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Popular Calculus Problems

derivative of \sqrt[5]{x^2}+4sqrt(x^3)	\frac{d}{dx}(\sqrt[5]{x^{2}}+4\sqrt{x^{3}})
(\partial)/(\partial y)(x^2sin(2y))	\frac{\partial\:}{\partial\:y}(x^{2}\sin(2y))
limit as x approaches-6 of sqrt(x-6)-x	\lim\:_{x\to\:-6}(\sqrt{x-6}-x)
tangent of cos(5+x^2)	tangent\:\cos(5+x^{2})
(\partial)/(\partial y)(-arctan(x/y))	\frac{\partial\:}{\partial\:y}(-\arctan(\frac{x}{y}))
inverse oflaplace (3^2)/(s(s+3)^2)	inverselaplace\:\frac{3^{2}}{s(s+3)^{2}}
integral of (7x^2+4x^{-2})	\int\:(7x^{2}+4x^{-2})dx
integral of-3cot(x)	\int\:-3\cot(x)dx
derivative of cos(xln(tan(x)))	\frac{d}{dx}(\cos(x)\ln(\tan(x)))
slope of (-2,-2),(2,-5)	slope\:(-2,-2),(2,-5)
integral of (x+1)sqrt(2-x)	\int\:(x+1)\sqrt{2-x}dx
taylor 7sin(x), pi/4	taylor\:7\sin(x),\frac{π}{4}
xdy-ydx+(y^2-1)dy=0	xdy-ydx+(y^{2}-1)dy=0
derivative of (sin(x+cos(x))^2)	\frac{d}{dx}((\sin(x)+\cos(x))^{2})
(7y^2-t^2)/(y^5)(dy)/(dt)+t/(2y^4)=0	\frac{7y^{2}-t^{2}}{y^{5}}\frac{dy}{dt}+\frac{t}{2y^{4}}=0
limit as x approaches 1 of 4/(sqrt(x+3))	\lim\:_{x\to\:1}(\frac{4}{\sqrt{x+3}})
y^'=8y^2sin(x)	y^{\prime\:}=8y^{2}\sin(x)
derivative of t^2(t+1)^{-1}	derivative\:t^{2}(t+1)^{-1}
derivative of 3x^{1/3}	derivative\:3x^{\frac{1}{3}}
y^{''}+2y^'-35y=0	y^{\prime\:\prime\:}+2y^{\prime\:}-35y=0
limit as x approaches 5-of 8/(x-5)	\lim\:_{x\to\:5-}(\frac{8}{x-5})
derivative of y=6^{-4x}	derivative\:y=6^{-4x}
d/(dt)(e^tt)	\frac{d}{dt}(e^{t}t)
derivative of (2+3x^3)	\frac{d}{dx}((2+3x)^{3})
inverse oflaplace e^t	inverselaplace\:e^{t}
limit as x approaches infinity+of e^{-x}	\lim\:_{x\to\:\infty\:+}(e^{-x})
integral of sin(y)-ysin(x)	\int\:\sin(y)-y\sin(x)dx
(\partial)/(\partial x)(e^{xy^2}+4zy^3)	\frac{\partial\:}{\partial\:x}(e^{xy^{2}}+4zy^{3})
(1+x^2)(dy)/(dx)+xy=0	(1+x^{2})\frac{dy}{dx}+xy=0
derivative of y=x^{-1/2}	derivative\:y=x^{-\frac{1}{2}}
derivative of x^2*y^2	\frac{d}{dx}(x^{2}\cdot\:y^{2})
integral of 1/(sqrt(9-16x^2))	\int\:\frac{1}{\sqrt{9-16x^{2}}}dx
derivative of 3x^4-2x^3+1	\frac{d}{dx}(3x^{4}-2x^{3}+1)
integral of 5csc^2(x)	\int\:5\csc^{2}(x)dx
integral of (x+2)/(2x^2-x)	\int\:\frac{x+2}{2x^{2}-x}dx
integral of e^{((x^2)/2)}	\int\:e^{(\frac{x^{2}}{2})}dx
