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Popular Calculus Problems

limit as x approaches+0 of x^3cos(pi/x)	\lim\:_{x\to\:+0}(x^{3}\cos(\frac{π}{x}))
(\partial)/(\partial x)(sin(2xy))	\frac{\partial\:}{\partial\:x}(\sin(2xy))
derivative of 16-1/625 x^2	\frac{d}{dx}(16-\frac{1}{625}x^{2})
maclaurin 1/(sqrt(4-x))	maclaurin\:\frac{1}{\sqrt{4-x}}
derivative of xe^{3y}	\frac{d}{dx}(xe^{3y})
1/t y^'= y/(t^2)-1/y	\frac{1}{t}y^{\prime\:}=\frac{y}{t^{2}}-\frac{1}{y}
(\partial)/(\partial y)(5y-2x)	\frac{\partial\:}{\partial\:y}(5y-2x)
2y^{''}+8y^'+80y=100cos(8t)	2y^{\prime\:\prime\:}+8y^{\prime\:}+80y=100\cos(8t)
(2x-1)dx+(7y+5)dy=0	(2x-1)dx+(7y+5)dy=0
derivative of 2e^{x-1}	\frac{d}{dx}(2e^{x-1})
integral of tan(x)*sec^2(x)	\int\:\tan(x)\cdot\:\sec^{2}(x)dx
derivative of cos^2(x-2sin(x))	\frac{d}{dx}(\cos^{2}(x)-2\sin(x))
derivative of x^6ln(x)	\frac{d}{dx}(x^{6}\ln(x))
derivative of-2cos(xsin(x)-2cos(x))	\frac{d}{dx}(-2\cos(x)\sin(x)-2\cos(x))
limit as x approaches pi of (tan(x))/(sin(2x))	\lim\:_{x\to\:π}(\frac{\tan(x)}{\sin(2x)})
maclaurin 9e^{-x}	maclaurin\:9e^{-x}
integral of 1/((16-x^2)^{3/2)}	\int\:\frac{1}{(16-x^{2})^{\frac{3}{2}}}dx
derivative of f(x)=3csc(4x)	derivative\:f(x)=3\csc(4x)
xy^'+4y=9x^5+2x^3	xy^{\prime\:}+4y=9x^{5}+2x^{3}
y^{''}-6y^'+9y=e^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=e^{3t}
integral of 1/(5+2t)	\int\:\frac{1}{5+2t}dt
2(x-y)dx+dy=0	2(x-y)dx+dy=0
laplacetransform sin(4x)	laplacetransform\:\sin(4x)
laplacetransform (t-1)^3	laplacetransform\:(t-1)^{3}
integral from 0 to 100 of 37cos(x/(80))	\int\:_{0}^{100}37\cos(\frac{x}{80})dx
limit as (x,y) approaches (0,1) of x^3y	\lim\:_{(x,y)\to\:(0,1)}(x^{3}y)
x^2y^{''}-2xy^'-4y=0,y(1)=0,y^'(1)=-5	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}-4y=0,y(1)=0,y^{\prime\:}(1)=-5
derivative of sin^6(x)	derivative\:\sin^{6}(x)
(dy)/(dx)-2y=2x	\frac{dy}{dx}-2y=2x
integral of t^2sin(2t)	\int\:t^{2}\sin(2t)dt
limit as x approaches+pi/2 of tan(x)	\lim\:_{x\to\:+\frac{π}{2}}(\tan(x))
y^{''}+y=7sin(2t)+5tcos(2t)	y^{\prime\:\prime\:}+y=7\sin(2t)+5t\cos(2t)
derivative of y=arccos(4x)	derivative\:y=\arccos(4x)
limit as x approaches infinity of sqrt(x+1)	\lim\:_{x\to\:\infty\:}(\sqrt{x+1})
derivative of cos^2(x)	derivative\:\cos^{2}(x)
integral of 5^xln(5)	\int\:5^{x}\ln(5)dx
derivative of (x^2)/(5(1-x))	derivative\:\frac{x^{2}}{5(1-x)}
integral of 9sin(3x)	\int\:9\sin(3x)dx
limit as x approaches-2 of sqrt(x^2-4)	\lim\:_{x\to\:-2}(\sqrt{x^{2}-4})
derivative of f(x)=x^{4/3}	derivative\:f(x)=x^{\frac{4}{3}}
integral from 2pi to infinity of sin(x)	\int\:_{2π}^{\infty\:}\sin(x)dx
integral of sin(pi/4 x)	\int\:\sin(\frac{π}{4}x)dx
derivative of sin(xy^2)	derivative\:\sin(xy^{2})
limit as x approaches-3 of (x^3+27)/(x^2+13x+30)	\lim\:_{x\to\:-3}(\frac{x^{3}+27}{x^{2}+13x+30})
laplacetransform sin(θ)	laplacetransform\:\sin(θ)
derivative of (d/(dx(sqrt(x)))^2)	\frac{d}{dx}((\frac{d}{dx}(\sqrt{x}))^{2})
(dy)/(dx)=2xe^{2y}	\frac{dy}{dx}=2xe^{2y}
derivative of 2arctan(y/x)	\frac{d}{dx}(2\arctan(\frac{y}{x}))
integral of (sqrt(2x-1))/x	\int\:\frac{\sqrt{2x-1}}{x}dx
derivative of x^2sin(4x)	derivative\:x^{2}\sin(4x)
(\partial)/(\partial x)(6x^5y^6+8x^7y^8)	\frac{\partial\:}{\partial\:x}(6x^{5}y^{6}+8x^{7}y^{8})
