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Popular Calculus Problems

limit as x approaches infinity of (4x^2)/(e^{4x)}	\lim\:_{x\to\:\infty\:}(\frac{4x^{2}}{e^{4x}})
(\partial)/(\partial x)(x^3+x^2*x^3-2y^2)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}\cdot\:x^{3}-2y^{2})
derivative of (x-2/(x^2+1))	\frac{d}{dx}(\frac{x-2}{x^{2}+1})
derivative of-16	\frac{d}{dx}(-16)
derivative of 5^{tan(5x})	\frac{d}{dx}(5^{\tan(5x)})
slope of (-5,3),(2,-3)	slope\:(-5,3),(2,-3)
(x^4(x-3)^3)^'	(x^{4}(x-3)^{3})^{\prime\:}
integral of-1/(y^2)	\int\:-\frac{1}{y^{2}}dy
derivative of cos(7x*7)	\frac{d}{dx}(\cos(7x)\cdot\:7)
integral of (10sin(5x))	\int\:(10\sin(5x))dx
derivative of 6*3^x	\frac{d}{dx}(6\cdot\:3^{x})
area y=2-x/2 ,x=2y^2	area\:y=2-\frac{x}{2},x=2y^{2}
integral of (9x+2)^2	\int\:(9x+2)^{2}dx
integral of (a+bx^5)/(6ax+bx^6)	\int\:\frac{a+bx^{5}}{6ax+bx^{6}}dx
y^{''}+4y^'-24y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-24y=0
integral of e^x+e^xx	\int\:e^{x}+e^{x}xdx
derivative of g(x)= 1/(sqrt(x))	derivative\:g(x)=\frac{1}{\sqrt{x}}
inverse oflaplace 6/s+(16)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{16}{s^{2}+16}
(d^2y)/(dx^2)=0	\frac{d^{2}y}{dx^{2}}=0
integral from-1 to 1 of e^x-1	\int\:_{-1}^{1}e^{x}-1dx
limit as x approaches-1+of x^2-3	\lim\:_{x\to\:-1+}(x^{2}-3)
xydx+(1+y)sqrt(1)-x^2dy=0	xydx+(1+y)\sqrt{1}-x^{2}dy=0
integral of (6x)/(e^{3x^2)}	\int\:\frac{6x}{e^{3x^{2}}}dx
area (x^2)/4-1, x/4+4,[-4,5]	area\:\frac{x^{2}}{4}-1,\frac{x}{4}+4,[-4,5]
y^'+y-4sin(x)=0	y^{\prime\:}+y-4\sin(x)=0
integral of (9x+3)/(x^2+1)	\int\:\frac{9x+3}{x^{2}+1}dx
integral from x to 4 of 0.125	\int\:_{x}^{4}0.125dy
(\partial)/(\partial x)(rln(r^2+s))	\frac{\partial\:}{\partial\:x}(r\ln(r^{2}+s))
integral of sqrt(4x^2-4x+10)	\int\:\sqrt{4x^{2}-4x+10}dx
integral from 0 to 2 of f(x^3)	\int\:_{0}^{2}f(x^{3})dx
(d^2x)/(dx^2)	\frac{d^{2}x}{dx^{2}}
xy^'+2y=(3e^{-4x})/x	xy^{\prime\:}+2y=\frac{3e^{-4x}}{x}
limit as x approaches-1+of x/(x^2-1)	\lim\:_{x\to\:-1+}(\frac{x}{x^{2}-1})
integral from 0 to 4 of 5e^{-x^2}	\int\:_{0}^{4}5e^{-x^{2}}dx
parity (cot(x))/x	parity\:\frac{\cot(x)}{x}
limit as x approaches 0 of (20sin(x))/4	\lim\:_{x\to\:0}(\frac{20\sin(x)}{4})
limit as x approaches 0 of x(e^x-1)ln(x)	\lim\:_{x\to\:0}(x(e^{x}-1)\ln(x))
integral of sin((pix)/3)	\int\:\sin(\frac{πx}{3})dx
(x+y)^2dx+(2xy+x^2-7)dy=0	(x+y)^{2}dx+(2xy+x^{2}-7)dy=0
area 1-x^2,x^2-1	area\:1-x^{2},x^{2}-1
derivative of f(x)=2x^2+4x+3	derivative\:f(x)=2x^{2}+4x+3
(t^2+25)(dy)/(dt)+2ty=t^2(t^2+25)	(t^{2}+25)\frac{dy}{dt}+2ty=t^{2}(t^{2}+25)
inverse oflaplace ((2s+2.5))/((s+0.5))	inverselaplace\:\frac{(2s+2.5)}{(s+0.5)}
parity ln(csc(x)-cot(x))	parity\:\ln(\csc(x)-\cot(x))
derivative of 1/((2x^3+3x+1)^{3/4)}	derivative\:\frac{1}{(2x^{3}+3x+1)^{\frac{3}{4}}}
normal of y=e^{2x},\at x=ln(2)	normal\:y=e^{2x},\at\:x=\ln(2)
(\partial)/(\partial y)(ycos(xy)+e^x)	\frac{\partial\:}{\partial\:y}(y\cos(xy)+e^{x})
derivative of \sqrt[3]{3x^4+4x^3}	derivative\:\sqrt[3]{3x^{4}+4x^{3}}
integral of cos^2(t)-sin^2(t)	\int\:\cos^{2}(t)-\sin^{2}(t)dt
(\partial)/(\partial x)(sin(x^1y^3))	\frac{\partial\:}{\partial\:x}(\sin(x^{1}y^{3}))
