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Popular Calculus Problems

(\partial)/(\partial x)(x^7-6xy-3y^2)	\frac{\partial\:}{\partial\:x}(x^{7}-6xy-3y^{2})
integral of (sin(x/2)+cos(x/2))^2	\int\:(\sin(\frac{x}{2})+\cos(\frac{x}{2}))^{2}dx
inverse oflaplace (2(s+1))/(s(s^2+s+2))	inverselaplace\:\frac{2(s+1)}{s(s^{2}+s+2)}
sum from n=1 to infinity of 4/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{4}{(n+1)!}
derivative of f(x)=7x^2	derivative\:f(x)=7x^{2}
derivative of 5/4 x^{4/3}	derivative\:\frac{5}{4}x^{\frac{4}{3}}
derivative of f(x)=ln(x-2)	derivative\:f(x)=\ln(x-2)
derivative of y=2cos(x+y)	derivative\:y=2\cos(x+y)
(d^2)/(dx^2)(x^2-y^2)	\frac{d^{2}}{dx^{2}}(x^{2}-y^{2})
d/(d{x)}({y}{z}({x})^3)	\frac{d}{d{x}}({y}{z}({x})^{3})
(\partial)/(\partial y)(0)	\frac{\partial\:}{\partial\:y}(0)
derivative of 2e^{2x}*x	\frac{d}{dx}(2e^{2x}\cdot\:x)
integral of sin(x)+6	\int\:\sin(x)+6dx
integral of (x^2+6x-8)/(x^3-4x)	\int\:\frac{x^{2}+6x-8}{x^{3}-4x}dx
(\partial)/(\partial y)(ln(3x+y))	\frac{\partial\:}{\partial\:y}(\ln(3x+y))
integral of (x-1)^2x	\int\:(x-1)^{2}xdx
derivative of (1-x/(1+x))	\frac{d}{dx}(\frac{1-x}{1+x})
limit as x approaches 0 of 4/x-4/(e^x-1)	\lim\:_{x\to\:0}(\frac{4}{x}-\frac{4}{e^{x}-1})
(\partial)/(\partial x)((6x+3y)ey)	\frac{\partial\:}{\partial\:x}((6x+3y)ey)
integral of 1/((x-3)(x+2))	\int\:\frac{1}{(x-3)(x+2)}dx
tangent of f(x)=x^2+6,(4,22)	tangent\:f(x)=x^{2}+6,(4,22)
slope of (1,6),(0.5,8)	slope\:(1,6),(0.5,8)
limit as x approaches 0 of (1-2x)^{1/2}	\lim\:_{x\to\:0}((1-2x)^{\frac{1}{2}})
inverse oflaplace (150)/(s(s^2+8s+25))	inverselaplace\:\frac{150}{s(s^{2}+8s+25)}
(\partial)/(\partial x)(1/({f)(x)})	\frac{\partial\:}{\partial\:x}(\frac{1}{{f}(x)})
derivative of (4x/(7-cot(x)))	\frac{d}{dx}(\frac{4x}{7-\cot(x)})
limit as x approaches 1-of 1/(1-x)	\lim\:_{x\to\:1-}(\frac{1}{1-x})
derivative of ln(sqrt(x^2+4))	\frac{d}{dx}(\ln(\sqrt{x^{2}+4}))
(\partial)/(\partial x)(e^{-2x}sin(y))	\frac{\partial\:}{\partial\:x}(e^{-2x}\sin(y))
sum from n=1 to infinity of (n^4)/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{4}}{4^{n}}
area x, 1/(x^2),[0,1]	area\:x,\frac{1}{x^{2}},[0,1]
derivative of ln((1-x^2^{-1/2}))	\frac{d}{dx}(\ln((1-x^{2})^{-\frac{1}{2}}))
derivative of 1/(sqrt(1+s^2))	derivative\:\frac{1}{\sqrt{1+s^{2}}}
integral of 8t^3-6t^{-2}	\int\:8t^{3}-6t^{-2}dt
limit as x approaches 5+of 2/(x-5)	\lim\:_{x\to\:5+}(\frac{2}{x-5})
integral of (e^x-1)^3	\int\:(e^{x}-1)^{3}dx
derivative of f(x)=sin(5x^2)	derivative\:f(x)=\sin(5x^{2})
limit as x approaches 0 of e^{x(1-s)}	\lim\:_{x\to\:0}(e^{x(1-s)})
integral of x^3cos(6x)	\int\:x^{3}\cos(6x)dx
integral of sin((npit)/2)	\int\:\sin(\frac{nπt}{2})dt
integral of (2x^2+1/((2x)^2))	\int\:(2x^{2}+\frac{1}{(2x)^{2}})dx
derivative of f(x)=-2xsin(x^2)	derivative\:f(x)=-2x\sin(x^{2})
(\partial)/(\partial c)((a^3b^4)/(c^2d^4))	\frac{\partial\:}{\partial\:c}(\frac{a^{3}b^{4}}{c^{2}d^{4}})
f(x)=arccos(sqrt(x))	f(x)=\arccos(\sqrt{x})
derivative of 3xe^{-3x}	\frac{d}{dx}(3xe^{-3x})
(\partial)/(\partial x)(2cos(4x))	\frac{\partial\:}{\partial\:x}(2\cos(4x))
taylor e^{e^t}	taylor\:e^{e^{t}}
integral of 5sec^2(5x)tan^5(5x)	\int\:5\sec^{2}(5x)\tan^{5}(5x)dx
derivative of ((x+1)/2)	\frac{d}{dx}(\frac{(x+1)}{2})
