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Popular Calculus Problems

derivative of sqrt(x)e^{-x}	\frac{d}{dx}(\sqrt{x}e^{-x})
integral from 1 to 2 of x^{1/2}	\int\:_{1}^{2}x^{\frac{1}{2}}dx
integral of 6/(3x-2)	\int\:\frac{6}{3x-2}dx
(\partial)/(\partial y)(x^2+y^2-4)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-4)
integral of arcsin(x)	\int\:\arcsin(x)dx
derivative of 2x^3-6x^2-18x-24	\frac{d}{dx}(2x^{3}-6x^{2}-18x-24)
derivative of \sqrt[5]{(5x)/(4x-3)}	derivative\:\sqrt[5]{\frac{5x}{4x-3}}
simplify 900x-1/3 x^3+2500	simplify\:900x-\frac{1}{3}x^{3}+2500
derivative of arccot(x+arccot(1/x))	\frac{d}{dx}(\arccot(x)+\arccot(\frac{1}{x}))
(\partial)/(\partial x)(8/x)	\frac{\partial\:}{\partial\:x}(\frac{8}{x})
d/(dt)(ln(((a+bt)/(a-bt))^{1/2}))	\frac{d}{dt}(\ln((\frac{a+bt}{a-bt})^{\frac{1}{2}}))
derivative of arctan(9t)	derivative\:\arctan(9t)
integral from 0 to 2 of x^2e^{-9x}	\int\:_{0}^{2}x^{2}e^{-9x}dx
derivative of 6(sec(x-tan(x))^{3/2})	\frac{d}{dx}(6(\sec(x)-\tan(x))^{\frac{3}{2}})
area x^2-11,10x,[-sqrt(11),0]y=0	area\:x^{2}-11,10x,[-\sqrt{11},0]y=0
derivative of-10^{3x^2-4}	\frac{d}{dx}(-10^{3x^{2}-4})
derivative of 2/(\sqrt[4]{x^3})	\frac{d}{dx}(\frac{2}{\sqrt[4]{x^{3}}})
sqrt(x)(dy)/(dx)=e^{y+sqrt(x)}	\sqrt{x}\frac{dy}{dx}=e^{y+\sqrt{x}}
tangent of x^2+2xy-y^2+x=27,(4,7)	tangent\:x^{2}+2xy-y^{2}+x=27,(4,7)
(dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1	\frac{dy}{dx}=\frac{y^{3}}{1-2xy^{2}},y(0)=1
(\partial)/(\partial x)(sin(z^2)cos(xy))	\frac{\partial\:}{\partial\:x}(\sin(z^{2})\cos(xy))
integral of 7x^{15}e^{-x^8}	\int\:7x^{15}e^{-x^{8}}dx
integral from 1 to 3 of 5/y	\int\:_{1}^{3}\frac{5}{y}dy
x^2y^'+x(x+2)y=x	x^{2}y^{\prime\:}+x(x+2)y=x
(x+2y)dx-xdy=0	(x+2y)dx-xdy=0
integral of (3x^4-5x^2+x)	\int\:(3x^{4}-5x^{2}+x)dx
taylor arctan(x^2),0	taylor\:\arctan(x^{2}),0
derivative of sqrt(log_{a)(-x^2-x})	\frac{d}{dx}(\sqrt{\log_{a}(-x^{2}-x)})
derivative of (e^{3x}-1^5)	\frac{d}{dx}((e^{3x}-1)^{5})
derivative of y=ln(ln(1/x))	derivative\:y=\ln(\ln(\frac{1}{x}))
tangent of f(x)=2x^2+8x-2	tangent\:f(x)=2x^{2}+8x-2
derivative of 7/(x^2)	derivative\:\frac{7}{x^{2}}
limit as x approaches infinity of (4^x)/(5^{x+1)}	\lim\:_{x\to\:\infty\:}(\frac{4^{x}}{5^{x+1}})
integral of (2x+3)/(x(x-4)^2(x^2+2))	\int\:\frac{2x+3}{x(x-4)^{2}(x^{2}+2)}dx
integral of 1/((x-7)(x+1))	\int\:\frac{1}{(x-7)(x+1)}dx
derivative of e^{3ln(x^2})	\frac{d}{dx}(e^{3\ln(x^{2})})
integral of (1/((x-7)^2))	\int\:(\frac{1}{(x-7)^{2}})dx
limit as x approaches 0 of sin(-x^2)	\lim\:_{x\to\:0}(\sin(-x^{2}))
integral of pi(x^2-x^4)	\int\:π(x^{2}-x^{4})dx
integral of (sin(ln(y)))/y	\int\:\frac{\sin(\ln(y))}{y}dy
integral of 1/((1+x^2)^3)	\int\:\frac{1}{(1+x^{2})^{3}}dx
maclaurin 1/(1-x^3)	maclaurin\:\frac{1}{1-x^{3}}
derivative of 5sin(x+4cos(x))	\frac{d}{dx}(5\sin(x)+4\cos(x))
integral of sec^4(4x)tan(4x)	\int\:\sec^{4}(4x)\tan(4x)dx
integral of 17z^3e^z	\int\:17z^{3}e^{z}dz
integral of xe^{x/4}	\int\:xe^{\frac{x}{4}}dx
integral of (3x^2)/(sqrt(4x-x^2))	\int\:\frac{3x^{2}}{\sqrt{4x-x^{2}}}dx
(dy)/(dx)=sin(3x)	\frac{dy}{dx}=\sin(3x)
(dy)/(dx)=e^{3x}+8y	\frac{dy}{dx}=e^{3x}+8y
(\partial)/(\partial y)((xy)^{1/2})	\frac{\partial\:}{\partial\:y}((xy)^{\frac{1}{2}})