limit as x approaches 7+of 3	\lim\:_{x\to\:7+}(3)
(\partial)/(\partial x)(e^{x^2+y^2+1})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y^{2}+1})
limit as x approaches infinity of 1/((2x+1)^{1/x)}	\lim\:_{x\to\:\infty\:}(\frac{1}{(2x+1)^{\frac{1}{x}}})
limit as x approaches infinity of xe	\lim\:_{x\to\:\infty\:}(xe)
integral of e^x(sin(x))	\int\:e^{x}(\sin(x))dx
inverse oflaplace 2/(s(s^2+4s))	inverselaplace\:\frac{2}{s(s^{2}+4s)}
integral from 6 to 8 of (84)/((x-6)^3)	\int\:_{6}^{8}\frac{84}{(x-6)^{3}}dx
(dy)/(dx)=2ysin(x)	\frac{dy}{dx}=2y\sin(x)
2xy(dy)/(dx)+x^2-y^2=0	2xy\frac{dy}{dx}+x^{2}-y^{2}=0
tangent of f(x)=sqrt(x),(9,3)	tangent\:f(x)=\sqrt{x},(9,3)
area y= 3/x ,y=12x,y= 1/12 x	area\:y=\frac{3}{x},y=12x,y=\frac{1}{12}x
derivative of y=sqrt(x(x+2))	derivative\:y=\sqrt{x(x+2)}
f(x)=(sqrt(x))/(4+x)	f(x)=\frac{\sqrt{x}}{4+x}
derivative of y=ln(8+ln(x))	derivative\:y=\ln(8+\ln(x))
integral of 1/(sqrt(x^2-196))	\int\:\frac{1}{\sqrt{x^{2}-196}}dx
limit as x approaches 0+of ln(1/(5x))	\lim\:_{x\to\:0+}(\ln(\frac{1}{5x}))
integral of sin(x)cos(x)sqrt(1+cos^2(x))	\int\:\sin(x)\cos(x)\sqrt{1+\cos^{2}(x)}dx
limit as x approaches 0 of e^{-7x}	\lim\:_{x\to\:0}(e^{-7x})
limit as x approaches 4 of x^2(-16x)/(x-4)	\lim\:_{x\to\:4}(x^{2}\frac{-16x}{x-4})
derivative of (e^{2x}-1/(e^{2x)+1})	\frac{d}{dx}(\frac{e^{2x}-1}{e^{2x}+1})
y^{''}+14y^'+100y=10sin(2pix)+5sin(pix)	y^{\prime\:\prime\:}+14y^{\prime\:}+100y=10\sin(2π\cdot\:x)+5\sin(π\cdot\:x)
integral of 1/((x^2+1)^2(x^2-1))	\int\:\frac{1}{(x^{2}+1)^{2}(x^{2}-1)}dx
3y^{''}+y^'+2y=0	3y^{\prime\:\prime\:}+y^{\prime\:}+2y=0
integral of (4x^2)/(sqrt(x^3+8))	\int\:\frac{4x^{2}}{\sqrt{x^{3}+8}}dx
(\partial)/(\partial x)((1-x-4y)^{1/2})	\frac{\partial\:}{\partial\:x}((1-x-4y)^{\frac{1}{2}})
(\partial)/(\partial x)(5e^{x^5y})	\frac{\partial\:}{\partial\:x}(5e^{x^{5}y})
derivative of f(x)=(x^2+2x+1)/(x^2-2x+1)	derivative\:f(x)=\frac{x^{2}+2x+1}{x^{2}-2x+1}
integral of 7sin(5x)sin(x)	\int\:7\sin(5x)\sin(x)dx
limit as x approaches 0 of 4x-\|x\|	\lim\:_{x\to\:0}(4x-\left\|x\right\|)
integral of-xe^{(-x^2)/2}	\int\:-xe^{\frac{-x^{2}}{2}}dx
x^{''}-5x^'+6x=cos(t)*e^{-t}	x^{\prime\:\prime\:}-5x^{\prime\:}+6x=\cos(t)\cdot\:e^{-t}
