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Popular Calculus Problems

derivative of (9x/(ln(x)))	\frac{d}{dx}(\frac{9x}{\ln(x)})
f(x)=sqrt((x+1)/x)	f(x)=\sqrt{\frac{x+1}{x}}
tangent of (x-6/x)^8	tangent\:(x-\frac{6}{x})^{8}
derivative of (3x^2+4x+3/(x^2+1))	\frac{d}{dx}(\frac{3x^{2}+4x+3}{x^{2}+1})
derivative of 2sec(x)+5cot(x)	derivative\:2\sec(x)+5\cot(x)
integral from 0 to pi of 2cos^2(x/2)	\int\:_{0}^{π}2\cos^{2}(\frac{x}{2})dx
(\partial)/(\partial y)(xyz)	\frac{\partial\:}{\partial\:y}(xyz)
y^{''}+5y^'+11y=33	y^{\prime\:\prime\:}+5y^{\prime\:}+11y=33
(dy)/(dt)=3cos(t)-5y	\frac{dy}{dt}=3\cos(t)-5y
(\partial)/(\partial x)(sin(12x)cos(2y))	\frac{\partial\:}{\partial\:x}(\sin(12x)\cos(2y))
integral from 6 to 8 of (74)/((x-6)^3)	\int\:_{6}^{8}\frac{74}{(x-6)^{3}}dx
limit as x approaches infinity+of 5x-1	\lim\:_{x\to\:\infty\:+}(5x-1)
integral from 1 to 7 of 1	\int\:_{1}^{7}1
integral of (1+((ln(x))^2)/x)	\int\:(1+\frac{(\ln(x))^{2}}{x})dx
integral of (9x^2-5x+4)	\int\:(9x^{2}-5x+4)dx
derivative of sin^2(2x-cos(2x))	\frac{d}{dx}(\sin^{2}(2x)-\cos(2x))
(\partial)/(\partial y)(3x^2y^2+x/y)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}+\frac{x}{y})
limit as x approaches 5 of 4x+\|x-5\|	\lim\:_{x\to\:5}(4x+\left\|x-5\right\|)
sum from n=1 to infinity of (x^n)/(12^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{12^{n}}
d/(dt)(cos(t))	\frac{d}{dt}(\cos(t))
(dy)/(dx)+sin^2(x)y=cos^2(x)y	\frac{dy}{dx}+\sin^{2}(x)y=\cos^{2}(x)y
tangent of y= 1/(2+3x),(1, 1/5)	tangent\:y=\frac{1}{2+3x},(1,\frac{1}{5})
limit as x approaches+2 of e^{1/(x-2)}	\lim\:_{x\to\:+2}(e^{\frac{1}{x-2}})
(-4sin(2x))^'	(-4\sin(2x))^{\prime\:}
derivative of f(x)=(20)/((x+3)^2)	derivative\:f(x)=\frac{20}{(x+3)^{2}}
derivative of 8^{cos(x})	\frac{d}{dx}(8^{\cos(x)})
tangent of f(x)=-x^2+4x,\at x=3	tangent\:f(x)=-x^{2}+4x,\at\:x=3
integral of (sin(x))/(sin(x)+1)	\int\:\frac{\sin(x)}{\sin(x)+1}dx
(dX)/(dX)	\frac{dX}{dX}
laplacetransform 5e^{-3(t-2)}	laplacetransform\:5e^{-3(t-2)}
y^{''}-2y^'+y=2t-1-(6te^t+6e^t)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=2t-1-(6te^{t}+6e^{t})
derivative of sqrt(1+T^2)	derivative\:\sqrt{1+T^{2}}
derivative of (4x-3/(x^2-2x))	\frac{d}{dx}(\frac{4x-3}{x^{2}-2x})
derivative of f(x)=tan^7(x)	derivative\:f(x)=\tan^{7}(x)
taylor e^x+1/(1+x),0	taylor\:e^{x}+\frac{1}{1+x},0
integral of 19tan^3(θ)	\int\:19\tan^{3}(θ)dθ
(\partial)/(\partial y)(x^5-6x+4y^3-y^2)	\frac{\partial\:}{\partial\:y}(x^{5}-6x+4y^{3}-y^{2})
integral of 1/(x+\sqrt[3]{x)}	\int\:\frac{1}{x+\sqrt[3]{x}}dx
derivative of 6x^4-3	derivative\:6x^{4}-3
integral of x^4(x^5-4)^8	\int\:x^{4}(x^{5}-4)^{8}dx
f(x)= 3/(3x+1)	f(x)=\frac{3}{3x+1}
derivative of (x^5+2x+6/(x^{1/3)})	\frac{d}{dx}(\frac{x^{5}+2x+6}{x^{\frac{1}{3}}})
derivative of f(x)=cos(5x^2)	derivative\:f(x)=\cos(5x^{2})
integral of (y-1)^2	\int\:(y-1)^{2}dy
(\partial)/(\partial x)(4ye^x)	\frac{\partial\:}{\partial\:x}(4ye^{x})
d/(dθ)(tan(θ))	\frac{d}{dθ}(\tan(θ))
derivative of x*y	\frac{d}{dx}(x\cdot\:y)
derivative of (ln(cos^2(x))^2)	\frac{d}{dx}((\ln(\cos^{2}(x)))^{2})
area 3(x^3-x),0,-1,0	area\:3(x^{3}-x),0,-1,0
integral of z/(z^2+1)	\int\:\frac{z}{z^{2}+1}dz
d/(dt)(arctan(t))	\frac{d}{dt}(\arctan(t))
