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Popular Calculus Problems
derivative of e^x(sin(x+cos(x)))
d
dx
(
e
x
(
sin
(
x
)
+
cos
(
x
)
)
)
taylor x^3-2x^2+3x+5(2)
taylor
x
3
−
2
x
2
+
3
x
+
5
(
2
)
integral from e^2 to e^5 of (1/x)
∫
e
2
e
5
(
1
x
)
dx
slope ofintercept (2,5),(0,-9)
slopeintercept
(
2
,
5
)
,
(
0
,
−
9
)
derivative of u/(u^2+5)
derivative
u
u
2
+
5
integral of e^{(-0.1x)}
∫
e
(
−
0
.
1
x
)
dx
derivative of x^2-x+5
d
dx
(
x
2
−
x
+
5
)
integral from-1 to 1 of x^3-3x^2-x+3
∫
−
1
1
x
3
−
3
x
2
−
x
+
3
dx
integral of (5x^2+7x+5)/((x^2+1)^2)
∫
5
x
2
+
7
x
+
5
(
x
2
+
1
)
2
dx
derivative of (x+5(x-1)(x-7))
d
dx
(
(
x
+
5
)
(
x
−
1
)
(
x
−
7
)
)
integral of sin^5(xco)s^6x
∫
sin
5
(
xco
)
s
6
xdx
derivative of f(x)=(x^3-7x^2+7)/(x^2)
derivative
f
(
x
)
=
x
3
−
7
x
2
+
7
x
2
(\partial)/(\partial x)(y^6sin(2x))
∂
∂
x
(
y
6
sin
(
2
x
)
)
limit as x approaches infinity of-3x
lim
x
→
∞
(
−
3
x
)
derivative of a+1/x
d
dx
(
a
+
1
x
)
area 1-x^2,x^2
area
1
−
x
2
,
x
2
integral from 0 to 1 of 4x^4e^{-x}
∫
0
1
4
x
4
e
−
x
dx
derivative of (7^2)/y-ln(y)-1
derivative
7
2
y
−
ln
(
y
)
−
1
derivative of 2*5^x
derivative
2
·
5
x
integral of (10x)/(sqrt(64x^4-49))
∫
1
0
x
√
6
4
x
4
−
4
9
dx
derivative of sin(xtan(x))
d
dx
(
sin
(
x
)
tan
(
x
)
)
((f(x))^2)'
(
(
f
(
x
)
)
2
)
′
derivative of cos(2xe^{2x})
d
dx
(
cos
(
2
x
)
e
2
x
)
limit as x approaches 1 of \sqrt[3]{(x^3-1)/(x^2-3x+2)}
lim
x
→
1
(
3
√
x
3
−
1
x
2
−
3
x
+
2
)
limit as x approaches-1 of (2x+3)/(x+1)
lim
x
→
−
1
(
2
x
+
3
x
+
1
)
(2e^x)^'
(
2
e
x
)
′
integral from 0 to 6 of 1/((x-4)^{2/3)}
∫
0
6
1
(
x
−
4
)
2
3
dx
integral of 9cos(sqrt(x))
∫
9
cos
(
√
x
)
dx
integral of (5x^4+4)/(x^5+4x)
∫
5
x
4
+
4
x
5
+
4
x
dx
integral from 0 to pi/4 of sec^2(t)
∫
0
π
4
sec
2
(
t
)
dt
(dy)/(dx)=(1-2x)/(4x-x^2)
dy
dx
=
1
−
2
x
4
x
−
x
2
derivative of y+6y^3
derivative
y
+
6
y
3
slope of f(x)=(x-x^2)/(3x^2+2)
slope
f
(
x
)
=
x
−
x
2
3
x
2
+
2
integral of (3x^2)/5+(7x^3)/8
∫
3
x
2
5
+
7
x
3
8
dx
integral of-10x^5e^{x^6}
∫
−
1
0
x
5
e
x
6
dx
integral of 3/(x(x+1))
∫
3
x
(
x
+
1
)
dx
integral of ((x^3-1))/(x(x+1)^2)
∫
(
x
3
−
1
)
x
(
x
+
1
)
2
dx
integral of sec(3x)tan(3x)
∫
sec
(
3
x
)
tan
(
3
x
)
dx
integral of (3/x-(10)/(x^6))
∫
(
3
x
−
1
0
x
6
)
dx
derivative of 1/((2x+1^3))
d
dx
(
1
(
2
x
+
1
)
3
)
integral of 1+t
∫
1
+
tdt
derivative of ((x+30sqrt(x^2+100))/x)
d
dx
(
(
x
+
3
0
)
√
x
2
+
1
0
0
x
)
derivative of f(x)=sqrt(9+\sqrt{4x)}
derivative
f
(
x
)
=
√
9
+
√
4
x
integral of x^5+8x^3-9x^2+7x-5
∫
x
5
+
8
x
3
−
9
x
2
+
7
x
−
5
dx
integral of-x^3+1/(x^2)
∫
−
x
3
+
1
x
2
dx
integral of (4e^{-3/(x^5)})/(x^6)
∫
4
e
−
3
x
5
x
6
dx
(\partial)/(\partial y)((x+y)e^{y^2})
∂
∂
y
(
(
x
+
y
)
e
y
2
)
laplacetransform 3t+4
laplacetransform
3
t
+
4
derivative of f(x)=sqrt(x^3+x^2+x+1)
derivative
f
(
x
)
=
√
x
3
+
x
2
+
x
+
1
derivative of sqrt(x)-1/(\sqrt[4]{x})
d
dx
(
√
x