expand (-2cos(2x)-sin(3x))^2	expand\:(-2\cos(2x)-\sin(3x))^{2}
limit as x approaches 1/2 of arcsin(x)	\lim\:_{x\to\:\frac{1}{2}}(\arcsin(x))
slope of f(x)=x^2+x-3	slope\:f(x)=x^{2}+x-3
3t^4y^{''}+7t^3y^'=0	3t^{4}y^{\prime\:\prime\:}+7t^{3}y^{\prime\:}=0
sum from n=0 to infinity of 1/((n+10))	\sum\:_{n=0}^{\infty\:}\frac{1}{(n+10)}
integral of 14tan^3(x)	\int\:14\tan^{3}(x)dx
y^{''}-2y+y=0	y^{\prime\:\prime\:}-2y+y=0
integral from-4 to 6 of f(x)	\int\:_{-4}^{6}f(x)dx
limit as x approaches 0 of (ln(x))/1	\lim\:_{x\to\:0}(\frac{\ln(x)}{1})
y^'-9xy=0	y^{\prime\:}-9xy=0
derivative of f(x)=3253(86.3)^x	derivative\:f(x)=3253(86.3)^{x}
(\partial)/(\partial x)(xln(y)-yln(x))	\frac{\partial\:}{\partial\:x}(x\ln(y)-y\ln(x))
limit as n approaches infinity of n/5	\lim\:_{n\to\:\infty\:}(\frac{n}{5})
limit as x approaches 5 of 12	\lim\:_{x\to\:5}(12)
derivative of x^4+2/x	\frac{d}{dx}(x^{4}+\frac{2}{x})
derivative of 3x^2+2x+4	\frac{d}{dx}(3x^{2}+2x+4)
integral from 0 to 2 of 1/(x^{1/3)}	\int\:_{0}^{2}\frac{1}{x^{\frac{1}{3}}}dx
(sqrt(x^3))^'	(\sqrt{x^{3}})^{\prime\:}
f(x)=sqrt(x-3)	f(x)=\sqrt{x-3}
integral of 2x^6	\int\:2x^{6}dx
integral of e^2xcos(3x)	\int\:e^{2}x\cos(3x)dx
integral of x^3e^{x^2}	\int\:x^{3}e^{x^{2}}dx
(\partial)/(\partial x)(sin(xyz^3))	\frac{\partial\:}{\partial\:x}(\sin(xyz^{3}))
integral from 0 to 5 of e^{3x}	\int\:_{0}^{5}e^{3x}dx
4y^{''}-16y^'+19y=0	4y^{\prime\:\prime\:}-16y^{\prime\:}+19y=0
derivative of 2x^2cos(x)	\frac{d}{dx}(2x^{2}\cos(x))
(y^')/y =x	\frac{y^{\prime\:}}{y}=x
tangent of (6x)/(2+x^2)	tangent\:\frac{6x}{2+x^{2}}
(\partial)/(\partial y)(e^{2y}sin(-2x))	\frac{\partial\:}{\partial\:y}(e^{2y}\sin(-2x))
derivative of f(x)=(2x+3)^{11}(4-5x)^9	derivative\:f(x)=(2x+3)^{11}(4-5x)^{9}
limit as x approaches 1+of 1	\lim\:_{x\to\:1+}(1)
9/10 x^2dy-18dx=0	\frac{9}{10}x^{2}dy-18dx=0
(\partial)/(\partial x)(x^3+x^2y-y^2-4y)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y-y^{2}-4y)
derivative of 4x+5	\frac{d}{dx}(4x+5)
limit as x approaches 5+of 2/(x+5)	\lim\:_{x\to\:5+}(\frac{2}{x+5})
(\partial)/(\partial x)(ax+by^2+cx^2y)	\frac{\partial\:}{\partial\:x}(ax+by^{2}+cx^{2}y)
derivative of arctan(tan(x))	\frac{d}{dx}(\arctan(\tan(x)))
limit as x approaches 0+of xln(x^2)	\lim\:_{x\to\:0+}(x\ln(x^{2}))
area y=9-x^2,y=0,x	area\:y=9-x^{2},y=0,x
derivative of ((3x-1)/(x^{2/3)})	\frac{d}{dx}(\frac{(3x-1)}{x^{\frac{2}{3}}})
(\partial)/(\partial x)(4+xln(xy-5))	\frac{\partial\:}{\partial\:x}(4+x\ln(xy-5))
derivative of x(2-x)	\frac{d}{dx}(x(2-x))
integral of (5x)/(e^{2x)}	\int\:\frac{5x}{e^{2x}}dx
integral of (7x+8)/(7x^2+16x+9)	\int\:\frac{7x+8}{7x^{2}+16x+9}dx
derivative of 1/(x^{11})	\frac{d}{dx}(\frac{1}{x^{11}})
limit as x approaches 3+of (18-6x)/(3-x)	\lim\:_{x\to\:3+}(\frac{18-6x}{3-x})
derivative of 2\sqrt[3]{x^7}	\frac{d}{dx}(2\sqrt[3]{x^{7}})
integral of x^2-8x+12	\int\:x^{2}-8x+12dx
derivative of ln(x+sqrt(1-x^2))	\frac{d}{dx}(\ln(x+\sqrt{1-x^{2}}))
sum from n=0 to infinity of (5/4)(2/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{5}{4})(\frac{2}{3})^{n}

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