral of 1/((a+bx)^2)
∫
1
(
a
+
bx
)
2
dx
tangent y=5-9x^2
tangent
y
=
5
−
9
x
2
integral of 1/(16x^4-1)
∫
1
1
6
x
4
−
1
dx
derivative of e^{{r}(t,xt})
d
dx
(
e
r
(
t
,
x
)
t
)
integral of (3e^{3t})/(3+e^{3t)}
∫
3
e
3
t
3
+
e
3
t
dt
지역 y=((25-x^2)^{1/2}),y= 4/3 x,x=5
area
y
=
(
(
2
5
−
x
2
)
1
2
)
,
y
=
4
3
x
,
x
=
5
derivative ((1+x^2)/(1-x^2))^{17}
derivative
(
1
+
x
2
1
−
x
2
)
1
7
(dy)/(dx)=sin(17x)
dy
dx
=
sin
(
1
7
x
)
limit as x approaches 1 of (4-x)/(x-1)
lim
x
→
1
(
4
−
x
x
−
1
)
integral of (x+1)*e^{4x+1}
∫
(
x
+
1
)
·
e
4
x
+
1
dx
derivative \sqrt[3]{4x-5}
derivative
3
√
4
x
−
5
integral of 3x^2-sqrt(x)
∫
3
x
2
−
√
x
dx
(6y+2t-7)dt+(4y+6t-1)dy=0
(
6
y
+
2
t
−
7
)
dt
+
(
4
y
+
6
t
−
1
)
dy
=
0
limit as x approaches 1 of 4/((x-1)^2)
lim
x
→
1
(
4
(
x
−
1
)
2
)
(\partial)/(\partial x)((5x)/((x+y)^3))
∂
∂
x
(
5
x
(
x
+
y
)
3
)
integral of (sqrt(81-x^2))/x
∫
√
8
1
−
x
2
x
dx
integral from 0 to 3 of 5-(x-1)^2
∫
0
3
5
−
(
x
−
1
)
2
dx
(\partial)/(\partial x)(asqrt(x))
∂
∂
x
(
a
√
x
)
integral from x to 1 of 2
∫
x
1
2
dy
derivative of ln(sec(x+tan(x))sin(x))
d
dx
(
ln
(
sec
(
x
)
+
tan
(
x
)
)
sin
(
x
)
)
integral of (arcsin(x))
∫
(
arcsin
(
x
)
)
dx
derivative of ln(sqrt(((x-3)/(x-1))))
d
dx
(
ln
(
√
(
x
−
3
)
x
−
1
)
)
derivative of sin(at)
d
dx
(
sin
(
at
)
)
(\partial)/(\partial x)(5xe^{sqrt(xy)})
∂
∂
x
(
5
xe
√
xy
)
limit as x approaches-1 of (x^4-1)/(x-1)
lim
x
→
−
1
(
x
4
−
1
x
−
1
)
derivative 2^{3x^2}
derivative
2
3
x
2
integral of (cos(2x))/(sin^2(2x))
∫
cos
(
2
x
)
sin
2
(
2
x
)
dx
integral of e^xsqrt(19+e^x)
∫
e
x
√
1
9
+
e
x
dx
derivative x^2(4-x)^2
derivative
x
2
(
4
−
x
)
2
integral of (2x^2+4x-6)/x
∫
2
x
2
+
4
x
−
6
x
dx
integral from 0 to 1 of (3y)/(e^{2y)}
∫
0
1
3
y
e
2
y
dy
integral of ln(2x+2)
∫
ln
(
2
x
+
2
)
dx
derivative of x^2-6x+7
d
dx
(
x
2
−
6
x
+
7
)
derivative of (x^2-1/(x^2+1))
d
dx
(
x
2
−
1
x
2
+
1
)
integral of 17tan^5(x)sec^4(x)
∫
1
7
tan
5
(
x
)
sec
4
(
x
)
dx
integral of x^{-1.1}
∫
x
−
1
.
