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Popular Calculus Problems

derivative of (x-1/x ^4)	\frac{d}{dx}((x-\frac{1}{x})^{4})
limit as x approaches 5 of-x^2+8x-5	\lim\:_{x\to\:5}(-x^{2}+8x-5)
(\partial)/(\partial z)(3yz^2)	\frac{\partial\:}{\partial\:z}(3yz^{2})
integral from 1 to 10 of sqrt(5x-1)	\int\:_{1}^{10}\sqrt{5x-1}dx
derivative of x^{-3}y^{-4}	\frac{d}{dx}(x^{-3}y^{-4})
limit as n approaches infinity of n^0	\lim\:_{n\to\:\infty\:}(n^{0})
derivative of f(x)=3^{(x^5)}	derivative\:f(x)=3^{(x^{5})}
y^'+by=0	y^{\prime\:}+by=0
integral of (x^2)/(sqrt((2-x^2)))	\int\:\frac{x^{2}}{\sqrt{(2-x^{2})}}dx
(x)^2y^{''}+3(x)y^'-3y=(x)^3	(x)^{2}y^{\prime\:\prime\:}+3(x)y^{\prime\:}-3y=(x)^{3}
derivative of 1/(t^2)	derivative\:\frac{1}{t^{2}}
integral from 0 to 1 of x*e^x	\int\:_{0}^{1}x\cdot\:e^{x}dx
derivative of y=x-x^3	derivative\:y=x-x^{3}
integral of (x^2-5)/((x+1)^3)	\int\:\frac{x^{2}-5}{(x+1)^{3}}dx
integral from 0 to pi of 20sin^4(x)	\int\:_{0}^{π}20\sin^{4}(x)dx
integral of 3xcos(3x)	\int\:3x\cos(3x)dx
y^'-2y=3e^{2t}	y^{\prime\:}-2y=3e^{2t}
derivative of sqrt(x^2+15)	\frac{d}{dx}(\sqrt{x^{2}+15})
limit as x approaches-2 of-7	\lim\:_{x\to\:-2}(-7)
integral of (4x+3)(2x^2+3x)	\int\:(4x+3)(2x^{2}+3x)dx
derivative of (x+1)^2(x^2+1)^{-3}	derivative\:(x+1)^{2}(x^{2}+1)^{-3}
limit as x approaches 0+of (x-2)/(\|x\|)	\lim\:_{x\to\:0+}(\frac{x-2}{\left\|x\right\|})
derivative of T	derivative\:T
y^{''}-2y+y=(e^x)/(1+x^2)	y^{\prime\:\prime\:}-2y+y=\frac{e^{x}}{1+x^{2}}
y^'sin(x)+ycos(x)=0,y(pi/4)=1	y^{\prime\:}\sin(x)+y\cos(x)=0,y(\frac{π}{4})=1
limit as x approaches 0+of (1/x)^{ln(x)}	\lim\:_{x\to\:0+}((\frac{1}{x})^{\ln(x)})
derivative of cos(ln(x))	derivative\:\cos(\ln(x))
integral from 0 to 1 of (e^{-2x})/2	\int\:_{0}^{1}\frac{e^{-2x}}{2}dx
limit as x approaches 0 of sinh(x)cot(x)	\lim\:_{x\to\:0}(\sinh(x)\cot(x))
sum from n=0 to infinity of nx^n	\sum\:_{n=0}^{\infty\:}nx^{n}
(dy)/(dx)+12y=5	\frac{dy}{dx}+12y=5
x^2(dy)/(dx)=y-xy,y(-1)=-2	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-2
integral of (x^3)/(sqrt(49+x^2))	\int\:\frac{x^{3}}{\sqrt{49+x^{2}}}dx
f(x)=arcsec(6x)	f(x)=\arcsec(6x)
integral of 3/(sqrt(1-2x))	\int\:\frac{3}{\sqrt{1-2x}}dx
taylor e^{x^5},0	taylor\:e^{x^{5}},0
limit as x approaches 1 of x^2-4	\lim\:_{x\to\:1}(x^{2}-4)
limit as x approaches 0 of (1-2x)^{1/x}	\lim\:_{x\to\:0}((1-2x)^{\frac{1}{x}})
integral of 1/(3-2x^2)	\int\:\frac{1}{3-2x^{2}}dx
derivative of sin(x)ln(5x)	derivative\:\sin(x)\ln(5x)
derivative of sqrt(2e^{x^3)+1}	derivative\:\sqrt{2e^{x^{3}}+1}
d/(dy)(2xe^{xy}+x^2ye^{xy})	\frac{d}{dy}(2xe^{xy}+x^{2}ye^{xy})
(\partial)/(\partial y)(y^2-cos(xy))	\frac{\partial\:}{\partial\:y}(y^{2}-\cos(xy))
integral of 2tan(x)	\int\:2\tan(x)dx
derivative of-1/((2x+8^{3/2)})	\frac{d}{dx}(-\frac{1}{(2x+8)^{\frac{3}{2}}})
integral of+1/(x^2)	\int\:+\frac{1}{x^{2}}dx
d/(dt)(cos(2t))	\frac{d}{dt}(\cos(2t))
y^{''}-2y^'+y=x^2-1	y^{\prime\:\prime\:}-2y^{\prime\:}+y=x^{2}-1
tangent of y=(sqrt(5))^x,\at x=6	tangent\:y=(\sqrt{5})^{x},\at\:x=6
limit as x approaches-2 of (-1)/((x+2))	\lim\:_{x\to\:-2}(\frac{-1}{(x+2)})
