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Popular Calculus Problems

(d^2-6d+9)y=0	(`d`²−6`d`+9)`y`=0
x^{'''}-2x^{''}=0	`x`^{′ ′ ′}−2`x`^{′ ′}=0
(x+1)y^'=y^2	(`x`+1)`y`^′=`y`²
y^'x^2=y	`y`^′`x`²=`y`
x^'=4x+2e^t*x	`x`^′=4`x`+2`e`^t· `x`
y^'=-4xy^2	`y`^′=−4`xy`²
(xy+x^3y)y^'=1+y^2	(`xy`+`x`³`y`)`y`^′=1+`y`²
y^'+sin(x)y=5sin(x)	`y`^′+sin(`x`)`y`=5sin(`x`)
y^'=3x+e^x	`y`^′=3`x`+`e`^x
y^'ye^{-x}=0	`y`^′`ye`^−x=0
f^{''}(x)=3x+1	`f`^{′ ′}(`x`)=3`x`+1
2y^{'''}=e^xy^{'''}	2`y`^{′ ′ ′}=`e`^x`y`^{′ ′ ′}
f^'(x)=4x+9	`f`^′(`x`)=4`x`+9
2y^'+y^3=0	2`y`^′+`y`³=0
2x^2y^'=x^2+y^2	2`x`²`y`^′=`x`²+`y`²
x^3y^{'''}-x^2y^'=0	`x`³`y`^{′ ′ ′}−`x`²`y`^′=0
5x(x+4y)y^'=5y(x-4y)	5`x`(`x`+4`y`)`y`^′=5`y`(`x`−4`y`)
3y^'+7y=x^3-2x^2+1	3`y`^′+7`y`=`x`³−2`x`²+1
y^'=xy-3x+3y+3y-9	`y`^′=`x`· `y`−3· `x`+3· `y`+3· `y`−9
y^'=y+e^x,y(0)=(x+c)e^x,y(0)= 1/2	`y`^′=`y`+`e`^x,`y`(0)=(`x`+`c`)`e`^x,`y`(0)=12
y^'=(x+y)2	`y`^′=(`x`+`y`)2
y^'=2y+(x^2)+5	`y`^′=2`y`+(`x`²)+5
(x-1)y^'+xy=sin(x)	(`x`−1)`y`^′+`xy`=sin(`x`)
y^'-y=2xe^{2x}	`y`^′−`y`=2· `x`· `e`^2x
y^'+y+e^{-x}=0	`y`^′+`y`+`e`^−x=0
y^'=2xy+1	`y`^′=2`xy`+1
(y^')/(t+3y)=3	`y`^′`t`+3`y` =3
1+xy=xy^'	1+`xy`=`xy`^′
Find the Antiderivative f(x)=5x-6	`integral` `f`(`x`)=5`x`−6
Using L'Hospital's Rule limit as x approaches 0 of (e^(5x)-1-5x)/(x^2)	`lhopital` lim _{x→ 0}((`e`^5x−1−5`x`)(`x`²) )
Find the Derivative - d/dx y=4/x	`ddx` `y`=4`x`
Find the Derivative - d/dx 1/x	`derivative` `ddx` (1`x` )
Find the Derivative - d/dx y=3x	`ddx` `y`=3`x`
Find the Slope (2,5) , (3,6)	`slope` (2,5),(3,6)
Find the Difference Quotient f(x)=4x+3	`diffquot` `f`=4`x`+3
Find the Antiderivative cos(theta)	`integral` cos(θ)
Find the Derivative - d/dx cos(x)	`derivative` `ddx` (cos(`x`))
Evaluate the Integral integral of 1/(e^x) with respect to x	∫ (1(`e`^x) )`dx`
Find the Derivative - d/dx y=sec(x)+tan(x)	`ddx` `y`=sec(`x`)+tan(`x`)
Divide infinity/2	`longdivision` lim _{x→ ∞}(`x`2 )
Find the Antiderivative sin(theta)	`integral` sin(θ)
Find the Derivative - d/dx csc(x)	`derivative` `ddx` (csc(`x`))
Find the Derivative - d/dx 1/(1-x)	`derivative` `ddx` (1(1−`x`) )
Find the 2nd Derivative y=cos(x)	`secondderivative` `y`=cos(`x`)
Find the Derivative - d/dx y=sinh(cosh(x))	`ddx` `y`=sinh(cosh(`x`))
Evaluate the Difference Quotient (f(x+h)-f(x))/h , f(x)=3/(x^2)	`diffquot` `f`=(`f`(`x`+`h`)−`f`)`h`
Find the Derivative - d/dx sec(2x)	`derivative` `ddx` (sec(2`x`))
Find the Derivative - d/dx y=xe^x	`ddx` `y`=`xe`^x
Find the Derivative - d/dx x/2	`derivative` `ddx` (`x`2 )
Find the Antiderivative square root of X	`integral` √`X`
Find the Derivative - d/dx e^(-x/2)	`derivative` `ddx` (`e`^−x2)
Find the Antiderivative f(x)=sin(x)	`integral` `f`(`x`)=sin(`x`)
Find the Derivative - d/dx cos(x)^2	`derivative` `ddx` (cos²(`x`))
Find the Derivative - d/dx (d^2y)/(dx^2)	`derivative` `ddx` ((`d`²`y`(`d`,`x`))(`dx`²) )
