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Popular Calculus Problems

tangent of f(x)=4e^x+x,(0,4)	tangent\:f(x)=4e^{x}+x,(0,4)
(\partial)/(\partial x)(1/3 t^6-6t^4+t)	\frac{\partial\:}{\partial\:x}(\frac{1}{3}t^{6}-6t^{4}+t)
y(dy)/(dx)2y=2+x^2	y\frac{dy}{dx}2y=2+x^{2}
(2cos(t))^'	(2\cos(t))^{\prime\:}
tangent of (16x)/(x^2+16)	tangent\:\frac{16x}{x^{2}+16}
integral of-12cos(ln(x))	\int\:-12\cos(\ln(x))dx
(\partial)/(\partial t)(1+(t-y)^2)	\frac{\partial\:}{\partial\:t}(1+(t-y)^{2})
integral of (x^3+4x^2+x-1)/(x^3+x^2)	\int\:\frac{x^{3}+4x^{2}+x-1}{x^{3}+x^{2}}dx
y^{''}+y=2+x^2	y^{\prime\:\prime\:}+y=2+x^{2}
derivative of 6^4x^3+x^5-180sqrt(4x^2)	\frac{d}{dx}(6^{4}x^{3}+x^{5}-180\sqrt{4x^{2}})
derivative of (-e^{-x}x-e^{-x}/(x^2))	\frac{d}{dx}(\frac{-e^{-x}x-e^{-x}}{x^{2}})
integral from-7 to 7 of (1+sqrt(49-x^2))	\int\:_{-7}^{7}(1+\sqrt{49-x^{2}})dx
(dy)/(dx)=(x^2+2y^2)/(xy)	\frac{dy}{dx}=\frac{x^{2}+2y^{2}}{xy}
tangent of f(x)= 1/((x-5)),\at x=-3	tangent\:f(x)=\frac{1}{(x-5)},\at\:x=-3
inverse oflaplace (2s+1)/(s^2-2s+2)	inverselaplace\:\frac{2s+1}{s^{2}-2s+2}
integral from 2 to 3 of 3x^2	\int\:_{2}^{3}3x^{2}dx
derivative of sqrt(2x+3)	derivative\:\sqrt{2x+3}
derivative of (1+10^{ln(x})^6)	\frac{d}{dx}((1+10^{\ln(x)})^{6})
integral of 1/(sqrt(3-2x-x^2))	\int\:\frac{1}{\sqrt{3-2x-x^{2}}}dx
derivative of (x^3+x+2/(x-1))	\frac{d}{dx}(\frac{x^{3}+x+2}{x-1})
(\partial)/(\partial x)((7xy^2)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{7xy^{2}}{x^{2}+y^{4}})
integral of (cos(x))/(sin^2(x)+2sin(x))	\int\:\frac{\cos(x)}{\sin^{2}(x)+2\sin(x)}dx
integral of 2e^{-x/4}	\int\:2e^{-\frac{x}{4}}dx
limit as x approaches 9+of 6	\lim\:_{x\to\:9+}(6)
y^'=y-x+1	y^{\prime\:}=y-x+1
integral of b^{4x}	\int\:b^{4x}dx
(\partial)/(\partial x)((x^2-y^2)^{0.5})	\frac{\partial\:}{\partial\:x}((x^{2}-y^{2})^{0.5})
integral of xsqrt(2x+1)	\int\:x\sqrt{2x+1}dx
(\partial)/(\partial y)(-(sin(2xy))/(xy))	\frac{\partial\:}{\partial\:y}(-\frac{\sin(2xy)}{xy})
derivative of x^{-3/4}+x^{3/4}	derivative\:x^{-\frac{3}{4}}+x^{\frac{3}{4}}
derivative of 2ln(2x+5)	\frac{d}{dx}(2\ln(2x+5))
derivative of x/(1+2x)	\frac{d}{dx}(\frac{x}{1+2x})
