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Popular Calculus Problems

y^'-y=4te^{2t},y(0)=1	y^{\prime\:}-y=4te^{2t},y(0)=1
ty^'+ty=1-y	t\cdot\:y^{\prime\:}+t\cdot\:y=1-y
(\partial)/(\partial x)(xe^{sqrt(4xy)})	\frac{\partial\:}{\partial\:x}(xe^{\sqrt{4xy}})
integral of 8sin^3(xco)s^7x	\int\:8\sin^{3}(xco)s^{7}xdx
laplacetransform-sin(3t)	laplacetransform\:-\sin(3t)
derivative of y=(x^3+7)/x	derivative\:y=\frac{x^{3}+7}{x}
derivative of 5x^2-x^{1/3}	\frac{d}{dx}(5x^{2}-x^{\frac{1}{3}})
integral of (3v)/(1-4v^2)	\int\:\frac{3v}{1-4v^{2}}dv
tangent of f(x)=x^5+3x^2+2x,\at x=-1	tangent\:f(x)=x^{5}+3x^{2}+2x,\at\:x=-1
tangent of 3x^2-4x+6	tangent\:3x^{2}-4x+6
limit as x approaches-infinity of-2e^x	\lim\:_{x\to\:-\infty\:}(-2e^{x})
(\partial)/(\partial y)((x-y)/(xy+2))	\frac{\partial\:}{\partial\:y}(\frac{x-y}{xy+2})
slope of f(5)=4x^2+3x-8/(x^2)	slope\:f(5)=4x^{2}+3x-\frac{8}{x^{2}}
sum from n=1 to infinity of n/(n^2+1)x^n	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+1}x^{n}
tangent of y=x^2-2,(-2,2)	tangent\:y=x^{2}-2,(-2,2)
inverse oflaplace (s^2+4)/(s^2+4s+8)	inverselaplace\:\frac{s^{2}+4}{s^{2}+4s+8}
(\partial)/(\partial y)(x^2+3xy)	\frac{\partial\:}{\partial\:y}(x^{2}+3xy)
xy^{''}+5y^'=x	xy^{\prime\:\prime\:}+5y^{\prime\:}=x
integral of (1+x^2)/(1-x^2)	\int\:\frac{1+x^{2}}{1-x^{2}}dx
integral of 2t-3	\int\:2t-3dt
integral of (ln(x)+1)	\int\:(\ln(x)+1)dx
derivative of (6x^{4x})	\frac{d}{dx}((6x)^{4x})
integral of 1/((5x-2)^{5/2)}	\int\:\frac{1}{(5x-2)^{\frac{5}{2}}}dx
(\partial)/(\partial x)(2/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{2}{x^{2}+y^{2}})
(y^3-1)e^xdx+3y^2(e^x+1)dy=0	(y^{3}-1)e^{x}dx+3y^{2}(e^{x}+1)dy=0
slope ofintercept (2,-7),(-5,2)	slopeintercept\:(2,-7),(-5,2)
limit as x approaches 5 of x^2-5	\lim\:_{x\to\:5}(x^{2}-5)
integral of e^{sin^2(x)}sin(2x)	\int\:e^{\sin^{2}(x)}\sin(2x)dx
integral from 1/2 to 1 of 3/(sqrt(x)\sqrt{2-x)}	\int\:_{\frac{1}{2}}^{1}\frac{3}{\sqrt{x}\sqrt{2-x}}dx
integral of 1/((x-1)sqrt(x^2-2x))	\int\:\frac{1}{(x-1)\sqrt{x^{2}-2x}}dx
derivative of 5sqrt(x)	derivative\:5\sqrt{x}
tangent of y=8excos(x)	tangent\:y=8ex\cos(x)
integral from-infinity to 0 of xe^{6x}	\int\:_{-\infty\:}^{0}xe^{6x}dx
limit as x approaches 0 of x^{5x}	\lim\:_{x\to\:0}(x^{5x})
derivative of f(x)=(2x-8)/(20)[7.1]	derivative\:f(x)=\frac{2x-8}{20}[7.1]
(\partial)/(\partial x)(0)	\frac{\partial\:}{\partial\:x}(0)
taylor 1/x 2	taylor\:\frac{1}{x}2
integral of (nx)^{(n-1)/n}	\int\:(nx)^{\frac{n-1}{n}}dx
derivative of (sqrt(x)+4x(x^{3/2}-x))	\frac{d}{dx}((\sqrt{x}+4x)(x^{\frac{3}{2}}-x))
integral of (sec(x))/2	\int\:\frac{\sec(x)}{2}dx
limit as x approaches+7/8 of x^4	\lim\:_{x\to\:+\frac{7}{8}}(x^{4})
derivative of sinh(cosh(x^3))	\frac{d}{dx}(\sinh(\cosh(x^{3})))
derivative of sqrt(1+2tan(x))	\frac{d}{dx}(\sqrt{1+2\tan(x)})
derivative of (8x/(e^x))	\frac{d}{dx}(\frac{8x}{e^{x}})
area y=e^{2x},y=e^{-2x},x=1	area\:y=e^{2x},y=e^{-2x},x=1
derivative of y=(f(x))/(g(x))	derivative\:y=\frac{f(x)}{g(x)}
(\partial)/(\partial y)(x^2y+4y-7)	\frac{\partial\:}{\partial\:y}(x^{2}y+4y-7)
f(x)=(2x-3)^{ln(x)}	f(x)=(2x-3)^{\ln(x)}
integral of (x^{1.1}+7x^{2.5})	\int\:(x^{1.1}+7x^{2.5})dx
limit as x approaches 2 of 3x^3-1	\lim\:_{x\to\:2}(3x^{3}-1)
