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일반적인 미적분학 문제
derivative of 2e^{-x}cos(x)
d
dx
(
2
e
−
x
cos
(
x
)
)
derivative f(x)=(2x^2+2x+4)/(sqrt(x))
derivative
f
(
x
)
=
2
x
2
+
2
x
+
4
√
x
integral of e^{x^2-1}
∫
e
x
2
−
1
dx
derivative 1/(s^2+16)
derivative
1
s
2
+
1
6
tangent f(x)=sqrt(4x+33),(4,7)
tangent
f
(
x
)
=
√
4
x
+
3
3
,
(
4
,
7
)
(\partial)/(\partial y)(sin(xy^2))
∂
∂
y
(
sin
(
xy
2
)
)
integral from-1 to 1 of x^4-2x^2+1
∫
−
1
1
x
4
−
2
x
2
+
1
dx
integral of y/(y^2-1)
∫
y
y
2
−
1
dy
동등성 sin(cos(tan(x)))
parity
sin
(
cos
(
tan
(
x
)
)
)
(\partial)/(\partial y)(x/(y+2z))
∂
∂
y
(
x
y
+
2
z
)
sum from n=1 to infinity of (-0.75)^n
∑
n
=
1
∞
(
−
0
.
7
5
)
n
integral of x(x-5)
∫
x
(
x
−
5
)
dx
지역 y=2x^2ln(x),y=8ln(x)
area
y
=
2
x
2
ln
(
x
)
,
y
=
8
ln
(
x
)
integral of (48)/((t+1)^4)-3
∫
4
8
(
t
+
1
)
4
−
3
dt
(dy}{dx}=\frac{x^7-8y)/x
dy
dx
=
x
7
−
8
y
x
integral from 0 to 1 of e^{2sqrt(x)}
∫
0
1
e
2
√
x
dx
2xydx-(1+x^2)dy=0
2
xydx
−
(
1
+
x
2
)
dy
=
0
integral of (x^2)/(sqrt(4-25x^2))
∫
x
2
√
4
−
2
5
x
2
dx
integral of 1/(x(sqrt(x-1)))
∫
1
x
(
√
x
−
1
)
dx
y^'-(cos(x))y=(e^{sin(x)})/(sqrt(1-x^2))
y
′
−
(
cos
(
x
)
)
y
=
e
sin
(
x
)
√
1
−
x
2
derivative of 3sin(x+8cos(x))
d
dx
(
3
sin
(
x
)
+
8
cos
(
x
)
)
limit as x approaches 0+of sin(x)*ln(3x)
lim
x
→
0
+
(
sin
(
x
)
·
ln
(
3
x
)
)
integral from 0 to 2 of 6x^2
∫
0
2
6
x
2
dx
integral from-1 to 1 of xsqrt(1-x^2)
∫
−
1
1
x
√
1
−
x
2
dx
integral of sin(24x)cos(15x)
∫
sin
(
2
4
x
)
cos
(
1
5
x
)
dx
derivative of 8/(sqrt(x-2))
d
dx
(
8
√
x
−
2
)
integral of x^2*e^{x^3+4}
∫
x
2
·
e
x
3
+
4
dx
derivative of r(θ,xcos(θ))
d
dx
(
r
(
θ
,
x
)
cos
(
θ
)
)
derivative y=4arcsin(5)x^5
derivative
y
=
4
arcsin
(
5
)
x
5
테일러 (1+x)^{-1}
taylor
(
1
+
x
)
−
1
tangent y=-3x^3-2x^2-x+3,(-1,5)
tangent
y
=
−
3
x
3
−
2
x
2
−
x
+
3
,
(
−
1
,
5
)
derivative-1/(x^2)
derivative
−
1
x
2
(dy)/(dx)=20x
dy
dx
=
2
0
x
integral of x/((x^2+1))
∫
x
(
x
2
+
1
)
dx
(\partial)/(\partial x)(6x^{4y})
∂
∂
x
(
6
x
4
y
)
integral of x^3sqrt(1-x)
∫
x
3
√
1
−
x
dx
derivative of 4-(25/(6x^{1/6)})
d
dx
(
4
−
2
5
6
x
1
6
)
derivative of ln(3x^2+7)
d
dx
(
ln
(
3
x
2
+
7
)
)
tangent f(x)=x-1/x ,\at x=1
tangent
f
(
x
)
=
x
−
1
x
,
at
x
=
1
y^{''}+81y=4tan(9x)
y
′
′
+
8
1
y
=
4
tan
(
9
x
)
limit as x approaches 4 of x/4+1
lim
x
→
4
(
x
4
+
1
)
integral of 6.5sqrt(x)
∫
6
.
