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일반적인 미적분학 문제
integral of 3e^{2t}
∫
3
e
2
t
dt
integral of 6e^{5x+e^{5x}}
∫
6
e
5
x
+
e
5
x
dx
d/(dy)(-x/y)
d
dy
(
−
x
y
)
limit as x approaches infinity of ax^2
lim
x
→
∞
(
ax
2
)
integral of (3x)/(e^x)
∫
3
x
e
x
dx
derivative of x^2sin(1/(ax))
d
dx
(
x
2
sin
(
1
ax
)
)
limit as x approaches 1-of 2/(x^2-1)
lim
x
→
1
−
(
2
x
2
−
1
)
derivative of e^{-1/2 x^2}
d
dx
(
e
−
1
2
x
2
)
limit as x approaches 4 of sqrt(x^2+9)
lim
x
→
4
(
√
x
2
+
9
)
derivative f(x)=(5+x^4)^{3x}
derivative
f
(
x
)
=
(
5
+
x
4
)
3
x
(\partial)/(\partial y)(x^3+ky^2-5xy)
∂
∂
y
(
x
3
+
ky
2
−
5
xy
)
derivative of (x^2-7^2)
d
dx
(
(
x
2
−
7
)
2
)
tangent y=-(8x)/(x^2+1)
tangent
y
=
−
8
x
x
2
+
1
tangent f(x)=(e^x)/(x+6),(0, 1/6)
tangent
f
(
x
)
=
e
x
x
+
6
,
(
0
,
1
6
)
derivative f(x)=(x+2sqrt(x))e^x
derivative
f
(
x
)
=
(
x
+
2
√
x
)
e
x
integral of (13)/(13+e^x)
∫
1
3
1
3
+
e
x
dx
(dy)/(dx)=6-3x^2
dy
dx
=
6
−
3
x
2
integral of e^x*x^{-1}
∫
e
x
·
x
−
1
dx
(dy}{dx}=\frac{4sqrt(y)ln(x))/x
dy
dx
=
4
√
y
ln
(
x
)
x
경사지intercept (1.23)(2.46)
slopeintercept
(
1
.
2
3
)
(
2
.
4
6
)
integral from pi/2 to pi of 2cot(x/2)
∫
π
2
π
2
cot
(
x
2
)
dx
f(x)=(xcos(x)-sin(x))/(x^2)
f
(
x
)
=
x
cos
(
x
)
−
sin
(
x
)
x
2
limit as x approaches-3-of 1/((x+3)^4)
lim
x
→
−
3
−
(
1
(
x
+
3
)
4
)
derivative (11)/x
derivative
1
1
x
derivative (cot(x))/(sin(x))
derivative
cot
(
x
)
sin
(
x
)
derivative of csc^3(pixarccot(sin(x)))
d
dx
(
csc
3
(
π
x
)
arccot
(
sin
(
x
)
)
)
derivative of x^3-6x
d
dx
(
x
3
−
6
x
)
limit as x approaches 0-of 12e^{(-2)/x}
lim
x
→
0
−
(
1
2
e
−
2
x
)
integral of e^{-x/(0.2)}
∫
e
−
x
0
.
2
dx
integral of t/(sqrt(t+3))
∫
t
√
t
+
3
dt
integral from 5 to 6 of xsqrt(x-5)
∫
5
6
x
√
x
−
5
dx
integral of (2e^{3x})/(5-4e^{3x)}
∫
2
e
3
x
5
−
4
e
3
x
dx
y^{'''}-12y^{''}+47y^'-66y=0
y
′
′
′
−
1
2
y
′
′
+
4
7
y
′
−
6
6
y
=
0
integral of (ln(2x^5))/(x^2)
∫
ln
(
2
x
5
)
x
2
dx
integral of-(2000x)/(sqrt(25-x^2))
∫
−
2
0
0
0
x
√
2
5
−
x
2
dx
integral of-18x^{-19}
∫
−
1
8
x
−
1
9
dx
integral of 0.0012h^2
∫
0
.
0
0
1
2
h
2
dh
limit as x approaches pi of x+cos(x)
lim
x
→
π
(
x
+
cos
(
x
)
)
integral of (sqrt(9x^2-25))/(x^3)
∫
√
9
x
2
−
2
5
x
3
dx
derivative (8x^7)/(5y^4)
derivative
8
x
7
5
y
4
inverse라플라스 1/(s*(s+1)^2)
inverselaplace
1
s
·
(
s
+
1
)
2
derivative 9^x
derivative
9
x
integral of (sin^2(θ))/(cos(θ))
∫
sin
2
(
θ
)
cos
(
θ
)
d
θ
limit as x approaches 5 of sqrt(x^2+24)
lim
x
→
5
(
√
x
2
+
2
4
)
integral of sin(7x)*cos(3x)
∫
sin
(
7
x
)
·
cos
(
3
x
)
dx
derivative of |x-5|
d
dx
(
|
x
−
5
|
)
경사지 (-5.6)(4)
slope
(
−
5
.