(\partial)/(\partial t)(tan(t))	\frac{\partial\:}{\partial\:t}(\tan(t))
(2x)y^'=x+3y	(2x)y^{\prime\:}=x+3y
inverse oflaplace s+2	inverselaplace\:s+2
y^{''}-6y^'+9y=30t^2e^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=30t^{2}e^{3t}
derivative of sqrt((27x^3/8))	\frac{d}{dx}(\sqrt{\frac{27x^{3}}{8}})
inverse oflaplace 1/(1+as)	inverselaplace\:\frac{1}{1+as}
integral of 8x^5	\int\:8x^{5}dx
derivative of ln(x^{12})	\frac{d}{dx}(\ln(x^{12}))
derivative of (250x/(x+3))	\frac{d}{dx}(\frac{250x}{x+3})
limit as x approaches 0-of 1/(1+e 1/x)	\lim\:_{x\to\:0-}(\frac{1}{1+e\frac{1}{x}})
derivative of 2+\sqrt[5]{x}	derivative\:2+\sqrt[5]{x}
(\partial)/(\partial x)((q(x,r,s,t)x+r)/(sx+t))	\frac{\partial\:}{\partial\:x}(\frac{q(x,r,s,t)x+r}{sx+t})
derivative of sinh(cosh(x))	\frac{d}{dx}(\sinh(\cosh(x)))
derivative of x-2/x	\frac{d}{dx}(x-\frac{2}{x})
tangent of f(x)=x^3-6x,(2,-4)	tangent\:f(x)=x^{3}-6x,(2,-4)
integral from-1 to 3 of (2x^2+1)	\int\:_{-1}^{3}(2x^{2}+1)dx
(\partial)/(\partial y)(ln(x^3+y^4))	\frac{\partial\:}{\partial\:y}(\ln(x^{3}+y^{4}))
(\partial)/(\partial t)(rsin(t))	\frac{\partial\:}{\partial\:t}(r\sin(t))
tangent of f(x)=2x^2+5,\at x=1	tangent\:f(x)=2x^{2}+5,\at\:x=1
derivative of (1+3x^4^5)	\frac{d}{dx}((1+3x^{4})^{5})
integral from 0 to 4 of (16-x^2)^2	\int\:_{0}^{4}(16-x^{2})^{2}dx
derivative of y=(2x+3)^2	derivative\:y=(2x+3)^{2}
limit as x approaches 0 of e^xln(x+1)	\lim\:_{x\to\:0}(e^{x}\ln(x+1))
integral of 4sin^3(x)cos(x)	\int\:4\sin^{3}(x)\cos(x)dx
integral of 1/((x^2-4)^{(3/2))}	\int\:\frac{1}{(x^{2}-4)^{(\frac{3}{2})}}dx
tangent of (x-1)/(x+1)	tangent\:\frac{x-1}{x+1}
derivative of e^x(x-5)	\frac{d}{dx}(e^{x}(x-5))
taylor 2e^z	taylor\:2e^{z}
derivative of (3x-7/(2x+4))	\frac{d}{dx}(\frac{3x-7}{2x+4})
derivative of f(x)=(7+tan(x))/(5-tan(x))	derivative\:f(x)=\frac{7+\tan(x)}{5-\tan(x)}
(\partial)/(\partial x)(-3ycos(3x))	\frac{\partial\:}{\partial\:x}(-3y\cos(3x))
(xy^2-3y)dx+(x^2y-3x)dy=0	(xy^{2}-3y)dx+(x^{2}y-3x)dy=0
integral of (1-x)/(3e^x)	\int\:\frac{1-x}{3e^{x}}dx
limit as x approaches 3 of x^2-4	\lim\:_{x\to\:3}(x^{2}-4)
limit as x approaches 0 of ((1+x)^3-1)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{3}-1}{x})
derivative of sin(pi/(sqrt(x)))	\frac{d}{dx}(\sin(\frac{π}{\sqrt{x}}))
limit as x approaches 0 of 1/(sin(x^2))	\lim\:_{x\to\:0}(\frac{1}{\sin(x^{2})})
integral of 5/(x(x^4+1))	\int\:\frac{5}{x(x^{4}+1)}dx
integral of (2x^2+16)/(x(x-2)^3)	\int\:\frac{2x^{2}+16}{x(x-2)^{3}}dx
derivative of (x^3/(1-x^2))	\frac{d}{dx}(\frac{x^{3}}{1-x^{2}})
slope of x^2-2	slope\:x^{2}-2
integral of (5x)/((x^2+7)^2)	\int\:\frac{5x}{(x^{2}+7)^{2}}dx
derivative of (tan(x)/2)	\frac{d}{dx}(\frac{\tan(x)}{2})
integral from 1 to 2 of (\|x+1\|+2)	\int\:_{1}^{2}(\left\|x+1\right\|+2)dx
derivative of y= 1/(sin(x))	derivative\:y=\frac{1}{\sin(x)}
(d^3)/(dx^3)(3/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{3}{x^{2}})
derivative of sqrt(30)	derivative\:\sqrt{30}
derivative of 7/(\sqrt[4]{x})	\frac{d}{dx}(\frac{7}{\sqrt[4]{x}})
derivative of 8/(x+2)	\frac{d}{dx}(\frac{8}{x+2})
(\partial)/(\partial x)(y^2-x^2-8)	\frac{\partial\:}{\partial\:x}(y^{2}-x^{2}-8)

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