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Popular Calculus Problems

derivative of e^{xsqrt(9x+10)}	derivative\:e^{x\sqrt{9x+10}}
integral of e^{cos(x)}sin(x)	\int\:e^{\cos(x)}\sin(x)dx
(\partial)/(\partial x)(-2sin(x))	\frac{\partial\:}{\partial\:x}(-2\sin(x))
y^{''}-2y^'-3y=0,y(0)=2,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=0,y(0)=2,y^{\prime\:}(0)=2
(y+4)y^'=2xy+4y	(y+4)y^{\prime\:}=2xy+4y
taylor 1/(X-1),12	taylor\:\frac{1}{X-1},12
derivative of 2x^3-2x	\frac{d}{dx}(2x^{3}-2x)
integral of xsin(s)	\int\:x\sin(s)dx
derivative of y=(7)(6^{sqrt(x-8)})	derivative\:y=(7)(6^{\sqrt{x-8}})
x^2(dy)/(dx)+4xy-e^x=0	x^{2}\frac{dy}{dx}+4xy-e^{x}=0
(2y-8x^2)dx+xdy=0	(2y-8x^{2})dx+xdy=0
derivative of e^{x*sin(x})	\frac{d}{dx}(e^{x\cdot\:\sin(x)})
limit as x approaches 2+of 1/(x-2)	\lim\:_{x\to\:2+}(\frac{1}{x-2})
derivative of f(x)=(arcsin(5x+3))^3	derivative\:f(x)=(\arcsin(5x+3))^{3}
y^{''}-y^'-2y=x^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=x^{2}
derivative of (3x-1^3)	\frac{d}{dx}((3x-1)^{3})
integral of (ln(x+4))/(x^2)	\int\:\frac{\ln(x+4)}{x^{2}}dx
derivative of sqrt(9+\sqrt{4x)}	\frac{d}{dx}(\sqrt{9+\sqrt{4x}})
(\partial)/(\partial x)(2cos(x+2y))	\frac{\partial\:}{\partial\:x}(2\cos(x+2y))
derivative of x^2sin^4(x)+xcos^{-2}(x)	derivative\:x^{2}\sin^{4}(x)+x\cos^{-2}(x)
integral of (x^2-x)/(x+1)	\int\:\frac{x^{2}-x}{x+1}dx
(\partial)/(\partial x)(4y^3cos(3x))	\frac{\partial\:}{\partial\:x}(4y^{3}\cos(3x))
derivative of h(x)=e^x	derivative\:h(x)=e^{x}
limit as x approaches infinity of 1+2x	\lim\:_{x\to\:\infty\:}(1+2x)
sum from n=1 to infinity of (n+1)^2	\sum\:_{n=1}^{\infty\:}(n+1)^{2}
integral of 5e^x-8cosh(x)	\int\:5e^{x}-8\cosh(x)dx
integral of 3(x+10)^3	\int\:3(x+10)^{3}dx
derivative of f(x)=x^x	derivative\:f(x)=x^{x}
limit as z approaches-3 of 3/(12-4z)	\lim\:_{z\to\:-3}(\frac{3}{12-4z})
(\partial)/(\partial y)(ysin(x)y)	\frac{\partial\:}{\partial\:y}(y\sin(x)y)
derivative of (x-0.1(x-0.5)(x-0.6))	\frac{d}{dx}((x-0.1)(x-0.5)(x-0.6))
derivative of x^2(6-x^3)	\frac{d}{dx}(x^{2}(6-x)^{3})
integral of 1/(x^2+8x+20)	\int\:\frac{1}{x^{2}+8x+20}dx
limit as x approaches 0 of 4/x-4/(\|x\|)	\lim\:_{x\to\:0}(\frac{4}{x}-\frac{4}{\left\|x\right\|})
y^'+y=5sin(2x)	y^{\prime\:}+y=5\sin(2x)
(\partial)/(\partial x)(sin(nx)e^{-n^2t})	\frac{\partial\:}{\partial\:x}(\sin(nx)e^{-n^{2}t})
limit as x approaches infinity of 1-e^x	\lim\:_{x\to\:\infty\:}(1-e^{x})
limit as x approaches-1 of x^2+4	\lim\:_{x\to\:-1}(x^{2}+4)
integral of 1/(5+sqrt(2x))	\int\:\frac{1}{5+\sqrt{2x}}dx
integral of sqrt(x)-9cos(x)	\int\:\sqrt{x}-9\cos(x)dx
area y= 5/x ,y= 5/(x^2),x=6	area\:y=\frac{5}{x},y=\frac{5}{x^{2}},x=6
limit as x approaches 0 of x^{x^x}	\lim\:_{x\to\:0}(x^{x^{x}})
(x^2+1)(dy)/(dx)+xy-x=0	(x^{2}+1)\frac{dy}{dx}+xy-x=0
derivative of 2^{7x}	\frac{d}{dx}(2^{7x})
sum from n=0 to infinity of 3(x-2)^n	\sum\:_{n=0}^{\infty\:}3(x-2)^{n}
tangent of x^2-14x+48	tangent\:x^{2}-14x+48
derivative of (e^{5x^2-2x}/(cot(7^x)))	\frac{d}{dx}(\frac{e^{5x^{2}-2x}}{\cot(7^{x})})
derivative of 8cos^3(x)	\frac{d}{dx}(8\cos^{3}(x))
derivative of arctan(sqrt(8x^2-1))	derivative\:\arctan(\sqrt{8x^{2}-1})
(\partial)/(\partial x)(1/(sin(x^2-y^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sin(x^{2}-y^{2})})