limit as x approaches 0 of (cos(2x))/(sin(2x))	\lim\:_{x\to\:0}(\frac{\cos(2x)}{\sin(2x)})
f(x)=-2cos(2x)	f(x)=-2\cos(2x)
sum from n=1 to infinity of ne^{-2n}	\sum\:_{n=1}^{\infty\:}ne^{-2n}
integral of 6x^2\sqrt[3]{x}	\int\:6x^{2}\sqrt[3]{x}dx
inverse oflaplace (s^2+12)/(s^4-16)	inverselaplace\:\frac{s^{2}+12}{s^{4}-16}
integral of (29x^2)/(sqrt(x^2-4))	\int\:\frac{29x^{2}}{\sqrt{x^{2}-4}}dx
integral of 1/8 t	\int\:\frac{1}{8}tdt
integral of ((x))/((4x^{(2))-12x+25)}	\int\:\frac{(x)}{(4x^{(2)}-12x+25)}dx
limit as x approaches 4 of (x-5)/((x-4)^2)	\lim\:_{x\to\:4}(\frac{x-5}{(x-4)^{2}})
xy^'+2y=-4sin(x)	xy^{\prime\:}+2y=-4\sin(x)
integral of (sec^4(t))/(tan^2(t))	\int\:\frac{\sec^{4}(t)}{\tan^{2}(t)}dt
derivative of (x^2+2x/(4-5x))	\frac{d}{dx}(\frac{x^{2}+2x}{4-5x})
tangent of f(x)=tan(x),\at x= pi/4	tangent\:f(x)=\tan(x),\at\:x=\frac{π}{4}
limit as x approaches 0 of (cos(7x)tan(7x))/x	\lim\:_{x\to\:0}(\frac{\cos(7x)\tan(7x)}{x})
(\partial)/(\partial y)(e^{xy})	\frac{\partial\:}{\partial\:y}(e^{xy})
limit as x approaches 3 of ((x^4-81))/(x-3)	\lim\:_{x\to\:3}(\frac{(x^{4}-81)}{x-3})
derivative of f(x)=(x^5-4x^3-7)^8	derivative\:f(x)=(x^{5}-4x^{3}-7)^{8}
laplacetransform 10e^{-10t}	laplacetransform\:10e^{-10t}
derivative of f(x)=ln(x^4)	derivative\:f(x)=\ln(x^{4})
integral of cos(1/3 x)	\int\:\cos(\frac{1}{3}x)dx
inverse oflaplace 1/((s-7)^3)	inverselaplace\:\frac{1}{(s-7)^{3}}
limit as x approaches infinity of 1^{2x}	\lim\:_{x\to\:\infty\:}(1^{2x})
integral of x^3*2^{-x}	\int\:x^{3}\cdot\:2^{-x}dx
derivative of \sqrt[6]{x^5}	\frac{d}{dx}(\sqrt[6]{x^{5}})
integral of 1/(2\sqrt[3]{x)+sqrt(x)}	\int\:\frac{1}{2\sqrt[3]{x}+\sqrt{x}}dx
derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2})	\frac{d}{dx}(\sqrt[3]{27x^{2}}-\frac{1}{\sqrt[3]{27x^{2}}})
f(x)=8ln(x)-x^2	f(x)=8\ln(x)-x^{2}
derivative of 7/(x-1)	\frac{d}{dx}(\frac{7}{x-1})
derivative of ((7x^2-8^4)/x)	\frac{d}{dx}(\frac{(7x^{2}-8)^{4}}{x})
taylor e^xcos(x)	taylor\:e^{x}\cos(x)
integral of 6e^2	\int\:6e^{2}dx
integral from-8 to 27 of 1/(\sqrt[3]{x)}	\int\:_{-8}^{27}\frac{1}{\sqrt[3]{x}}dx
laplacetransform e^{-5t}sin(2t)	laplacetransform\:e^{-5t}\sin(2t)
(2xy-sec^2(x))dx+(x^2+2y)dy=0	(2xy-\sec^{2}(x))dx+(x^{2}+2y)dy=0
derivative of xye^{-x^2-y^2}	\frac{d}{dx}(xye^{-x^{2}-y^{2}})
derivative of e^{(-4x})	\frac{d}{dx}(e^{(-4x)})
y^'+y= 1/(1+e^x)	y^{\prime\:}+y=\frac{1}{1+e^{x}}
integral from 0 to t of 5e^ssin(t-s)	\int\:_{0}^{t}5e^{s}\sin(t-s)ds
integral of (cos(x))/((sin^2(x))^{1/3)}	\int\:\frac{\cos(x)}{(\sin^{2}(x))^{\frac{1}{3}}}dx
limit as x approaches 0 of (sin(14x))/x	\lim\:_{x\to\:0}(\frac{\sin(14x)}{x})
integral of sin(e^x)	\int\:\sin(e^{x})dx
derivative of f(x)=8(2x-3)^3	derivative\:f(x)=8(2x-3)^{3}
slope ofintercept (-3,7),(6,-8)	slopeintercept\:(-3,7),(6,-8)
integral of cos(x/y)	\int\:\cos(\frac{x}{y})dx
integral of sin(9x)cos(3x)	\int\:\sin(9x)\cos(3x)dx
integral from 0 to ln(5) of e^x(3-4e^x)	\int\:_{0}^{\ln(5)}e^{x}(3-4e^{x})dx
(\partial)/(\partial x)(-2e^ysin(-x)+3y-4xy)	\frac{\partial\:}{\partial\:x}(-2e^{y}\sin(-x)+3y-4xy)
derivative of sqrt(120+x^3)	derivative\:\sqrt{120+x^{3}}
integral of 4x^{-5}+6x^{-1}-1	\int\:4x^{-5}+6x^{-1}-1dx

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