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일반적인 미적분학 문제
derivative (ln(x))/(x^9)
derivative
ln
(
x
)
x
9
derivative 4e^{6x}+2x
derivative
4
e
6
x
+
2
x
tangent f(x)=sqrt(32-x),\at x=7
tangent
f
(
x
)
=
√
3
2
−
x
,
at
x
=
7
derivative 4sqrt(x^3)
derivative
4
√
x
3
d/(dt)(3/t)
d
dt
(
3
t
)
derivative f(x)=4tan(x)
derivative
f
(
x
)
=
4
tan
(
x
)
derivative of 2arctan(sqrt(sin(x)))
d
dx
(
2
arctan
(
√
sin
(
x
)
)
)
tangent x^2+y^2=25,(3,-4)
tangent
x
2
+
y
2
=
2
5
,
(
3
,
−
4
)
derivative 2xe^{-2x}-3e^{x^3}
derivative
2
xe
−
2
x
−
3
e
x
3
(\partial)/(\partial x)(3xsin(y))
∂
∂
x
(
3
x
sin
(
y
)
)
(\partial)/(\partial y)(7x^{y/z})
∂
∂
y
(
7
x
y
z
)
y^'+(2y)/x = 2/x
y
′
+
2
y
x
=
2
x
integral of u/(u+1)
∫
u
u
+
1
du
limit as x approaches 2 of sin(1/x-1/2)
lim
x
→
2
(
sin
(
1
x
−
1
2
)
)
integral of xsqrt(4x+1)
∫
x
√
4
x
+
1
dx
f(x)=sqrt(5)x+sqrt(7x)
f
(
x
)
=
√
5
x
+
√
7
x
(x^2+1)y^'+3x(y-1)=0,y(0)=4
(
x
2
+
1
)
y
′
+
3
x
(
y
−
1
)
=
0
,
y
(
0
)
=
4
integral of (x^3+1)/(x^3+x^2)
∫
x
3
+
1
x
3
+
x
2
dx
derivative y=e^{-x}arctan(5e^x)
derivative
y
=
e
−
x
arctan
(
5
e
x
)
derivative x^2ln(x^2+1)
derivative
x
2
ln
(
x
2
+
1
)
implicit (dy)/(dx),y^3=x^8
implicit
dy
dx
,
y
3
=
x
8
integral of ((sqrt(x)+6)^4)/(2sqrt(x))
∫
(
√
x
+
6
)
4
2
√
x
dx
derivative sin(-1(4x+1))
derivative
sin
(
−
1
(
4
x
+
1
)
)
integral from 0 to pi/2 of sin^2(t)
∫
0
π
2
sin
2
(
t
)
dt
derivative of x^9ln(8x)
d
dx
(
x
9
ln
(
8
x
)
)
derivative of ln((4x^4sin(-7x)/(3x-3)))
d
dx
(
ln
(
4
x
4
sin
(
−
7
x
)
3
x
−
3
)
)
derivative of 2/(x^3+c)
d
dx
(
2
x
3
+
c
)
integral from 3 to 6 of 1/((4-x)^2)
∫
3
6
1
(
4
−
x
)
2
dx
inverse라플라스 (s^2+3)/(2s^2+5)
inverselaplace
s
2
+
3
2
s
2
+
5
derivative of (3/4 ^{(-4)/3})
d
dx
(
(
3
4
)
−
4
3
)
(\partial)/(\partial x)(x/(x^2+y^2+1))
∂
∂
x
(
x
x
2
+
y
2
+
1
)
derivative of 2\sqrt[5]{(x^3+1^2})
d
dx
(
2
5
√
(
x
3
+
1
)
2
)
(\partial)/(\partial x)(x^{0.5})
∂
∂
x
(
x
0
.
5
)
limit as x approaches 0 of ((2+x)^2)/x
lim
x
→
0
(
(
2
+
x
)
2
x
)
integral of 6/(x^3)+16x^3
∫
6
x
3
+
1
6
x
3
dx
(\partial)/(\partial t)(e^tcos(t))
∂
∂
t
(
e
t
cos
(
t
)
)
integral of tan^3(x)*sec^3(x)
∫
tan
3
(
x
)
·
sec
3
(
x
)
dx
tangent 5x^37x,\at x=2
tangent
5
x
3
7
x
,
at
x
=
2
derivative 2e^{-x}+e^{3x}
derivative
2
e
−
x
+
e
3
x
(\partial)/(\partial x)(ln(x^2z^2))
∂
∂
x
(
ln
(
x
2
z
2
)
)
integral of (1+x)/(1-x)
∫
1
+
x
1
−
x
dx
integral of (e^x-1)^2
∫
(
e
x
−
1
)
2
dx
derivative f(x)=a^{2x}
derivative
f
(
x
)
=
a
2
x
8yy^'=x
8
yy
′
=
x
derivative 6/(x^5)-2/x
derivative
6
x
5
−
2
x
(\partial)/(\partial x)(\sqrt[3]{(x+1)^2})
∂
∂
x
(
3
√
(
x
+
1
)
2
)
(\partial)/(\partial x)(z^3-x^2y)
∂
∂
x
(
z
3
−
x
2
y
)
integral of (7-3x-9x^2)
∫
(
7
−
3
x
−
9
x
2
)
dx
derivative of (2x^2+1/(x^2+7))
d
dx
(
2
x
2
+
1
x
2
+
7
)
derivative of sin(cos(2x))
d
dx
(
sin
(
cos
(
2
x
)
)
)
sum from n=1 to infinity of 1/(5^{n-1)}
∑
n
=
1
∞
1
5
n
−
1