6
)
(
4
)
integral of 1/(4x^2-8x+32)
∫
1
4
x
2
−
8
x
+
3
2
dx
integral of sqrt(1+5x^3)(15x^2)
∫
√
1
+
5
x
3
(
1
5
x
2
)
dx
integral of (c_{1})/(xcos^2(ln(x)))
∫
c
1
x
cos
2
(
ln
(
x
)
)
dx
limit as x approaches 1 of-x+1
lim
x
→
1
(
−
x
+
1
)
derivative of (ae^{x/2}/2-be^{-x})
d
dx
(
ae
x
2
2
−
be
−
x
)
derivative of 1/(sqrt(-25x^2+2y^2-50))
d
dx
(
1
√
−
2
5
x
2
+
2
y
2
−
5
0
)
limit as x approaches 4 of x+sqrt(x)
lim
x
→
4
(
x
+
√
x
)
derivative y=ln(xsqrt(x^2-2))
derivative
y
=
ln
(
x
√
x
2
−
2
)
경사지 (6,-1),(8,3)
slope
(
6
,
−
1
)
,
(
8
,
3
)
derivative of (ln(x)/(x^{6/5)})
d
dx
(
ln
(
x
)
x
6
5
)
derivative dln(x)+ax^n+be^x
derivative
d
ln
(
x
)
+
ax
n
+
be
x
integral from 0 to 7 of sqrt(1+x)
∫
0
7
√
1
+
x
dx
derivative f(x)=4sqrt(x)sin(x)
derivative
f
(
x
)
=
4
√
x
sin
(
x
)
integral of cos^2(2x)2
∫
cos
2
(
2
x
)
2
dx
limit as x approaches 0-of 5/x-5/x
lim
x
→
0
−
(
5
x
−
5
x
)
derivative sin(2x+1)
derivative
sin
(
2
x
+
1
)
derivative of (3x/(sqrt(2x+3)))
d
dx
(
3
x
√
2
x
+
3
)
x(dy)/(dx)=y+(x^2-4)^2
x
dy
dx
=
y
+
(
x
2
−
4
)
2
derivative of sinh(3x)
d
dx
(
sinh
(
3
x
)
)
지역 y=x^3,y=4x
area
y
=
x
3
,
y
=
4
x
integral of-9x^2+9x+2
∫
−
9
x
2
+
9
x
+
2
dx
limit as x approaches 1 of ((x^3))/(x-1)
lim
x
→
1
(
(
x
3
)
x
−
1
)
integral of 3xln(x)
∫
3
x
ln
(
x
)
dx
derivative of 7cos(2x)
d
dx
(
7
cos
(
2
x
)
)
derivative 10^x
derivative
1
0
x
integral of (x-1)/((x+3)^2)
∫
x
−
1
(
x
+
3
)
2
dx
integral from 0 to 1 of (x^{10}+10^x)
∫
0
1
(
x
1
0
+
1
0
x
)
dx
y'-2/t y=t^2e^t
y
′
−
2
t
y
=
t
2
e
t
integral of (3x-4)e^x
∫
(
3
x
−
4
)
e
x
dx
integral of sin(x/2)cos(x/2)
∫
sin
(
x
2
)
cos
(
x
2
)
dx
(\partial)/(\partial y)(4z)
∂
∂
y
(
4
z
)
derivative f(x)=1-(49)/(x^2)
derivative
f
(
x
)
=
1
−
4
9
x
2
integral of x^{-11}
∫
x
−
1
1
dx
integral of 2/(\sqrt[4]{x^3)}
∫
2
4
√
x
3
dx
tangent f(x)=(3x)/(x+1),(2,2)
tangent
f
(
x
)
=
3
x
x
+
1
,
(
2
,
2
)
integral from 0 to 3 of xsqrt(1+2x)
∫
0
3
x
√
1
+
2
x
dx
integral of (y^2+ln(x))
∫
(
y
2
+
ln
(
x
)
)
dy
integral from 0 to 5 of 7x-x^2-2x
∫
0
5
7
x
−
x
2
−
2
xdx
limit as x approaches 0 of sec(x)
lim
x
→
0
(
sec
(
x
)
)
integral of (x^4+2x+1)/(x^3-x^2-2x)
∫
x
4
+
2
x
+
1
x
3
−
x
2
−
2
x
dx
derivative f(x)=e^{ex}
derivative
f
(
x
)
=
e
ex
y^{''}-4y^'+3y=0,y(0)=-4,y^'(0)=5
y
′
′
−
4
y
′
+
3
y
=
0
,
y
(
0
)
=
−
4
,
y
′
(
0
)
=
5
(\partial)/(\partial x)(sqrt(33-3x^2-3y^2))
∂
∂
x
(
√
3
3
−
3
x
2
−
3
y
2
)
tangent f(x)= x/(x^2-1),\at x=2
tangent
f
(
x
)
=
x
x
2
−
1
,
at
x
=
2
derivative (5x^6+2x^3)^4
derivative
(
5
x
6
+
2
x
3
)
4
derivative f(x)=(5+x)(12-x)-2.2x
derivative
f
(
x
)
=
(
5
+
x
)
(
1
2
−
x
)
−
2
.
2
x
derivative of sec^2(pix)
d
dx
(
sec
2
(
π
x
)
)
derivative y=x^2+1
derivative
y
=
x
2
+
1
derivative of (x^4/(4-x^3))
d
dx
(
x
4
4
−
x
3
)
derivative cos(x)-4tan(x)
derivative
cos
(
x
)
−
4
tan
(
x
)
(\partial)/(\partial x)(8-x^2-3y^2)
∂
∂
x
(
8
−
x
2
−
3
y
2
)
derivative (2x^3+4)(x^4-4x)
derivative
(
2
x
3
+
4
)
(
x
4
−
4
x
)
derivative 6/(x^3)-6/(x^2)-1/x+350
derivative
6
x
3
−
6
x
2
−
1
x
+
3
5
0
1
..
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