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Popular Calculus Problems

derivative of f(4x^5)=8x^4	\frac{d}{dx}(f(4x^{5}))=8x^{4}
derivative of cos(6t)	derivative\:\cos(6t)
derivative of ((2x+7))/(sqrt(x))	derivative\:\frac{(2x+7)}{\sqrt{x}}
3y^{''}+3y^'-y=0	3y^{\prime\:\prime\:}+3y^{\prime\:}-y=0
tangent of x^3y^2=xy^3+6,(2,1)	tangent\:x^{3}y^{2}=xy^{3}+6,(2,1)
derivative of y=5x+ln(3x)	derivative\:y=5x+\ln(3x)
f^'(x)=4x+2	f^{\prime\:}(x)=4x+2
integral of x^2x^2+3	\int\:x^{2}x^{2}+3dx
(\partial)/(\partial x)((5x)/((3+y)))	\frac{\partial\:}{\partial\:x}(\frac{5x}{(3+y)})
y^{''}-2y^'=2x	y^{\prime\:\prime\:}-2y^{\prime\:}=2x
derivative of f(x)=x^{-2/5}+x^{2/5}	derivative\:f(x)=x^{-\frac{2}{5}}+x^{\frac{2}{5}}
(\partial)/(\partial y)((y^2)/(1+x^2))	\frac{\partial\:}{\partial\:y}(\frac{y^{2}}{1+x^{2}})
integral of (x-2)/(x^2-7x+12)	\int\:\frac{x-2}{x^{2}-7x+12}dx
(dy)/(dx)=(x(1+y^2))/(4y)	\frac{dy}{dx}=\frac{x(1+y^{2})}{4y}
derivative of x/2+3/2+4/(x+1)	\frac{d}{dx}(\frac{x}{2}+\frac{3}{2}+\frac{4}{x+1})
x(x-4)y^'+y=0	x(x-4)y^{\prime\:}+y=0
derivative of xln(2x)	derivative\:x\ln(2x)
integral of cos^4(x)	\int\:\cos^{4}(x)dx
d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t))	\frac{d}{dt}(a_{2}t\cos(2t)+a_{2}t\sin(2t))
integral of sqrt(1)	\int\:\sqrt{1}
derivative of (x+1^{2/3}-x^{2/3}+1)	\frac{d}{dx}((x+1)^{\frac{2}{3}}-x^{\frac{2}{3}}+1)
integral of (1-u^2)/(u+u^3)	\int\:\frac{1-u^{2}}{u+u^{3}}du
integral of 12x^2+e^x	\int\:12x^{2}+e^{x}dx
derivative of ln(arctan(4x^3))	\frac{d}{dx}(\ln(\arctan(4x^{3})))
integral of 2^{x+2}	\int\:2^{x+2}dx
integral of e^{-x/2}cos(x/2)	\int\:e^{-\frac{x}{2}}\cos(\frac{x}{2})dx
laplacetransform 10sin(3t)	laplacetransform\:10\sin(3t)
integral of (x+pi)sin(nx)	\int\:(x+π)\sin(nx)dx
y'=0.0014y(1700-y)	y\prime\:=0.0014y(1700-y)
laplacetransform 4cos^2(2t)	laplacetransform\:4\cos^{2}(2t)
derivative of (3x+7)/(4x-5)	derivative\:\frac{3x+7}{4x-5}
sum from n=0 to infinity of 37.06	\sum\:_{n=0}^{\infty\:}37.06
(\partial)/(\partial x)(6y(3x^2-y^2))	\frac{\partial\:}{\partial\:x}(6y(3x^{2}-y^{2}))
derivative of (x^3-8/(x^2-4))	\frac{d}{dx}(\frac{x^{3}-8}{x^{2}-4})
(d^2)/(dx^2)((x^2+1)/(x-3))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}+1}{x-3})
derivative of (5+x^4^{12})	\frac{d}{dx}((5+x^{4})^{12})
integral of 1/(v^2+1)	\int\:\frac{1}{v^{2}+1}dv
inverse oflaplace (2s+1)/(3s^2+5s)	inverselaplace\:\frac{2s+1}{3s^{2}+5s}
derivative of ln(ln(\sqrt[3]{x^9}))	\frac{d}{dx}(\ln(\ln(\sqrt[3]{x^{9}})))
(\partial)/(\partial y)(xsin(y)+ycos(x))	\frac{\partial\:}{\partial\:y}(x\sin(y)+y\cos(x))
integral of (x^2-4)/x	\int\:\frac{x^{2}-4}{x}dx
derivative of x^2sqrt(2x-3)	\frac{d}{dx}(x^{2}\sqrt{2x-3})
x^2y^'+4/3 xy=-4cos(3x)y^{-1/2}	x^{2}y^{\prime\:}+\frac{4}{3}xy=-4\cos(3x)y^{-\frac{1}{2}}
limit as x approaches 1+of 1/(x^2-1)	\lim\:_{x\to\:1+}(\frac{1}{x^{2}-1})
y^{''}-4y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}-4y=0,y(0)=0,y^{\prime\:}(0)=1
tangent of f(x)= 4/(1+x^2),(1,2)	tangent\:f(x)=\frac{4}{1+x^{2}},(1,2)
inverse oflaplace (3s+4)/(s^2+2)	inverselaplace\:\frac{3s+4}{s^{2}+2}
limit as x approaches 0 of x^2+3x-6	\lim\:_{x\to\:0}(x^{2}+3x-6)
5/2 y^4y^'-(sqrt(y^5+4))/(x^3)=0,y(1)=0	\frac{5}{2}y^{4}y^{\prime\:}-\frac{\sqrt{y^{5}+4}}{x^{3}}=0,y(1)=0
