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Popular Calculus Problems

tangent of y=(2x-1)(x+4),(1,5)	tangent\:y=(2x-1)(x+4),(1,5)
derivative of (12)/(x^5)-7/(\sqrt[5]{x)}	derivative\:\frac{12}{x^{5}}-\frac{7}{\sqrt[5]{x}}
derivative of sqrt((x^3-2x^{x^2-3)})	\frac{d}{dx}(\sqrt{(x^{3}-2x)^{x^{2}-3}})
derivative of x^2e^xsin(x)	\frac{d}{dx}(x^{2}e^{x}\sin(x))
derivative of f(x)=(x+9)/(x^2-7x+1)	derivative\:f(x)=\frac{x+9}{x^{2}-7x+1}
integral of x*sin(x^2)	\int\:x\cdot\:\sin(x^{2})dx
integral from-2 to 2 of x^2sqrt(1+4x^2)	\int\:_{-2}^{2}x^{2}\sqrt{1+4x^{2}}dx
integral of 5sin(6pix)	\int\:5\sin(6πx)dx
simplify ln((5x+2)(3x-4)^2)	simplify\:\ln((5x+2)(3x-4)^{2})
y^{''}-4y^'+4y=x^2	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=x^{2}
taylor (x+1)^{1/2}	taylor\:(x+1)^{\frac{1}{2}}
y^'=6x(y-1)^{2/3}	y^{\prime\:}=6x(y-1)^{\frac{2}{3}}
y^{''}+2sqrt(14)y^'+14y=0	y^{\prime\:\prime\:}+2\sqrt{14}y^{\prime\:}+14y=0
y^'+3/x y=x^2y^2	y^{\prime\:}+\frac{3}{x}y=x^{2}y^{2}
(\partial)/(\partial x)(e^{3x}cos(2x))	\frac{\partial\:}{\partial\:x}(e^{3x}\cos(2x))
integral of 1/(x^4)	\int\:\frac{1}{x^{4}}dx
derivative of (x^2/(1+x))	\frac{d}{dx}(\frac{x^{2}}{1+x})
derivative of 5/(x+1)	derivative\:\frac{5}{x+1}
derivative of sec(sqrt(x))	\frac{d}{dx}(\sec(\sqrt{x}))
integral from 1 to 2 of 11e^{1/x}	\int\:_{1}^{2}11e^{\frac{1}{x}}dx
integral of 4cos(θ)sin(θ)	\int\:4\cos(θ)\sin(θ)dθ
limit as x approaches 0+of (e^x-1)/x	\lim\:_{x\to\:0+}(\frac{e^{x}-1}{x})
inverse oflaplace 1/((s+1)^{1/2)}	inverselaplace\:\frac{1}{(s+1)^{\frac{1}{2}}}
slope of (-6,4),(-1,4)	slope\:(-6,4),(-1,4)
derivative of (x^{n-1}/n)	\frac{d}{dx}(\frac{x^{n-1}}{n})
sum from n=0 to infinity of (n^3)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{3}}{5^{n}}
(\partial)/(\partial x)(2x^3y+sin(x^2))	\frac{\partial\:}{\partial\:x}(2x^{3}y+\sin(x^{2}))
tangent of f(x)=(4x)/(x^2-5),(3,3)	tangent\:f(x)=\frac{4x}{x^{2}-5},(3,3)
limit as x approaches 7 of (x+2)/(x-7)	\lim\:_{x\to\:7}(\frac{x+2}{x-7})
integral of (e^{3x}+1)/(e^{2x)}	\int\:\frac{e^{3x}+1}{e^{2x}}dx
integral from 0 to 1 of (x-6)/(x^2-5x+6)	\int\:_{0}^{1}\frac{x-6}{x^{2}-5x+6}dx
(dy)/(dx)-e^{8x+y}=0	\frac{dy}{dx}-e^{8x+y}=0
integral of x*sin(2ax)	\int\:x\cdot\:\sin(2ax)dx