d/(dt)(a(1-cos(t)))	\frac{d}{dt}(a(1-\cos(t)))
(dy)/(dt)=e^t(y-1)^2	\frac{dy}{dt}=e^{t}(y-1)^{2}
simplify ln(3x)-1/6 x	simplify\:\ln(3x)-\frac{1}{6}x
limit as x approaches 2 of (x+2)/(x^2-4)	\lim\:_{x\to\:2}(\frac{x+2}{x^{2}-4})
integral of 1/(sqrt(x))sin(sqrt(x))	\int\:\frac{1}{\sqrt{x}}\sin(\sqrt{x})dx
integral of x/((x^2+1)(x^2+4))	\int\:\frac{x}{(x^{2}+1)(x^{2}+4)}dx
integral of (1+0.5t)e^{-0.004t}	\int\:(1+0.5t)e^{-0.004t}dt
(\partial)/(\partial x)(5x^2-2y)	\frac{\partial\:}{\partial\:x}(5x^{2}-2y)
integral of (x^{3/2}+8x+9)	\int\:(x^{\frac{3}{2}}+8x+9)dx
tangent of f(x)=-3x^2+6x+4,\at x=1	tangent\:f(x)=-3x^{2}+6x+4,\at\:x=1
limit as x approaches 0 of (ln(x+2))/x	\lim\:_{x\to\:0}(\frac{\ln(x+2)}{x})
(dy)/(dx)= y/(y-x)	\frac{dy}{dx}=\frac{y}{y-x}
area y=x^2,y=9	area\:y=x^{2},y=9
laplacetransform x^{7/2}	laplacetransform\:x^{\frac{7}{2}}
d/(dt)(te^{-2t})	\frac{d}{dt}(te^{-2t})
(\partial)/(\partial x)(cos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\cos(x^{2}+y^{2}))
integral of (2400x)sqrt(3+2x)	\int\:(2400x)\sqrt{3+2x}dx
derivative of 4+2x^{3/2}	\frac{d}{dx}(4+2x^{\frac{3}{2}})
sum from n=1 to infinity}\sqrt[n]{2 of-1	\sum\:_{n=1}^{\infty\:}\sqrt[n]{2}-1
derivative of ln((x+3^2))	\frac{d}{dx}(\ln((x+3)^{2}))
integral of (x^3)/(sqrt(x^2-36))	\int\:\frac{x^{3}}{\sqrt{x^{2}-36}}dx
(\partial)/(\partial y)(2sqrt(xy))	\frac{\partial\:}{\partial\:y}(2\sqrt{xy})
integral from-2pi to 2pi of sin^2(x)+1	\int\:_{-2π}^{2π}\sin^{2}(x)+1dx
integral from 1 to 2 of-(5ln(x))/(x^2)	\int\:_{1}^{2}-\frac{5\ln(x)}{x^{2}}dx
integral of (-5)/x	\int\:\frac{-5}{x}dx
integral of x^{-6}(x+1)	\int\:x^{-6}(x+1)dx
y^{''}-9y^'+18y=2sin(5t)	y^{\prime\:\prime\:}-9y^{\prime\:}+18y=2\sin(5t)
taylor e^{cos(sin(x^2))}	taylor\:e^{\cos(\sin(x^{2}))}
integral from-1 to 1 of-1	\int\:_{-1}^{1}-1dx
integral of (sqrt(x)-1/(sqrt(x)))^2	\int\:(\sqrt{x}-\frac{1}{\sqrt{x}})^{2}dx
(\partial)/(\partial x)(e^{-1})	\frac{\partial\:}{\partial\:x}(e^{-1})
limit as x approaches 3 of x^2-6x+8	\lim\:_{x\to\:3}(x^{2}-6x+8)
integral of cos(4θ)cos(-3θ)	\int\:\cos(4θ)\cos(-3θ)dθ
integral of 1/(t^2sqrt(4-t^2))	\int\:\frac{1}{t^{2}\sqrt{4-t^{2}}}dt
(\partial)/(\partial x)(-13e^xsin(y)-14y)	\frac{\partial\:}{\partial\:x}(-13e^{x}\sin(y)-14y)
d/(da)(sin(a)-sin(6a)+sin(5a))	\frac{d}{da}(\sin(a)-\sin(6a)+\sin(5a))
limit as x approaches 0 of e^{-4x}	\lim\:_{x\to\:0}(e^{-4x})
y^'=(1.5-0.8y)/(0.5+0.8x)	y^{\prime\:}=\frac{1.5-0.8y}{0.5+0.8x}
integral of x(e^{x^2}+2)	\int\:x(e^{x^{2}}+2)dx
derivative of arcsin(4x^4)	\frac{d}{dx}(\arcsin(4x^{4}))
derivative of 2cos(x+cos(2)(x))	\frac{d}{dx}(2\cos(x)+\cos(2)(x))
sum from n=1 to infinity of ar^{n-1}	\sum\:_{n=1}^{\infty\:}ar^{n-1}
integral of (6x^2+1)/x	\int\:\frac{6x^{2}+1}{x}dx
derivative of 1+4sin^2(x)	\frac{d}{dx}(1+4\sin^{2}(x))
derivative of x^{11}arcsin(x)	derivative\:x^{11}\arcsin(x)
2y(x^2+4)^2=(5x(y^2+1)^2)/(y^'(x^2+4))	2y(x^{2}+4)^{2}=\frac{5x(y^{2}+1)^{2}}{y^{\prime\:}(x^{2}+4)}
integral of (e^x-25^x)	\int\:(e^{x}-25^{x})dx
(\partial)/(\partial x)(xsin(yz))	\frac{\partial\:}{\partial\:x}(x\sin(yz))
yy^'+25x=0	yy^{\prime\:}+25x=0
derivative of-2x^{-1}	\frac{d}{dx}(-2x^{-1})
y^'=2x-y,y(0)=1	y^{\prime\:}=2x-y,y(0)=1

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