(\partial)/(\partial x)((u^2)/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{u^{2}}{x^{2}})
(\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)})	\frac{\partial\:}{\partial\:x}(-\frac{4}{x^{4}\sqrt[4]{x}})
(xdy)/(dx)+3y=x^3-x	\frac{xdy}{dx}+3y=x^{3}-x
y^'=2y^2+xy^2,y(0)=1	y^{\prime\:}=2y^{2}+xy^{2},y(0)=1
derivative of 1/(5-2x)	\frac{d}{dx}(\frac{1}{5-2x})
integral of (9-162x)/(sqrt(64-81x^2))	\int\:\frac{9-162x}{\sqrt{64-81x^{2}}}dx
integral of-2x*ln(x)	\int\:-2x\cdot\:\ln(x)dx
tangent of x^2-1/x	tangent\:x^{2}-\frac{1}{x}
integral of ((ln(x))^7)/x	\int\:\frac{(\ln(x))^{7}}{x}dx
integral from 3 to 6 of (2x-3)/6	\int\:_{3}^{6}\frac{2x-3}{6}dx
9y^{''}+12y^'-5y=0	9y^{\prime\:\prime\:}+12y^{\prime\:}-5y=0
integral from 0 to pi of x*sin^2(x)	\int\:_{0}^{π}x\cdot\:\sin^{2}(x)dx
y^{''}-y^'-6y=0,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=-1
integral of ((3x^2))/2	\int\:\frac{(3x^{2})}{2}dx
derivative of e^{x^2+6x}	\frac{d}{dx}(e^{x^{2}+6x})
integral of (5x+1)^4	\int\:(5x+1)^{4}dx
(d^2)/(dx^2)(1/(x^2+1))	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{2}+1})
derivative of f(x)=9-\|x-4\|\at x	derivative\:f(x)=9-\left\|x-4\right\|\at\:x
limit as x approaches 5-of 2/(x^2-25)	\lim\:_{x\to\:5-}(\frac{2}{x^{2}-25})
integral from-2 to 1 of (12x^5-36)	\int\:_{-2}^{1}(12x^{5}-36)dx
x^2y^{''}+xy^'-y=0,y(1)=1,y^'(1)=4	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=0,y(1)=1,y^{\prime\:}(1)=4
integral of (10)/((x+1)(x^2+9))	\int\:\frac{10}{(x+1)(x^{2}+9)}dx
simplify (e^{-x}-e^2)(e^x+e^{-5})	simplify\:(e^{-x}-e^{2})(e^{x}+e^{-5})
slope of (2,0),(32,-5)	slope\:(2,0),(32,-5)
integral of 27sec^4(x)	\int\:27\sec^{4}(x)dx
integral of (cot^5(x))/(sqrt(sin(x)))	\int\:\frac{\cot^{5}(x)}{\sqrt{\sin(x)}}dx
limit as x approaches-3 of x	\lim\:_{x\to\:-3}(x)
integral of (sin(x)+cos(x))/(sin^2(x))	\int\:\frac{\sin(x)+\cos(x)}{\sin^{2}(x)}dx
integral of sqrt(35-2x-x^2)	\int\:\sqrt{35-2x-x^{2}}dx
integral of arcosin(x)	\int\:arco\sin(x)dx
tangent of x^2-3	tangent\:x^{2}-3
f(x)=x^2-cos(2x)	f(x)=x^{2}-\cos(2x)
derivative of ln((x^2+1^2))	\frac{d}{dx}(\ln((x^{2}+1)^{2}))

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