derivative of sqrt(cos(e^{x^{2cos(x))})}	derivative\:\sqrt{\cos(e^{x^{2\cos(x)}})}
derivative of f(x)=(x^2+1)*e^{x-1}	derivative\:f(x)=(x^{2}+1)\cdot\:e^{x-1}
derivative of f(x)=(3x^2+3x-1)^4	derivative\:f(x)=(3x^{2}+3x-1)^{4}
integral of xsin(x)cos(x)	\int\:x\cdot\:\sin(x)\cdot\:\cos(x)dx
derivative of y=ln(4/x)	derivative\:y=\ln(\frac{4}{x})
area y=xe-0.1x,y=0,x=3	area\:y=xe-0.1x,y=0,x=3
(\partial)/(\partial y)(x/y+e^y)	\frac{\partial\:}{\partial\:y}(\frac{x}{y}+e^{y})
tangent of f(x)=-3cos(x),\at x=(3pi)/4	tangent\:f(x)=-3\cos(x),\at\:x=\frac{3π}{4}
tangent of f(x)=x^2-9,(-5,16)	tangent\:f(x)=x^{2}-9,(-5,16)
derivative of tan(x)-1	derivative\:\tan(x)-1
3y+x^4(dy)/(dx)=2xy	3y+x^{4}\frac{dy}{dx}=2xy
derivative of y=cot(2)(cos(x))	derivative\:y=\cot(2)(\cos(x))
derivative of 5^{x-1}	\frac{d}{dx}(5^{x-1})
derivative of G(t)=(4t)/(t+1)	derivative\:G(t)=\frac{4t}{t+1}
tangent of f(x)=x^2+5x,\at x=4	tangent\:f(x)=x^{2}+5x,\at\:x=4
integral of xe^{-x}-e^{-x}	\int\:xe^{-x}-e^{-x}dx
(\partial)/(\partial x)(3e^{3x})	\frac{\partial\:}{\partial\:x}(3e^{3x})
y^'=y(1-y),y(0)=8	y^{\prime\:}=y(1-y),y(0)=8
derivative of xcos(x)-sin(x)	derivative\:x\cos(x)-\sin(x)
(dy)/(dx)=(y^2-1)/(x^2-1),y(8)=8	\frac{dy}{dx}=\frac{y^{2}-1}{x^{2}-1},y(8)=8
derivative of (x^2+x^3)	\frac{d}{dx}((x^{2}+x)^{3})
derivative of (1+x^2/(1-x^2))	\frac{d}{dx}(\frac{1+x^{2}}{1-x^{2}})
integral from 1 to 2 of (11)/(x^3+3x)	\int\:_{1}^{2}\frac{11}{x^{3}+3x}dx
integral of 1/(x^2*sqrt(9+x^2))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{9+x^{2}}}dx
integral of x/(sqrt(25+x^2))	\int\:\frac{x}{\sqrt{25+x^{2}}}dx
tangent of f(x)=2x^3+3x^2-12x+5	tangent\:f(x)=2x^{3}+3x^{2}-12x+5
limit as n approaches infinity of n-1	\lim\:_{n\to\:\infty\:}(n-1)
(dy)/(dx)=(x^2)/(y(1+x^3))	\frac{dy}{dx}=\frac{x^{2}}{y(1+x^{3})}
derivative of-(5e^{5/x})/(x^2)	derivative\:-\frac{5e^{\frac{5}{x}}}{x^{2}}
laplacetransform 200e^{-2t}+100e^{-t}+10	laplacetransform\:200e^{-2t}+100e^{-t}+10
limit as x approaches 1 of sqrt(x-2)	\lim\:_{x\to\:1}(\sqrt{x-2})
d/(dy)(e^xcos(xy))	\frac{d}{dy}(e^{x}\cos(xy))
integral of (sqrt(x)+1/(4sqrt(x)))	\int\:(\sqrt{x}+\frac{1}{4\sqrt{x}})dx
laplacetransform h(t)=t-2	laplacetransform\:h(t)=t-2
integral of x(x+6)^7	\int\:x(x+6)^{7}dx