1
dx
limit as x approaches 4 of 2(x)^2-2x
lim
x
→
4
(
2
(
x
)
2
−
2
x
)
integral of (t^2)/(sqrt(4-t^2))
∫
t
2
√
4
−
t
2
dt
integral from 0 to 1 of x(x-1)e^{-x^2}
∫
0
1
x
(
x
−
1
)
e
−
x
2
dx
integral of (5x^2-5sin(x))
∫
(
5
x
2
−
5
sin
(
x
)
)
dx
derivative of sinh(2x)
d
dx
(
sinh
(
2
x
)
)
integral of 4cos(sqrt(4x))
∫
4
cos
(
√
4
x
)
dx
limit as x approaches 1+of (x-1)^{(x-1)}
lim
x
→
1
+
(
(
x
−
1
)
(
x
−
1
)
)
derivative (4-2x-x^2)/(x^2-6)
derivative
4
−
2
x
−
x
2
x
2
−
6
derivative B(x-2)^3
derivative
B
(
x
−
2
)
3
(\partial)/(\partial x)(xsin(x)e^{yx^2})
∂
∂
x
(
x
sin
(
x
)
e
yx
2
)
경사지intercept (6,-1),(3,-7)
slopeintercept
(
6
,
−
1
)
,
(
3
,
−
7
)
(\partial)/(\partial x)(xcos(yz))
∂
∂
x
(
x
cos
(
yz
)
)
integral of (2x-1)^5
∫
(
2
x
−
1
)
5
dx
derivative of cos(x^3*3x^2)
d
dx
(
cos
(
x
3
)
·
3
x
2
)
(\partial)/(\partial x)(7cos(x))
∂
∂
x
(
7
cos
(
x
)
)
integral from 0 to 2 of (x^2)
∫
0
2
(
x
2
)
dx
(dN)/(dt)=k(350-N)
dN
dt
=
k
(
3
5
0
−
N
)
derivative (14x+6x^2)/((7+6x)^2)
derivative
1
4
x
+
6
x
2
(
7
+
6
x
)
2
integral of (1+x)/(1+x^2)
∫
1
+
x
1
+
x
2
dx
limit as x approaches 3-of ((2))/(x-3)
lim
x
→
3
−
(
(
2
)
x
−
3
)
limit as x approaches-infinity of e^{-6x}-2e^{-2x}-1
lim
x
→
−
∞
(
e
−
6
x
−
2
e
−
2
x
−
1
)
integral of (x^2)/((1-x^3)^{3/2)}
∫
x
2
(
1
−
x
3
)
3
2
dx
integral from 0 to 4 of pi(4x^2)^2
∫
0
4
π
(
4
x
2
)
2
dx
(\partial)/(\partial x)(sqrt(5+2x+3xy^2))
∂
∂
x
(
√
5
+
2
x
+
3
xy
2
)
(\partial}{\partial x}(-\frac{2y)/x)
∂
∂
x
(
−
2
y
x
)
laplace변환 5e^{-3t}sin(t)
laplacetransform
5
e
−
3
t
sin
(
t
)
integral of cos(16x)cos(7x)
∫
cos
(
1
6
x
)
cos
(
7
x
)
dx
(d^2)/(dx^2)(x^r)
d
2
dx
2
(
x
r
)
inverse라플라스 1/(s^2+5)
inverselaplace
1
s
2
+
5
sum from n=0 to infinity of (n+1)(1/2)^n
∑
n
=
0
∞
(
n
+
1
)
(
1
2
)
n
테일러 1/(1-x^5)
taylor
1
1
−
x
5
integral from 0 to 1 of (29)/(x^5)
∫
0
1
2
9
x
5
dx
(dv}{dx}-\frac{2v)/x =-1
dv
dx
−
2
v
x
=
−
1
integral of (x^2-4)/(x^3-12x+3)
∫
x
2
−
4
x
3
−
1
2
x
+
3
dx
integral of 7^{x+2}
∫
7
x
+
2
dx
derivative of (x^2-100/(x-10))
d
dx
(
x
2
−
1
0
0
x
−
1
0
)
derivative-2e^x
derivative
−
2
e
x
integral of (e^x+cos(x)+t+1/t)
∫
(
e
x
+
cos
(
x
)
+
t
+
1
t
)
dx
(\partial)/(\partial x)((3x)/(2+y))
∂
∂
x
(
3
x
2
+
y
)
derivative of (xcos(x-sin(x))/(6x^2))
d
dx
(
x
cos
(
x
)
−
sin
(
x
)
6
x
2
)
derivative x^2ln(9x)
derivative
x
2
ln
(
9
x
)
derivative of sqrt(9x^2+5)
d
dx
(
√
9
x
2
+
5
)
integral from 0 to 0.5 of 8x-1/8 x
∫
0
0
.
5
8
x
−
1
8
xdx
sum from n=2 to infinity of 3/(2^n)
∑
n
=
2
∞
3
2
n
integral of 6x^2-3x
∫
6
x
2
−
3
xdx
derivative of-0.00000003x^3+9x-6000
d
dx
(
−
0
.
0
0
0
0
0
0
0
3
x
3
+
9
x
−
6
0
0
0
)
integral of (-3x^3+\sqrt[5]{x})/(5x)
∫
−
3
x
3
+
5
√
x
5
x
dx
integral of 14x^{13}
∫
1
4
x
1
3
dx
integral of ((sqrt(x)+5)^7)/(2sqrt(x))
∫
(
√
x
+
5
)
7
2
√
x
dx
테일러-(81x)/4
taylor
−
8
1
x
4
derivative g(x)=x^2+(7x)/2-3
derivative
g
(
x
)
=
x
2
+
7
x
2
−
3
(dy)/(dx)=(x^2)/(e^y)
dy
dx
=
x
2
e
y
integral from 0 to 9 of x^2
∫
0
9
x
2
dx
x(dy)/(dx)-y=x
x
dy
dx
−
y
=
x
(\partial)/(\partial y)(y^3sin(4x))
∂
∂
y
(
y
3
sin
(
4
x
)
)
derivative of (1+6x^2(x-x^2))
d
dx
(
(
1
+
6
x
2
)
(
x
−
x
2
)
)
1
..
1414
1415
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1417
1418
..
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