−
1
4
√
x
)
integral of e^xcos(e^x)
∫
e
x
cos
(
e
x
)
dx
area y=e^{3x},y=e^x,[0,1]
area
y
=
e
3
x
,
y
=
e
x
,
[
0
,
1
]
xy^'-y=y^3
xy
′
−
y
=
y
3
integral from 0 to 9 of x/((x+9)^4)
∫
0
9
x
(
x
+
9
)
4
dx
integral from 1 to 2 of (x-2)^{-2}
∫
1
2
(
x
−
2
)
−
2
dx
derivative of 2/(x^6)
derivative
2
x
6
integral from 0 to 1 of sin(pixcos(pi)x)
∫
0
1
sin
(
π
x
cos
(
π
)
x
)
dx
integral of \sqrt[3]{x}(x-4)
∫
3
√
x
(
x
−
4
)
dx
integral of 4x^3+1
∫
4
x
3
+
1
dx
tangent of f(x)=x^3-9x(3)
tangent
f
(
x
)
=
x
3
−
9
x
(
3
)
tangent of f(x)=tan^2(x),\at x=(-pi)/4
tangent
f
(
x
)
=
tan
2
(
x
)
,
at
x
=
−
π
4
(\partial)/(\partial x)((2x-5y)^2)
∂
∂
x
(
(
2
x
−
5
y
)
2
)
integral of y^3+10xy^4-2x
∫
y
3
+
1
0
xy
4
−
2
xdx
limit as x approaches-4-of (x+3)/(x+4)
lim
x
→
−
4
−
(
x
+
3
x
+
4
)
derivative of f(x)=xsqrt(8-x^2)
derivative
f
(
x
)
=
x
√
8
−
x
2
derivative of (x+2/(x+3))
d
dx
(
x
+
2
x
+
3
)
integral of 0.02
∫
0
.
0
2
integral of (sin(x))/(sqrt(7-cos^2(x)))
∫
sin
(
x
)
√
7
−
cos
2
(
x
)
dx
integral of (x^3-11x-26)/(x^2-2x-8)
∫
x
3
−
1
1
x
−
2
6
x
2
−
2
x
−
8
dx
integral of 1/(sin^4(3x)cos^2(3x))
∫
1
sin
4
(
3
x
)
cos
2
(
3
x
)
dx
d/(dy)((x+y)^2)
d
dy
(
(
x
+
y
)
2
)
derivative of (x^2)/(x^2-1)
derivative
x
2
x
2
−
1
limit as x approaches 0 of 6/(x^2)
lim
x
→
0
(
6
x
2
)
derivative of cos(θ)-θsin(θ)
derivative
cos
(
θ
)
−
θ
sin
(
θ
)
derivative of (ax+b/(cx-a))
d
dx
(
ax
+
b
cx
−
a
)
area x^2-3,y=1
area
x
2
−
3
,
y
=
1
derivative of (ln(x)^{cos(4x)})
d
dx
(
(
ln
(
x
)
)
cos
(
4
x
)
)
derivative of (x^2)/(12)
derivative
x
2
1
2
limit as x approaches+3-of sin(pi+x)+1
lim
x
→
+
3
−
(
sin
(
π
+
x
)
+
1
)
area y=20-x^2\land y=2x+5,-2<= x<= 8
area
y
=
2
0
−
x
2
and
y
=
2
x
+
5
,
−
2
≤
x
≤
8
integral of (22)/((121x^2+1)^2)
∫
2
2
(
1
2
1
x
2
+
1
)
2
dx
(\partial)/(\partial x)(xyz-cos(x+y+z))
∂
∂
x
(
xyz
−
cos
(
x
+
y
+
z
)
)
integral of-ge^{-ct} 1/c
∫
−
ge
−
ct
1
c
dt
(\partial)/(\partial x)(4x^2+2xy-8y^2)
∂
∂
x
(
4
x
2
+
2
xy
−
8
y
2
)
(\partial)/(\partial x)(-y/(x^2+y^2))
∂
∂
x
(
−
y
x
2
+
y
2
)
(\partial)/(\partial x)(tan(4+2x^2y^4z^2))
∂
∂
x
(
tan
(
4
+
2
x
2
y
4
z
2
)
)
integral of (-3cos(x)+4sec^2(x))
∫
(
−
3
cos
(
x
)
+
4
sec
2
(
x
)
)
dx
derivative of ye^{2x}
d
dx
(
ye
2
x
)
f(x)= x/7
f
(
x
)
=
x
7
limit as x approaches 0 of (sin^4(2x))/(4x^4)
lim
x
→
0
(
sin
4
(
2
x
)
4
x
4
)
(dv)/(dt)=0.64-v/(2940)*8,v(0)=0
dv
dt
=
0
.
6
4
−
v
2
9
4
0
·
8
,
v
(
0
)
=
0
integral of (t^3-3t)(2t)
∫
(
t
3
−
3
t
)
(
2
t
)
dt
(dx)/(dt)=8xt^5
dx
dt
=
8
xt
5
integral of sin^2(x)cos^3(x)
∫
sin
2
(
x
)
cos
3
(
x
)
dx
xy+y^2-x^2y^'=0
xy
+
y
2
−
x
2
y
′
=
0
derivative of 5^{x+2}
d
dx
(
5
x
+
2
)
derivative of 2/(7x^4)
d
dx
(
2
7
x
4
)
(\partial)/(\partial x)(cos(x^5+y))
∂
∂
x
(
cos
(
x
5
+
y
)
)
integral of 2xe^y
∫
2
xe
y
dx
derivative of f(x)=((x+3)(x+1))/(x^2-49)
derivative
f
(
x
)
=
(
x
+
3
)
(
x
+
1
)
x
2
−
4
9
1
..
1366
1367
1368
1369
1370
..
2459