integral of x/(x^4+25)	\int\:\frac{x}{x^{4}+25}dx
integral of 5/(sqrt(x))	\int\:\frac{5}{\sqrt{x}}dx
y^2+(x^2(dy)/(dx))=(xy)(dy)/(dx)	y^{2}+(x^{2}\frac{dy}{dx})=(xy)\frac{dy}{dx}
derivative of (x(2-x)/(e^x))	\frac{d}{dx}(\frac{x(2-x)}{e^{x}})
integral of (1/(ln(x)))	\int\:(\frac{1}{\ln(x)})dx
integral of x^2(x-5)sqrt(7-x)	\int\:x^{2}(x-5)\sqrt{7-x}dx
d/(dw)(te^{(w/t)})	\frac{d}{dw}(te^{(\frac{w}{t})})
(1/(x+1))^'	(\frac{1}{x+1})^{\prime\:}
integral of (sqrt(2x)-cos(6x))	\int\:(\sqrt{2x}-\cos(6x))dx
limit as x approaches infinity of 0.8^x	\lim\:_{x\to\:\infty\:}(0.8^{x})
integral of 3x^2sqrt(2x^3-5)	\int\:3x^{2}\sqrt{2x^{3}-5}dx
tangent of f(x)=4-x^2,\at x=1.154	tangent\:f(x)=4-x^{2},\at\:x=1.154
tangent of x^3-3x^2+2x-2,\at x=0	tangent\:x^{3}-3x^{2}+2x-2,\at\:x=0
(\partial)/(\partial x)(1/(x^2+2y))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}+2y})
derivative of e^{-ix}	\frac{d}{dx}(e^{-ix})
limit as x approaches 0 of (1+x) 1/x	\lim\:_{x\to\:0}((1+x)\frac{1}{x})
integral of (15)/(1+9x^2)	\int\:\frac{15}{1+9x^{2}}dx
area-4x+x^2+10,9-2x,2x+1	area\:-4x+x^{2}+10,9-2x,2x+1
derivative of y=sqrt(x)-2\sqrt[3]{x}	derivative\:y=\sqrt{x}-2\sqrt[3]{x}
derivative of (2)(e^{3sqrt(x)})	derivative\:(2)(e^{3\sqrt{x}})
implicit (dy)/(dx),x^2+xy+y^2=7	implicit\:\frac{dy}{dx},x^{2}+xy+y^{2}=7
integral from 0 to pi/3 of 2sec^2(x)	\int\:_{0}^{\frac{π}{3}}2\sec^{2}(x)dx
area f(x)=sqrt(x)+3,g(x)= 1/2 x+3	area\:f(x)=\sqrt{x}+3,g(x)=\frac{1}{2}x+3
integral from 0 to 5 of 1/((5-x)^{1/3)}	\int\:_{0}^{5}\frac{1}{(5-x)^{\frac{1}{3}}}dx
integral of (x^4+2x^3-3)/(x^3)	\int\:\frac{x^{4}+2x^{3}-3}{x^{3}}dx
derivative of 1/((1-x)^2)	derivative\:\frac{1}{(1-x)^{2}}
5sqrt(xy)((dy)/(dx))=1	5\sqrt{xy}(\frac{dy}{dx})=1
derivative of sqrt(3-7x-x^2)	\frac{d}{dx}(\sqrt{3-7x-x^{2}})
integral of (x^3)/(sqrt(x^4+4))	\int\:\frac{x^{3}}{\sqrt{x^{4}+4}}dx
inverse oflaplace s/(s^2+s-2)	inverselaplace\:\frac{s}{s^{2}+s-2}
tangent of y=3e^x,\at x=2	tangent\:y=3e^{x},\at\:x=2
(\partial)/(\partial y)(xe^y+ye^x)	\frac{\partial\:}{\partial\:y}(xe^{y}+ye^{x})
tangent of f(x)=x^2+6x-5,\at x=2	tangent\:f(x)=x^{2}+6x-5,\at\:x=2