derivative of (2x-1^3(x+1)^5)	\frac{d}{dx}((2x-1)^{3}(x+1)^{5})
t^2y^{''}+3ty^'+y= 1/t	t^{2}y^{\prime\:\prime\:}+3ty^{\prime\:}+y=\frac{1}{t}
limit as x approaches 0 of 1/(3+x)-1/3	\lim\:_{x\to\:0}(\frac{1}{3+x}-\frac{1}{3})
integral of sqrt(6+7t^2)	\int\:\sqrt{6+7t^{2}}dt
limit as x approaches 1+of ((x))/(ln(x))	\lim\:_{x\to\:1+}(\frac{(x)}{\ln(x)})
tangent of 4x(3-2x)^5,\at 2	tangent\:4x(3-2x)^{5},\at\:2
integral of arctan(2y)	\int\:\arctan(2y)dy
limit as x approaches 0 of 1/x+1/(x^2)	\lim\:_{x\to\:0}(\frac{1}{x}+\frac{1}{x^{2}})
limit as n approaches 0 of ln(n)	\lim\:_{n\to\:0}(\ln(n))
integral of x/(x^2+8)	\int\:\frac{x}{x^{2}+8}dx
derivative of 12x^2-2x^3	\frac{d}{dx}(12x^{2}-2x^{3})
area f(x)=x^3-x,[0,3]	area\:f(x)=x^{3}-x,[0,3]
integral of 1/((x-1)^{3/2)}	\int\:\frac{1}{(x-1)^{\frac{3}{2}}}dx
((y^'-e^{-t}+5)/y)=-5,y(0)=-2	(\frac{y^{\prime\:}-e^{-t}+5}{y})=-5,y(0)=-2
integral of 1/(k-x)	\int\:\frac{1}{k-x}dx
inverse oflaplace 3/(s^2+7)	inverselaplace\:\frac{3}{s^{2}+7}
integral of 8x	\int\:8xdx
tangent of y=16sqrt(x),(16,64)	tangent\:y=16\sqrt{x},(16,64)
derivative of arctan(3/(x+2))	\frac{d}{dx}(\arctan(\frac{3}{x+2}))
integral of (sin(x))/(2+cos(x))	\int\:\frac{\sin(x)}{2+\cos(x)}dx
tangent of f(x)=(x^2+15)(2x+18)	tangent\:f(x)=(x^{2}+15)(2x+18)
integral of (16)/(1+x^2)	\int\:\frac{16}{1+x^{2}}dx
(dy)/(dx)=2(1-y)	\frac{dy}{dx}=2(1-y)
(\partial)/(\partial y)((-1)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{-1}{x^{2}+y^{2}})
(\partial)/(\partial x)(e^{(4xy)})	\frac{\partial\:}{\partial\:x}(e^{(4xy)})
derivative of y=xlog_{e}(x)	derivative\:y=x\log_{e}(x)
limit as x approaches 4 of-2x^2+4x-4	\lim\:_{x\to\:4}(-2x^{2}+4x-4)
3(dy)/(dx)+8/(xy^2)=0	3\frac{dy}{dx}+\frac{8}{xy^{2}}=0
derivative of 2/(x+5)	\frac{d}{dx}(\frac{2}{x+5})
derivative of 1/(x+7)	\frac{d}{dx}(\frac{1}{x+7})
integral of t*cos(nt)	\int\:t\cdot\:\cos(nt)dt
simplify x+y	simplify\:x+y
limit as x approaches 0 of ((sin(7x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(7x))}{x})
integral of (x^2)ln(x)	\int\:(x^{2})\ln(x)dx
x(dy)/(dx)+xy^2=xy	x\frac{dy}{dx}+xy^{2}=xy
integral of sin^2(2x+5)	\int\:\sin^{2}(2x+5)dx
tangent of f(x)=sqrt(3x+7),(3,4)	tangent\:f(x)=\sqrt{3x+7},(3,4)
inverse oflaplace 1/(s(s^2+2s+2))	inverselaplace\:\frac{1}{s(s^{2}+2s+2)}
expand (x-2)^2(x+4)	expand\:(x-2)^{2}(x+4)
taylor x^{9/6},2	taylor\:x^{\frac{9}{6}},2
sum from n=0 to infinity of 1/(sin(n))	\sum\:_{n=0}^{\infty\:}\frac{1}{\sin(n)}
y^'=3y	y^{\prime\:}=3y
limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4)	\lim\:_{x\to\:1}(\frac{(\sqrt{26-x}-5)}{\sqrt{17-x}-4})
y^{''}-2y^'-3y=4e^{3t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=4e^{3t}
integral of-2e^{cos(x)}sin(x)	\int\:-2e^{\cos(x)}\sin(x)dx
integral of 6x(1-x)	\int\:6x(1-x)dx
integral of 8sin^2(x)cos(x)	\int\:8\sin^{2}(x)\cos(x)dx
y^{''}+2y^'+y=3x+8	y^{\prime\:\prime\:}+2y^{\prime\:}+y=3x+8
(\partial)/(\partial y)(e^{-xyz})	\frac{\partial\:}{\partial\:y}(e^{-xyz})
derivative of-sqrt(x)	\frac{d}{dx}(-\sqrt{x})

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