(\partial)/(\partial x)(cos(y-x))
∂
∂
x
(
cos
(
y
−
x
)
)
limit as x approaches-2 of 7x+12
lim
x
→
−
2
(
7
x
+
1
2
)
integral of (ln(17x))/x
∫
ln
(
1
7
x
)
x
dx
(\partial)/(\partial x)((x/2)^2)
∂
∂
x
(
(
x
2
)
2
)
integral from 0 to 1 of ln(x)
∫
0
1
ln
(
x
)
dx
derivative of (2x/(7-tan(x)))
d
dx
(
2
x
7
−
tan
(
x
)
)
integral from a to 2a of a-(a^3)/(x^2)
∫
a
2
a
a
−
a
3
x
2
dx
동등성 7ln(sec(x)+tan(x))
parity
7
ln
(
sec
(
x
)
+
tan
(
x
)
)
limit as x approaches 7 of cx+8
lim
x
→
7
(
cx
+
8
)
limit as θ approaches 0 of cot(θ)
lim
θ
→
0
(
cot
(
θ
)
)
(\partial)/(\partial y)(x^3y^5+2x^4y)
∂
∂
y
(
x
3
y
5
+
2
x
4
y
)
(\partial)/(\partial x)(-2cos(x))
∂
∂
x
(
−
2
cos
(
x
)
)
integral of 2arctan(5y)
∫
2
arctan
(
5
y
)
dy
limit as x approaches 0 of sin(5x)
lim
x
→
0
(
sin
(
5
x
)
)
derivative of ((x+1(x-2))/((x-1)(x+2)))
d
dx
(
(
x
+
1
)
(
x
−
2
)
(
x
−
1
)
(
x
+
2
)
)
f(x)=e^{x-1}-1
f
(
x
)
=
e
x
−
1
−
1
y^'-3y= y/x
y
′
−
3
y
=
y
x
integral of 6x^2-4x
∫
6
x
2
−
4
xdx
derivative of-(4e^{4/x}/(x^2))
d
dx
(
−
4
e
4
x
x
2
)
(\partial)/(\partial x)(-2e^xln(y))
∂
∂
x
(
−
2
e
x
ln
(
y
)
)
integral of (6/(5x^2)-1)
∫
(
6
5
x
2
−
1
)
dx
integral of 1/((x^2+8x+17)^2)
∫
1
(
x
2
+
8
x
+
1
7
)
2
dx
limit as x approaches 0 of (1+6x)^{4/x}
lim
x
→
0
(
(
1
+
6
x
)
4
x
)
(\partial)/(\partial x)(e^{3x^2+y}(x-y))
∂
∂
x
(
e
3
x
2
+
y
(
x
−
y
)
)
y^{''}-2y^'+y=xe^x+4
y
′
′
−
2
y
′
+
y
=
xe
x
+
4
integral of (x^2(x^3-1)^{10})
∫
(
x
2
(
x
3
−
1
)
1
0
)
dx
derivative of (e^2/(x(3x-5)))
d
dx
(
e
2
x
(
3
x
−
5
)
)
integral of (3x^2+5x+3)/((x^2+1)^2)
∫
3
x
2
+
5
x
+
3
(
x
2
+
1
)
2
dx
derivative f(x)=5x^2tan(1-sqrt(x))
derivative
f
(
x
)
=
5
x
2
tan
(
1
−
√
x
)
derivative x(x^2+7)^4
derivative
x
(
x
2
+
7
)
4
tangent 2x^3-2x^2+1
tangent
2
x
3
−
2
x
2
+
1
derivative of n*ln(x)
d
dx
(
n
·
ln
(
x
)
)
derivative of (3x^2-1/(6x^3+5))
d
dx
(
3
x
2
−
1
6
x
3
+
5
)
limit as x approaches 7+of 3/(x-7)
lim
x
→
7
+
(
3
x
−
7
)
integral from 5 to infinity of 1/(x^2-4)
∫
5
∞
1
x
2
−
4
dx
derivative of 1/(4x^2+2x)
d
dx
(
1
4
x
2
+
2
x
)
limit as x approaches 2 of 2+sqrt(3)
lim
x
→
2
(
2
+
√
3
)
derivative of (x^3+3x^2-5x+2/3)
d
dx
(
x
3
+
3
x
2
−
5
x
+
2
3
)
y^{'''}-2y^{''}-3y^'=0
y
′
′
′
−
2
y
′
′
−
3
y
′
=
0
limit as x approaches-1+of (-1)/(x^2-1)
lim
x
→
−
1
+
(
−
1
x
2
−
1
)
integral of e^{4x}sin(x)
∫
e
4
x
sin
(
x
)
dx
tangent x^2-5x+5(6.11)
tangent
x
2
−
5
x
+
5
(
6
.
1
1
)
derivative of \sqrt[4]{2^{x^3-6x}+ln(x})
d
dx
(
4
√
2
x
3
−
6
x
+
ln
(
x
)
)
integral from 1 to e^6 of 1/(x(2+ln(x)))
∫
1
e
6
1
x
(
2
+
ln
(
x
)
)
dx
derivative of csc(9x)
d
dx
(
csc
(
9
x
)
)
integral from 2 to 3 of 2/(sqrt(3-x))
∫
2
3
2
√
3
−
x
dx
integral of y/x+6x
∫
y
x
+
6
xdx
derivative of 1/x y
d
dx
(
1
x
y
)
derivative of 2e^x+4/(\sqrt[3]{x})
d
dx
(
2
e
x
+
4
3
√
x
)
1
..
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478
479
480
481
..
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