integral of 12(y^4+4y^2+1)^2(y^3+2y)	\int\:12(y^{4}+4y^{2}+1)^{2}(y^{3}+2y)dy
partialfraction x/(x+3)	partialfraction\:\frac{x}{x+3}
integral of 6sqrt(x+1)	\int\:6\sqrt{x+1}dx
inverse oflaplace (e^t-cos(t))/t	inverselaplace\:\frac{e^{t}-\cos(t)}{t}
integral of-2x^{-1}*x^{-2}	\int\:-2x^{-1}\cdot\:x^{-2}dx
y^{''}=-k^2*y	y^{\prime\:\prime\:}=-k^{2}\cdot\:y
tangent of f(x)=e^{x/3}	tangent\:f(x)=e^{\frac{x}{3}}
integral of xe^{1/2 x}	\int\:xe^{\frac{1}{2}x}dx
tangent of 2x^4+(3x)/5	tangent\:2x^{4}+\frac{3x}{5}
integral of cos((2pinx)/3)	\int\:\cos(\frac{2πnx}{3})dx
(d^2)/(dx^2)(21e^{1/x})	\frac{d^{2}}{dx^{2}}(21e^{\frac{1}{x}})
limit as x approaches infinity of (1-2/x)^{x+3}	\lim\:_{x\to\:\infty\:}((1-\frac{2}{x})^{x+3})
integral of 2x^{2/3}	\int\:2x^{\frac{2}{3}}dx
t^2y^'+ty=t^5	t^{2}y^{\prime\:}+ty=t^{5}
integral of (y+4)/y	\int\:\frac{y+4}{y}dy
integral from 0 to 2 of pi(4x)^2	\int\:_{0}^{2}π(4x)^{2}dx
integral of 1/(sqrt(169+x^2))	\int\:\frac{1}{\sqrt{169+x^{2}}}dx
(\partial)/(\partial x)(x^2ln(y)+5xy^3)	\frac{\partial\:}{\partial\:x}(x^{2}\ln(y)+5xy^{3})
derivative of x^2sqrt(8x-1)	derivative\:x^{2}\sqrt{8x-1}
derivative of (1-2x)/(4+x)	derivative\:\frac{1-2x}{4+x}
(\partial)/(\partial y)(2sqrt(y))	\frac{\partial\:}{\partial\:y}(2\sqrt{y})
integral of 3/(xsqrt(4-x^2))	\int\:\frac{3}{x\sqrt{4-x^{2}}}dx
slope of (-2,1),(1,6)	slope\:(-2,1),(1,6)
d/(du)(u^{-1})	\frac{d}{du}(u^{-1})
derivative of (x^2+3/2)	\frac{d}{dx}(\frac{x^{2}+3}{2})
integral of xsin(11-x)	\int\:x\sin(11-x)dx
derivative of f(x)=x^2(3+x)^{-5}	derivative\:f(x)=x^{2}(3+x)^{-5}
d/(dt)(e^t(cos(t)-sin(t)))	\frac{d}{dt}(e^{t}(\cos(t)-\sin(t)))
y^{''}+1/4 y=0,y(pi)=1,y^'(pi)=-3	y^{\prime\:\prime\:}+\frac{1}{4}y=0,y(π)=1,y^{\prime\:}(π)=-3
derivative of ((x-1/(x^2+x+1))^4)	\frac{d}{dx}((\frac{x-1}{x^{2}+x+1})^{4})
integral of sin(x)+3	\int\:\sin(x)+3dx
tangent of f(x)=x^2-x,\at x=3	tangent\:f(x)=x^{2}-x,\at\:x=3
integral of ((x^2+3x-2)/(sqrt(x)))	\int\:(\frac{x^{2}+3x-2}{\sqrt{x}})dx
derivative of log_{b}(x)	derivative\:\log_{b}(x)
derivative of 2sin(x+cos(3x))	\frac{d}{dx}(2\sin(x)+\cos(3x))

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