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Popular Calculus Problems

(\partial)/(\partial x)(ln(4x+5y))	\frac{\partial\:}{\partial\:x}(\ln(4x+5y))
limit as x approaches 0+of e^{-2x}ln(x)	\lim\:_{x\to\:0+}(e^{-2x}\ln(x))
taylor 1/x ,3	taylor\:\frac{1}{x},3
derivative of 1/2 xy	derivative\:\frac{1}{2}xy
derivative of 6x+16/3	derivative\:6x+\frac{16}{3}
(\partial)/(\partial x)(2sin(2x))	\frac{\partial\:}{\partial\:x}(2\sin(2x))
derivative of sqrt(5t)	derivative\:\sqrt{5t}
derivative of 1/(x^2(3x+1))	\frac{d}{dx}(\frac{1}{x^{2}(3x+1)})
(\partial)/(\partial x)(xy^2cos(2+x^2y))	\frac{\partial\:}{\partial\:x}(xy^{2}\cos(2+x^{2}y))
area 2sin(x),[0,pi]	area\:2\sin(x),[0,π]
tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6	tangent\:f(x)=\frac{5}{2\sqrt{5x+6}},\at\:x=6
(\partial)/(\partial x)(sqrt(3x))	\frac{\partial\:}{\partial\:x}(\sqrt{3x})
y^'-4y=7e^{4x}	y^{\prime\:}-4y=7e^{4x}
integral of 1/(x^2+11x+30)	\int\:\frac{1}{x^{2}+11x+30}dx
integral of x*e^{-ax}	\int\:x\cdot\:e^{-ax}dx
integral of (x^2)/((x^2+4x+5)^2)	\int\:\frac{x^{2}}{(x^{2}+4x+5)^{2}}dx
derivative of 1/(2x+5)	\frac{d}{dx}(\frac{1}{2x+5})
integral of (cos^2(x))/(1-sin(x))	\int\:\frac{\cos^{2}(x)}{1-\sin(x)}dx
limit as x approaches 2 of 9x	\lim\:_{x\to\:2}(9x)
tangent of sqrt(5x+6),\at x=2	tangent\:\sqrt{5x+6},\at\:x=2
tangent of y=e^{3x},\at x= 1/3 ln(3)	tangent\:y=e^{3x},\at\:x=\frac{1}{3}\ln(3)
y(x+1)+(dy)/(dx)=0	y(x+1)+\frac{dy}{dx}=0
derivative of 6-x^2	derivative\:6-x^{2}
integral from-sqrt(y) to sqrt(y of)x	\int\:_{-\sqrt{y}}^{\sqrt{y}}xdx
derivative of 2xe^{-3x}	\frac{d}{dx}(2xe^{-3x})
derivative of x^6(x-4^5)	\frac{d}{dx}(x^{6}(x-4)^{5})
derivative of (1-2x^3)	\frac{d}{dx}((1-2x)^{3})
integral of (7+5x)/(1+x^2)	\int\:\frac{7+5x}{1+x^{2}}dx
derivative of ln(3+4x)	\frac{d}{dx}(\ln(3+4x))
integral of tan^3(4x)sec^2(4x)	\int\:\tan^{3}(4x)\sec^{2}(4x)dx
(x^{-3})^'	(x^{-3})^{\prime\:}
integral of sqrt(x/(2-x))	\int\:\sqrt{\frac{x}{2-x}}dx
integral of log_{e}(x^2)	\int\:\log_{e}(x^{2})dx
laplacetransform e^{5t}(-2cos(t)+12sin(t))	laplacetransform\:e^{5t}(-2\cos(t)+12\sin(t))
(\partial)/(\partial x)(ysqrt(1+x^7))	\frac{\partial\:}{\partial\:x}(y\sqrt{1+x^{7}})
integral of (11x^2)/((144+x^2)^2)	\int\:\frac{11x^{2}}{(144+x^{2})^{2}}dx
derivative of x^6ln(7x)	\frac{d}{dx}(x^{6}\ln(7x))
derivative of y= 1/((x^2-1)(x^2+3x+3))	derivative\:y=\frac{1}{(x^{2}-1)(x^{2}+3x+3)}
derivative of x^{9/4}	\frac{d}{dx}(x^{\frac{9}{4}})
derivative of f(θ)=sqrt(11θ)	derivative\:f(θ)=\sqrt{11θ}
f(s)=sqrt((s^2+1)/(s^2+4))	f(s)=\sqrt{\frac{s^{2}+1}{s^{2}+4}}
integral from 1 to 4 of x-(x-2)^2	\int\:_{1}^{4}x-(x-2)^{2}dx
limit as x approaches 2 of sqrt((6-x)-2)	\lim\:_{x\to\:2}(\sqrt{(6-x)-2})
derivative of (90/(x^9))	\frac{d}{dx}(\frac{90}{x^{9}})
derivative of sqrt(6t+8)	derivative\:\sqrt{6t+8}
integral of xsqrt(3x+1)	\int\:x\sqrt{3x+1}dx
integral from 5 to infinity of 1/(x^2+x)	\int\:_{5}^{\infty\:}\frac{1}{x^{2}+x}dx
derivative of f(x)=(x^2)/(x+1)	derivative\:f(x)=\frac{x^{2}}{x+1}
integral from 0 to 16 of 0.8(16-x)	\int\:_{0}^{16}0.8(16-x)dx