5
√
x
dx
inverse라플라스 ((10s+3))/(s^2+4s+29)
inverselaplace
(
1
0
s
+
3
)
s
2
+
4
s
+
2
9
limit as x approaches 0+of x^{-5}
lim
x
→
0
+
(
x
−
5
)
(\partial)/(\partial x)(8x)
∂
∂
x
(
8
x
)
integral of 4pix^2
∫
4
π
x
2
dx
normal y=8xe^x,(0,0)
normal
y
=
8
xe
x
,
(
0
,
0
)
derivative f(x)=(x^2-2e^x)/(x+3e^x)
derivative
f
(
x
)
=
x
2
−
2
e
x
x
+
3
e
x
integral of 1/3 sec^2(8x)
∫
1
3
sec
2
(
8
x
)
dx
integral of sin(2t)cos(t)
∫
sin
(
2
t
)
cos
(
t
)
dt
derivative y=(5x-4)(2x^3-x^2+1)
derivative
y
=
(
5
x
−
4
)
(
2
x
3
−
x
2
+
1
)
y^{''}+3y^'+0=5
y
′
′
+
3
y
′
+
0
=
5
integral from 0 to 1/3 of 2/(1+9x^2)
∫
0
1
3
2
1
+
9
x
2
dx
tangent f(x)=x^3-16x+5,\at x=4
tangent
f
(
x
)
=
x
3
−
1
6
x
+
5
,
at
x
=
4
integral from 0 to 2 of 1/(x^2-5x+4)
∫
0
2
1
x
2
−
5
x
+
4
dx
derivative of 2/(1+e^{-x})
d
dx
(
2
1
+
e
−
x
)
sum from n=0 to infinity of 3(-1/2)^n
∑
n
=
0
∞
3
(
−
1
2
)
n
limit as x approaches 2 of 4/((x-2)^5)
lim
x
→
2
(
4
(
x
−
2
)
5
)
tangent f(x)=x+e^x-1/x ,\at x=1
tangent
f
(
x
)
=
x
+
e
x
−
1
x
,
at
x
=
1
integral of-(2x)/(x^4-1)
∫
−
2
x
x
4
−
1
dx
limit as x approaches pi/3 of cos(x)
lim
x
→
π
3
(
cos
(
x
)
)
limit as x approaches 1 of (-x+1)/(x-1)
lim
x
→
1
(
−
x
+
1
x
−
1
)
integral of 12x^2(2x^3+3)^7
∫
1
2
x
2
(
2
x
3
+
3
)
7
dx
integral of (x+5)/(sqrt(x))
∫
x
+
5
√
x
dx
integral of (26x^3-52x^2+8)/(x^2-2x)
∫
2
6
x
3
−
5
2
x
2
+
8
x
2
−
2
x
dx
integral of cot(16x)
∫
cot
(
1
6
x
)
dx
limit as x approaches 0-of 5/(x^3)
lim
x
→
0
−
(
5
x
3
)
derivative x^{18}
derivative
x
1
8
derivative of tan(2xcot(2x))
d
dx
(
tan
(
2
x
)
cot
(
2
x
)
)
laplace변환 35
laplacetransform
3
5
derivative f(x)=5e^x+8/(\sqrt[3]{x)}
derivative
f
(
x
)
=
5
e
x
+
8
3
√
x
(\partial)/(\partial y)(x^2y-xy^2)
∂
∂
y
(
x
2
y
−
xy
2
)
derivative y=(tan(x)-1)/(sec(x))
derivative
y
=
tan
(
x
)
−
1
sec
(
x
)
y^{'''}-9y^{''}+y^'-9y=0
y
′
′
′
−
9
y
′
′
+
y
′
−
9
y
=
0
y^{''}-4y^'+3y=(2x+1)e^{-x}
y
′
′
−
4
y
′
+
3
y
=
(
2
x
+
1
)
e
−
x
limit as x approaches 0-of 0/(x^2|x|)
lim
x
→
0
−
(
0
x
2
|
x
|
)
derivative of sqrt((e^x/3))
d
dx
(
√
e
x
3
)
integral from 4y^2+4z^2 to 4 of x
∫
4
y
2
+
4
z
2
4
xdx
derivative of (x^2-1(x^3+3x))
d
dx
(
(
x
2
−
1
)
(
x
3
+
3
x
)
)
(y^2)^'
(
y
2
)
′
derivative f(x)=x^2-sqrt(x)+2
derivative
f
(
x
)
=
x
2
−
√
x
+
2
(dy)/(dx)y=x^{-12}
dy
dx
y
=
x
−
1
2
(\partial)/(\partial y)(x^2y+e^{xy})
∂
∂
y
(
x
2
y
+
e
xy
)
derivative of x+6
d
dx
(
x
+
6
)
integral of 3cos^5(x)sin^4(x)
∫
3
cos
5
(
x
)
sin
4
(
x
)
dx
integral of (4x)/(sqrt(2x^2+1))
∫
4
x
√
2
x
2
+
1
dx
limit as x approaches infinity of 1/x+2
lim
x
→
∞
(
1
x
+
2
)
y^{''}+(a+b)y=0
y
′
′
+
(
a
+
b
)
y
=
0
integral of sin^9(x)
∫
sin
9
(
x
)
dx
integral of 6/(sqrt(x+6)+\sqrt{x)}
∫
6
√
x
+
6
+
√
x
dx
integral of g(x)
∫
g
(
x
)
dx
sum from n=1 to infinity of arctan(12n)
∑
n
=
1
∞
arctan
(
1
2
n
)
integral of x(x+6)^{1/2}
∫
x
(
x
+
6
)
1
2
dx
integral of 1/(5x+2)
∫
1
5
x
+
2
dx
integral from 1 to sqrt(2 of)xe^{3x^2}
∫
1
√
2
xe
3
x
2
dx
(dy)/(dx)= y/x
dy
dx
=
y
x
(\partial)/(\partial y)((cy)/(x^2+y^2))
∂
∂
y
(
cy
x
2
+
y
2
)
(4+x)y^'=y^3
(
4
+
x
)
y
′
=
y
3
limit as x approaches 2 of 1/(sqrt(x-1))
lim
x
→
2
(
1
√
x
−
1
)
sum from i=1 to infinity of (i)*1/(6^i)
∑
i
=
1
∞
(
i
)
·
1
6
i
1
..
312
313
314
315
316
..
2459