slope of (-6,-5),(4,4)	slope\:(-6,-5),(4,4)
derivative of sin(xcsc(x))	\frac{d}{dx}(\sin(x)\csc(x))
y^'=y(xy^3+4)	y^{\prime\:}=y(xy^{3}+4)
integral of e^{at}sin(t)	\int\:e^{at}\sin(t)dt
integral of sec^2(x/4)	\int\:\sec^{2}(\frac{x}{4})dx
integral of e^{3t}sin(t)	\int\:e^{3t}\sin(t)dt
(\partial}{\partial y}(\frac{2y)/x)	\frac{\partial\:}{\partial\:y}(\frac{2y}{x})
inverse oflaplace 1/(s^3+4s^2+3s)	inverselaplace\:\frac{1}{s^{3}+4s^{2}+3s}
integral of (arctan(x))	\int\:(\arctan(x))dx
derivative of cosh(ln(x))	\frac{d}{dx}(\cosh(\ln(x)))
integral from 0 to 2 of 6	\int\:_{0}^{2}6dx
integral of 1/(xsqrt(x-1))	\int\:\frac{1}{x\sqrt{x-1}}dx
derivative of e^{-h/7}	derivative\:e^{-\frac{h}{7}}
derivative of x*e^{-x^2}	\frac{d}{dx}(x\cdot\:e^{-x^{2}})
limit as x approaches 0+of (tan(6x))^2	\lim\:_{x\to\:0+}((\tan(6x))^{2})
(\partial)/(\partial x)(sqrt(x^5+y^7))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{5}+y^{7}})
integral of sqrt(1+(1/(2x)-x/2)^2)	\int\:\sqrt{1+(\frac{1}{2x}-\frac{x}{2})^{2}}dx
y^{''}+9y=6sin(3t)	y^{\prime\:\prime\:}+9y=6\sin(3t)
derivative of 2sec(x)	derivative\:2\sec(x)
derivative of 4^{2-2x}	\frac{d}{dx}(4^{2-2x})
integral from 0 to 1 of 2x(4-x^2)	\int\:_{0}^{1}2x(4-x^{2})dx
(\partial)/(\partial x)(10xye^{-(x^2+y^2)})	\frac{\partial\:}{\partial\:x}(10xye^{-(x^{2}+y^{2})})
integral from-1 to 1 of x/((x^2+1)^2)	\int\:_{-1}^{1}\frac{x}{(x^{2}+1)^{2}}dx
derivative of f(x)=tan(4x)	derivative\:f(x)=\tan(4x)
laplacetransform 4	laplacetransform\:4
derivative of-4cos(t)	derivative\:-4\cos(t)
sum from n=0 to infinity of (3n)/(4n-1)	\sum\:_{n=0}^{\infty\:}\frac{3n}{4n-1}
derivative of y=arctan(ln(2)x^5)	derivative\:y=\arctan(\ln(2)x^{5})
derivative of f(x)=5x^5+2/(sqrt(x))	derivative\:f(x)=5x^{5}+\frac{2}{\sqrt{x}}
(\partial)/(\partial x)((x^2+y^2)^5)	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{5})
derivative of y=sqrt(x^2-x+9)	derivative\:y=\sqrt{x^{2}-x+9}
(dy)/((5-3y)^2)=(dx)/(2(4-x))	\frac{dy}{(5-3y)^{2}}=\frac{dx}{2(4-x)}
laplacetransform e^{-0.75t}cos(4t)	laplacetransform\:e^{-0.75t}\cos(4t)
tangent of f(x)= 1/2 x^2,\at x=2	tangent\:f(x)=\frac{1}{2}x^{2},\at\:x=2
integral of (1-x^2)/(1-x)	\int\:\frac{1-x^{2}}{1-x}dx
integral of (t+1)/(3t^2+6t-5)	\int\:\frac{t+1}{3t^{2}+6t-5}dt
(\partial)/(\partial y)(xe^w)	\frac{\partial\:}{\partial\:y}(xe^{w})
limit as x approaches 2-of (3x)/(x-2)	\lim\:_{x\to\:2-}(\frac{3x}{x-2})
derivative of f(x)=(x^2+3x)^2	derivative\:f(x)=(x^{2}+3x)^{2}
integral of 8/(x^2sqrt(x^2+16))	\int\:\frac{8}{x^{2}\sqrt{x^{2}+16}}dx
limit as x approaches infinity of sqrt(81x^2+x-9x)	\lim\:_{x\to\:\infty\:}(\sqrt{81x^{2}+x-9x})
integral of 7e^{9x}	\int\:7e^{9x}dx
integral of y*e^{-y}	\int\:y\cdot\:e^{-y}dy
(2y+2t-9)dt+(8y+2t-1)dy=0	(2y+2t-9)dt+(8y+2t-1)dy=0
derivative of (7x/(x-1))	\frac{d}{dx}(\frac{7x}{x-1})
limit as x approaches 0 of x^x	\lim\:_{x\to\:0}(x^{x})
integral of sec^2(x/3)	\int\:\sec^{2}(\frac{x}{3})dx
(\partial)/(\partial x)(ln(4x))	\frac{\partial\:}{\partial\:x}(\ln(4x))
derivative of y=5x^2-10x-6x^{-2}	derivative\:y=5x^{2}-10x-6x^{-2}
derivative of (sin(x)/(cos(x)))	\frac{d}{dx}(\frac{\sin(x)}{\cos(x)})
(\partial)/(\partial x)(-(x-y)/(x^2(x+y)))	\frac{\partial\:}{\partial\:x}(-\frac{x-y}{x^{2}(x+y)})

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