sqrt(1-4t^2)ds+2sqrt(1-s^2)dt=0	\sqrt{1-4t^{2}}ds+2\sqrt{1-s^{2}}dt=0
integral of (x^2-5x+4)	\int\:(x^{2}-5x+4)dx
integral of cos(4x)cos(2x)	\int\:\cos(4x)\cos(2x)dx
derivative of ar(xcos(x))	\frac{d}{dx}(ar(x)\cos(x))
integral of (-x-1)/(x^2+3)	\int\:\frac{-x-1}{x^{2}+3}dx
integral of sqrt(x)sqrt(x^{3/2)}-1	\int\:\sqrt{x}\sqrt{x^{\frac{3}{2}}}-1dx
area sin(x),cos(x),x=-pi/6	area\:\sin(x),\cos(x),x=-\frac{π}{6}
derivative of x^2e^{5x}	\frac{d}{dx}(x^{2}e^{5x})
derivative of sqrt(7+4x)	derivative\:\sqrt{7+4x}
integral from 0 to 4 of-x^2	\int\:_{0}^{4}-x^{2}dx
limit as x approaches 2 of 4-2x	\lim\:_{x\to\:2}(4-2x)
(dy)/(dx)-y=3e^x+12e^{4x}	\frac{dy}{dx}-y=3e^{x}+12e^{4x}
integral of x^2*sqrt(16-x^2)	\int\:x^{2}\cdot\:\sqrt{16-x^{2}}dx
derivative of (x-15/(sqrt(x)-\sqrt{15)})	\frac{d}{dx}(\frac{x-15}{\sqrt{x}-\sqrt{15}})
derivative of sqrt(4x+8)	derivative\:\sqrt{4x+8}
limit as x approaches 1 of x-3	\lim\:_{x\to\:1}(x-3)
derivative of y=x*e^{4-x}	derivative\:y=x\cdot\:e^{4-x}
area y=sqrt(x-1),x-y=1	area\:y=\sqrt{x-1},x-y=1
derivative of (5x^{4x})	\frac{d}{dx}((5x)^{4x})
derivative of (sec(sin(sqrt(x^2+6^x)))^4)	\frac{d}{dx}((\sec(\sin(\sqrt{x^{2}+6^{x}})))^{4})
integral of 9x^3e^x	\int\:9x^{3}e^{x}dx
derivative of (x^2/((2+x)))	\frac{d}{dx}(\frac{x^{2}}{(2+x)})
x((dy)/(dx))+y=4x+1	x(\frac{dy}{dx})+y=4x+1
derivative of sqrt(x)-4	derivative\:\sqrt{x}-4
area y=sin(x),y=3x,x= pi/2 ,x=pi	area\:y=\sin(x),y=3x,x=\frac{π}{2},x=π
derivative of \sqrt[3]{x^3+6x+7}	\frac{d}{dx}(\sqrt[3]{x^{3}+6x+7})
derivative of f(x)=(-4)/(x^3)	derivative\:f(x)=\frac{-4}{x^{3}}
integral of (x^3+x^2+x+2)/(x^4+3x^2+2)	\int\:\frac{x^{3}+x^{2}+x+2}{x^{4}+3x^{2}+2}dx
integral of (1-2x-x^2)/((x+1)^2)	\int\:\frac{1-2x-x^{2}}{(x+1)^{2}}dx
derivative of 5/((2x)^3)	derivative\:\frac{5}{(2x)^{3}}
integral from 0 to 1/4 of xarcsin(4x)	\int\:_{0}^{\frac{1}{4}}x\arcsin(4x)dx
derivative of ((m^2))/4+((3m))/2+2	derivative\:\frac{(m^{2})}{4}+\frac{(3m)}{2}+2
dy-(y-1)dx=0	dy-(y-1)dx=0
integral of 12sin^3(x)cos^2(x)	\int\:12\sin^{3}(x)\cos^{2}(x)dx
derivative of tan(2x^6)	\frac{d}{dx}(\tan(2)x^{6})
integral of e^{-6r}	\int\:e^{-6r}dr
y^'=5(x-2)y^{1/2}-y/(x-2)	y^{\prime\:}=5(x-2)y^{\frac{1}{2}}-\frac{y}{x-2}
(\partial)/(\partial x)(1x,4y)	\frac{\partial\:}{\partial\:x}(1x,4y)
limit as x approaches 1+of 1-cos(2(x-1))	\lim\:_{x\to\:1+}(1-\cos(2(x-1)))
derivative of sin(θ)cos(θ)	derivative\:\sin(θ)\cos(θ)
integral of-sec(x)	\int\:-\sec(x)dx
limit as x approaches-27 of 6/(x+27)	\lim\:_{x\to\:-27}(\frac{6}{x+27})
integral from 0 to-0.4 of 400x	\int\:_{0}^{-0.4}400xdx
derivative of (-2x^3-1/((x^3-1)^2))	\frac{d}{dx}(\frac{-2x^{3}-1}{(x^{3}-1)^{2}})
integral of y^6	\int\:y^{6}dy
yy^'=x(1+y^2)	yy^{\prime\:}=x(1+y^{2})
derivative of e^{e^{2x}}	\frac{d}{dx}(e^{e^{2x}})
integral of (2x+1)/(x^2+2x+65)	\int\:\frac{2x+1}{x^{2}+2x+65}dx
derivative of (3x^2+1/(2x))	\frac{d}{dx}(\frac{3x^{2}+1}{2x})
integral of sin^3(b)cos^3(b)	\int\:\sin^{3}(b)\cos^{3}(b)
limit as x approaches-2 of x^4+5^x-2	\lim\:_{x\to\:-2}(x^{4}+5^{x}-2)

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