(\partial)/(\partial y)(cos(x)+xcos(y)-y)	\frac{\partial\:}{\partial\:y}(\cos(x)+x\cos(y)-y)
sum from n=0 to infinity of (2/4)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{4})^{n}
integral of 5x+12	\int\:5x+12dx
sum from n=0 to infinity of n*(1/6)^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(\frac{1}{6})^{n}
xy^'+2y-2x^2y^2=0	xy^{\prime\:}+2y-2x^{2}y^{2}=0
integral of 1/(sqrt(x^2+6x+13))	\int\:\frac{1}{\sqrt{x^{2}+6x+13}}dx
integral from 1 to 4 of 3e^{sqrt(x)}	\int\:_{1}^{4}3e^{\sqrt{x}}dx
derivative of tan(pi)	\frac{d}{dx}(\tan(π))
area x=1,y=6x(2-x^2)^2	area\:x=1,y=6x(2-x^{2})^{2}
limit as x approaches-4-of (-4x^3)/(4+x)	\lim\:_{x\to\:-4-}(\frac{-4x^{3}}{4+x})
limit as x approaches a+of x^n	\lim\:_{x\to\:a+}(x^{n})
integral of (x^6+4x^3+4)/(x^3-4x^2)	\int\:\frac{x^{6}+4x^{3}+4}{x^{3}-4x^{2}}dx
derivative of cos(x+x^5)	\frac{d}{dx}(\cos(x)+x^{5})
(dy)/(dx)+5xy=4x	\frac{dy}{dx}+5xy=4x
integral of (sqrt(w))/(sqrt(1-\sqrt{w))}	\int\:\frac{\sqrt{w}}{\sqrt{1-\sqrt{w}}}dw
limit as x approaches 1 of 2/((x-1)^4)	\lim\:_{x\to\:1}(\frac{2}{(x-1)^{4}})
integral of u^{-1}	\int\:u^{-1}du
(\partial)/(\partial x)(3x^2+5y^7+9xy)	\frac{\partial\:}{\partial\:x}(3x^{2}+5y^{7}+9xy)
integral from 2 to 4 of (1-(x-3)^2)	\int\:_{2}^{4}(1-(x-3)^{2})dx
(\partial)/(\partial x)(sqrt(x+1))	\frac{\partial\:}{\partial\:x}(\sqrt{x+1})
integral from 1 to 4 of yln(y)	\int\:_{1}^{4}y\ln(y)dy
sum from n=0 to infinity of (e/2)^n	\sum\:_{n=0}^{\infty\:}(\frac{e}{2})^{n}
integral of xln(x+3)	\int\:x\ln(x+3)dx
integral from 1 to e of 8t^2ln(t)	\int\:_{1}^{e}8t^{2}\ln(t)dt
derivative of f(x)=sqrt(x^2+6x-1)	derivative\:f(x)=\sqrt{x^{2}+6x-1}
y^{'''}-y^{''}-y^'+y=5	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-y^{\prime\:}+y=5
integral of 7cot^5(x)sin^4(x)	\int\:7\cot^{5}(x)\sin^{4}(x)dx
integral from 0 to 1 of (36)/((2x+1)^3)	\int\:_{0}^{1}\frac{36}{(2x+1)^{3}}dx
integral of 1/x+1/(x^2)+1/(x^3)	\int\:\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}dx
integral of sin(2x)sin(7x)	\int\:\sin(2x)\sin(7x)dx
(dy}{dx}=\frac{sin(x))/y ,y(0)=1	\frac{dy}{dx}=\frac{\sin(x)}{y},y(0)=1
(\partial)/(\partial x)(y*e^{-x})	\frac{\partial\:}{\partial\:x}(y\cdot\:e^{-x})

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