derivative of 6x	derivative\:6x
y^{''}+a=0	y^{\prime\:\prime\:}+a=0
xy^'+2y=((3e^{-3x}))/x	xy^{\prime\:}+2y=\frac{(3e^{-3x})}{x}
f^'(x)=x^4	f^{\prime\:}(x)=x^{4}
integral of sec^4(θ)	\int\:\sec^{4}(θ)dθ
s	s
(\partial)/(\partial y)(xe^{6y})	\frac{\partial\:}{\partial\:y}(xe^{6y})
derivative of (2^{3x}/(ln(3)))	\frac{d}{dx}(\frac{2^{3x}}{\ln(3)})
integral of sin(5x-3)	\int\:\sin(5x-3)dx
derivative of f(x)=sqrt((x^2)sin(x-2))	derivative\:f(x)=\sqrt{(x^{2})\sin(x-2)}
derivative of e^x(x-1(x^2-1))	\frac{d}{dx}(e^{x}(x-1)(x^{2}-1))
integral of (1-x^3)^2x^2	\int\:(1-x^{3})^{2}x^{2}dx
integral from-1 to 1 of (y^2-2)-e^y	\int\:_{-1}^{1}(y^{2}-2)-e^{y}dy
taylor (e^{x^2}-1)/x	taylor\:\frac{e^{x^{2}}-1}{x}
limit as n approaches infinity of-n^2	\lim\:_{n\to\:\infty\:}(-n^{2})
derivative of 2x^3(1-x^2^4)	\frac{d}{dx}(2x^{3}(1-x^{2})^{4})
xy^'-2y+8=0	xy^{\prime\:}-2y+8=0
integral of e^{4x+5}	\int\:e^{4x+5}dx
laplacetransform e^{-8s}	laplacetransform\:e^{-8s}
limit as x approaches 2 of x^2+4	\lim\:_{x\to\:2}(x^{2}+4)
integral from 1/2 to 1 of x^{-3}-8	\int\:_{\frac{1}{2}}^{1}x^{-3}-8dx
sum from n=1 to infinity of x^n8^n	\sum\:_{n=1}^{\infty\:}x^{n}8^{n}
integral of (3x-2)/(sqrt(x))	\int\:\frac{3x-2}{\sqrt{x}}dx
inverse oflaplace 1/((s)(s+2)(s+3))	inverselaplace\:\frac{1}{(s)(s+2)(s+3)}
y^'=(e^{x-y})/(1+e^x),y(1)=0	y^{\prime\:}=\frac{e^{x-y}}{1+e^{x}},y(1)=0
derivative of \sqrt[9]{3+tan(x})	\frac{d}{dx}(\sqrt[9]{3+\tan(x)})
derivative of y=(6x^2+2x+8)/(sqrt(x))	derivative\:y=\frac{6x^{2}+2x+8}{\sqrt{x}}
integral of (1+sin(x))/(cos(x))	\int\:\frac{1+\sin(x)}{\cos(x)}dx
integral from 0 to 9 of sqrt(x^2+81)	\int\:_{0}^{9}\sqrt{x^{2}+81}dx
integral of ((x-2)^4)/(sqrt(4x-x^2))	\int\:\frac{(x-2)^{4}}{\sqrt{4x-x^{2}}}dx
area y=\|10x\|,y=x^2-11	area\:y=\left\|10x\right\|,y=x^{2}-11
(dx)/(dt)=2 x/t-0.194t	\frac{dx}{dt}=2\frac{x}{t}-0.194t
(\partial)/(\partial x)(ln(x^6-y^6))	\frac{\partial\:}{\partial\:x}(\ln(x^{6}-y^{6}))
d/(dM)((2pir^{3/2})/(sqrt(GM)))	\frac{d}{dM}(\frac{2πr^{\frac{3}{2}}}{\sqrt{GM}})
derivative of x^3-4/x	\frac{d}{dx}(x^{3}-\frac{4}{x})
tangent of y=(2x)/((x+1)^2),(0,0)	tangent\:y=\frac{2x}{(x+1)^{2}},(0,0)
y^'+(cot(x))y=sin^2(x)	y^{\prime\:}+(\cot(x))y=\sin^{2}(x)
derivative of (ln(x))/(5x^2)	derivative\:\frac{\ln(x)}{5x^{2}}
(\partial)/(\partial x)(e^{2x+7y})	\frac{\partial\:}{\partial\:x}(e^{2x+7y})
y^{''}+6y^'+9y=6t^2e^{-3t}	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=6t^{2}e^{-3t}
(\partial)/(\partial x)(xe^{x^2-y})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}-y})
limit as x approaches 0 of (9e^x-9)/x	\lim\:_{x\to\:0}(\frac{9e^{x}-9}{x})
derivative of f(x)=4sec(4x)	derivative\:f(x)=4\sec(4x)
integral of (6x^5+7)sqrt(x^6+7x)	\int\:(6x^{5}+7)\sqrt{x^{6}+7x}dx
derivative of log_{e}(sec(1/(5x)))	derivative\:\log_{e}(\sec(\frac{1}{5x}))
inverse oflaplace 5/(s^2)	inverselaplace\:\frac{5}{s^{2}}
integral of e^{2t}cos(e^t)	\int\:e^{2t}\cos(e^{t})dt
limit as x approaches+3+of (x+9)/(x-3)	\lim\:_{x\to\:+3+}(\frac{x+9}{x-3})
derivative of 3tan^2(x)	\frac{d}{dx}(3\tan^{2}(x))
derivative of r/(sqrt(r^2+9))	derivative\:\frac{r}{\sqrt{r^{2}+9}}

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