Evaluate the Integral integral of sec(theta) with respect to theta	∫ (sec(θ))`d`θ
Find the Derivative - d/dx y=csc(x)^2	`ddx` `y`=csc²(`x`)
Find the Antiderivative 1/(x^-2)	`integral` 1(`x`⁻²)
Find the Derivative - d/dx sin(2x)	`derivative` `ddx` (sin(2`x`))
Find the Derivative - d/dx 1/(1+x^2)	`derivative` `ddx` (1(1+`x`²) )
Find the Derivative - d/dx y=5x	`ddx` `y`=5`x`
Find the Slope (-4,2) , (4,-4)	`slope` (−4,2),(4,−4)
Find the Derivative - d/dx sin(x^2)	`derivative` `ddx` (sin(`x`²))
Evaluate the Integral integral of e^(xy) with respect to x	∫ (`e`^xy)`dx`
Find the Derivative - d/dx sec(x)^2	`derivative` `ddx` (sec²(`x`))
Find the Derivative - d/dx y=2e^x	`ddx` `y`=2`e`^x
Find the Derivative - d/dx xcos(x)	`derivative` `ddx` (`x`cos(`x`))
Find the Derivative - d/dx cos(x)sec(x)	`derivative` `ddx` (cos(`x`)sec(`x`))
Find the Derivative - d/dx e^(3x)	`derivative` `ddx` (`e`^3x)
Find the Slope (4,0) , (0,3)	`slope` (4,0),(0,3)
Divide infinity/4	`longdivision` lim _{x→ ∞}(`x`4 )
Find dy/dx y=cos(x)	`dydx` `y`=cos(`x`)
Find the Derivative - d/dx cos(3x)	`derivative` `ddx` (cos(3`x`))
Find the Second Derivative f(x)=arctan(x)	`secondderivative` `f`(`x`)=arctan(`x`)
Find the Derivative - d/dx e^(-2x)	`derivative` `ddx` (`e`^−2x)
Find the Derivative - d/dx xy	`derivative` `ddx` (`xy`)
Find the Volume y=0 , x=2 , y = square root of x	`volumeabout` `x`,`y`=0,`x`=2,`y`=√`x`
Find the Antiderivative csc(x)cot(x)	`integral` csc(`x`)cot(`x`)
Find the Derivative - d/dx x/(x+1)	`derivative` `ddx` (`x`(`x`+1) )
Find the Antiderivative -1/u	`integral` −1`u`
Find dy/dx y=2x	`dydx` `y`=2`x`
Find the Derivative - d/dx x^(1/2)	`derivative` `ddx` (`x`¹²)
Find the Derivative - d/dx y=sin(x)	`ddx` `y`=sin(`x`)
Find the 2nd Derivative f(x)=cos(2x)	`secondderivative` `f`(`x`)=cos(2`x`)
Find the Derivative - d/dy -2y	`derivative` `ddy` (−2`y`)
Find the Derivative - d/dx 2x	`derivative` `ddx` (2`x`)
Find the Derivative - d/dx sin(3x)	`derivative` `ddx` (sin(3`x`))
Find the Derivative - d/dx 2cos(x)	`derivative` `ddx` (2cos(`x`))
Find the Derivative - d/dx 1/(2x)	`derivative` `ddx` (1(2`x`) )
Find the Derivative - d/dx y=5/x	`ddx` `y`=5`x`
Find the Derivative - d/dx y=(sec(x))/x	`ddx` `y`=(sec(`x`))`x`
Find the Derivative - d/dx tan(2x)	`derivative` `ddx` (tan(2`x`))
Find the Derivative - d/dx 1-sin(x)	`derivative` `ddx` (1−sin(`x`))
Find the Antiderivative f(x)=cos(2x)	`integral` `f`(`x`)=cos(2`x`)
Find the Derivative - d/dθ sin(theta)cos(theta)	`derivative` `dd`θ (sin(θ)cos(θ))
Find the Slope (4,5) , (9,11)	`slope` (4,5),(9,11)
Find the Derivative - d/dx c/x	`derivative` `ddx` (`cx` )
Find the Derivative - d/dt e^t	`derivative` `ddt` (`e`^t)
Find the Integral 1/(y^2)	∫ 1(`y`²) `dy`
Find the Derivative - d/dx (e^x)/x	`derivative` `ddx` ((`e`^x)`x` )
limit as x approaches infinity of ( square root of x+x^2)/(2x-x^2)	lim _{x→ ∞}(`x`,`x`,(√`x`+`x`²)(2`x`−`x`²) )