derivative of y=(x+1)^2	derivative\:y=(x+1)^{2}
(dy)/(dx)=-xe^y	\frac{dy}{dx}=-xe^{y}
(\partial)/(\partial x)(8sin(xy))	\frac{\partial\:}{\partial\:x}(8\sin(xy))
d/(dy)(1/(4y^2))	\frac{d}{dy}(\frac{1}{4y^{2}})
(\partial)/(\partial y)((3xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{3xy}{x^{2}+y^{2}})
2y(dy)/(dx)=x(y^2+1)	2y\frac{dy}{dx}=x(y^{2}+1)
cos(x)dy+(ysin(x)-cos^4(x))dx=0	\cos(x)dy+(y\sin(x)-\cos^{4}(x))dx=0
tangent of f(x)=x+2sin(x)	tangent\:f(x)=x+2\sin(x)
(\partial)/(\partial x)((x^2+xy)^3)	\frac{\partial\:}{\partial\:x}((x^{2}+xy)^{3})
2xydx+x^2dy=0	2xydx+x^{2}dy=0
limit as x approaches 3+of x^2+2x	\lim\:_{x\to\:3+}(x^{2}+2x)
(dy)/(dx)=((5y))/((2x+3)(3x+2))	\frac{dy}{dx}=\frac{(5y)}{(2x+3)(3x+2)}
0.125y^{''}+4y^'+20y=0	0.125y^{\prime\:\prime\:}+4y^{\prime\:}+20y=0
(\partial)/(\partial y)(x/(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{x}{1+x^{2}+y^{2}})
integral from 0 to 1 of (9x)/(e^{2x)}	\int\:_{0}^{1}\frac{9x}{e^{2x}}dx
limit as x approaches 2-of \sqrt[3]{2-x}	\lim\:_{x\to\:2-}(\sqrt[3]{2-x})
derivative of 1+3/x	\frac{d}{dx}(1+\frac{3}{x})
integral of 1/(50+t)	\int\:\frac{1}{50+t}dt
derivative of f(x)=3t^4-7t^3+2	derivative\:f(x)=3t^{4}-7t^{3}+2
limit as x approaches 1 of sin(3pix)	\lim\:_{x\to\:1}(\sin(3pix))
derivative of e^{-20x}	derivative\:e^{-20x}
derivative of ln((3x/(x^2+4)))	\frac{d}{dx}(\ln(\frac{3x}{x^{2}+4}))
derivative of cosh^2(x)	\frac{d}{dx}(\cosh^{2}(x))
(dy)/(dx)=8x^3e^{-2y},y(1)=0	\frac{dy}{dx}=8x^{3}e^{-2y},y(1)=0
derivative of (x^2+14/(x^8))	\frac{d}{dx}(\frac{x^{2}+14}{x^{8}})
y^{''}+4y^'+6.25y=3.125(x+1)^2	y^{\prime\:\prime\:}+4y^{\prime\:}+6.25y=3.125(x+1)^{2}
y^'=2xy^{-2}	y^{\prime\:}=2xy^{-2}
derivative of ln^2(1-2x)	\frac{d}{dx}(\ln^{2}(1-2x))
derivative of f(x)= x/(ln(x))	derivative\:f(x)=\frac{x}{\ln(x)}
y^{''}+6y^'+19y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+19y=0
y^{''}=0	y^{\prime\:\prime\:}=0
integral of 1/(25+(x-6)^2)	\int\:\frac{1}{25+(x-6)^{2}}dx
inverse oflaplace 1/(5s^2+0.2s)	inverselaplace\:\frac{1}{5s^{2}+0.2s}
(\partial)/(\partial y)(e^{5y}cos(-5x))	\frac{\partial\:}{\partial\:y}(e^{5y}\cos(-5x))
integral of e^xsin(4x)	\int\:e^{x}\sin(4x)dx
derivative of log_{3}(4x+1)	\frac{d}{dx}(\log_{3}(4x+1))
(\partial)/(\partial y)(-9sin(3x+yz))	\frac{\partial\:}{\partial\:y}(-9\sin(3x+yz))
limit as x approaches pi/8 of tan(24x)	\lim\:_{x\to\:\frac{π}{8}}(\tan(24x))
derivative of tan(8x)	derivative\:\tan(8x)
integral from 0 to 1 of 9(e^{1/x})/(x^3)	\int\:_{0}^{1}9\frac{e^{\frac{1}{x}}}{x^{3}}dx
(\partial)/(\partial y)(8e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:y}(8e^{yz}\cos(xyz))
slope of (4.8)(2.12)	slope\:(4.8)(2.12)
derivative of sqrt(xe^{2x)}	\frac{d}{dx}(\sqrt{xe^{2x}})
integral of sin^2(pi/4+t/2)	\int\:\sin^{2}(\frac{π}{4}+\frac{t}{2})dt
limit as x approaches-7 of x^2-49	\lim\:_{x\to\:-7}(x^{2}-49)
derivative of 1/(t^2+5t-1)	derivative\:\frac{1}{t^{2}+5t-1}
tangent of y=(4x)/(x^2+1),(-1,-2)	tangent\:y=\frac{4x}{x^{2}+1},(-1,-2)
area x^3-13x^2+30x,-x^3+13x^2-30x	area\:x^{3}-13x^{2}+30x,-x^{3}+13x^{2}-30x
laplacetransform-(e^{-3(t-1)})/3-1/3	laplacetransform\:-\frac{e^{-3(t-1)}}{3}-\frac{1}{3}

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