integral of ((8x^2+3x-6))/((x^2-4)(x+2))	\int\:\frac{(8x^{2}+3x-6)}{(x^{2}-4)(x+2)}dx
(\partial)/(\partial y)(2arctan(x/y))	\frac{\partial\:}{\partial\:y}(2\arctan(\frac{x}{y}))
(dy)/(dx)=4y^2x	\frac{dy}{dx}=4y^{2}x
integral of cot(10x)	\int\:\cot(10x)dx
integral of (x^2+24)/(x(x-2)^3)	\int\:\frac{x^{2}+24}{x(x-2)^{3}}dx
derivative of (e^x/(7+e^x))	\frac{d}{dx}(\frac{e^{x}}{7+e^{x}})
derivative of cos(2arctan(x))	derivative\:\cos(2\arctan(x))
integral of sin(5x+pi/6)	\int\:\sin(5x+\frac{π}{6})dx
derivative of (e^x+x)^4	derivative\:(e^{x}+x)^{4}
(\partial)/(\partial x)(-1/((1+x)^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{(1+x)^{2}})
f(x)=pix^2	f(x)=πx^{2}
derivative of cos(a^9+x^9)	derivative\:\cos(a^{9}+x^{9})
limit as x approaches 0 of cos(1/x)	\lim\:_{x\to\:0}(\cos(\frac{1}{x}))
derivative of 4/((1-x^3))	\frac{d}{dx}(\frac{4}{(1-x)^{3}})
integral of (e^x)^3	\int\:(e^{x})^{3}dx
limit as x approaches pi of cos(x-pi)	\lim\:_{x\to\:π}(\cos(x-π))
integral of 0.2+25x-200x^2+675x^3-900x^4+400x^5	\int\:0.2+25x-200x^{2}+675x^{3}-900x^{4}+400x^{5}dx
integral of 1/(x(2x+5)^2)	\int\:\frac{1}{x(2x+5)^{2}}dx
derivative of 25^x	\frac{d}{dx}(25^{x})
sum from n=0 to infinity of 8(-1/2)^n	\sum\:_{n=0}^{\infty\:}8(-\frac{1}{2})^{n}
derivative of 8x-2	\frac{d}{dx}(8x-2)
integral of 5cos(x)-csc^2(x)	\int\:5\cos(x)-\csc^{2}(x)dx
integral of x/(81x^4-1)	\int\:\frac{x}{81x^{4}-1}dx
derivative of e^{x-5}-x	\frac{d}{dx}(e^{x-5}-x)
integral from 1 to 4 of t^2ln(4t)	\int\:_{1}^{4}t^{2}\ln(4t)dt
y^'+6y=t+e^{-4t}	y^{\prime\:}+6y=t+e^{-4t}
integral of (x^4+1)/(x(x^2+1)^2)	\int\:\frac{x^{4}+1}{x(x^{2}+1)^{2}}dx
derivative of e^{4x}	derivative\:e^{4x}
area y=6x^2ln(x),y=24ln(x)	area\:y=6x^{2}\ln(x),y=24\ln(x)
derivative of f(x)=tan(3x)	derivative\:f(x)=\tan(3x)
derivative of ln(3x-1)	derivative\:\ln(3x-1)
sum from n=3 to infinity of 1/((2n-5)^3)	\sum\:_{n=3}^{\infty\:}\frac{1}{(2n-5)^{3}}
derivative of t^2sin(t)	derivative\:t^{2}\sin(t)
(\partial)/(\partial x)((8x)/(x^2+6y^2))	\frac{\partial\:}{\partial\:x}(\frac{8x}{x^{2}+6y^{2}})
limit as x approaches 0 of (sqrt(9+x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{9+x}}{x})
derivative of ln(\sqrt[5]{x})	derivative\:\ln(\sqrt[5]{x})
integral of (e^{2x})/(2-e^{2x)}	\int\:\frac{e^{2x}}{2-e^{2x}}dx
y^{''}-1/t y^'+2/(t^2)y=0	y^{\prime\:\prime\:}-\frac{1}{t}y^{\prime\:}+\frac{2}{t^{2}}y=0
integral of xsqrt(4-3x^2)	\int\:x\sqrt{4-3x^{2}}dx
(\partial)/(\partial x)(arcsin(x/(y^2)))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{x}{y^{2}}))
derivative of y=e^pi	derivative\:y=e^{π}
limit as x approaches pi/2 of (sin(x)-cos(x))^{tan(x)}	\lim\:_{x\to\:\frac{π}{2}}((\sin(x)-\cos(x))^{\tan(x)})
integral of 8xe^{9x}	\int\:8xe^{9x}dx
limit as x approaches 0 of ((484+x)^{0.5}-22)/x	\lim\:_{x\to\:0}(\frac{(484+x)^{0.5}-22}{x})
tangent of f(x)=x^4-10x^2+9,\at x=2	tangent\:f(x)=x^{4}-10x^{2}+9,\at\:x=2
integral of 2sqrt(x+1)	\int\:2\sqrt{x+1}dx
derivative of arctan(sqrt(7x^2-1))	\frac{d}{dx}(\arctan(\sqrt{7x^{2}-1}))
derivative of (8x^2+2x+4/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+2x+4}{\sqrt{x}})
integral of 9x^2ln(x)	\int\:9x^{2}\ln(x)dx
derivative of (1-x/2 ^{e^{x^2}})	\frac{d}{dx}((1-\frac{x}{2})^{e^{x^{2}}})

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