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Popular Calculus Problems

limit as n approaches infinity of n/2	\lim\:_{n\to\:\infty\:}(\frac{n}{2})
derivative of 0.09e^xsqrt(x)	derivative\:0.09e^{x}\sqrt{x}
sum from n=0 to infinity of 8(1/2)^{n-1}	\sum\:_{n=0}^{\infty\:}8(\frac{1}{2})^{n-1}
roots x^2y	roots\:x^{2}y
integral of 15sin^2(θ)	\int\:15\sin^{2}(θ)dθ
limit as x approaches 3 of 3/((x-3)^2)	\lim\:_{x\to\:3}(\frac{3}{(x-3)^{2}})
derivative of ln((x^2/5+9/x))	\frac{d}{dx}(\ln(\frac{x^{2}}{5}+\frac{9}{x}))
tangent of y=2x^2-sqrt(x),(1,1)	tangent\:y=2x^{2}-\sqrt{x},(1,1)
derivative of sqrt(5x)+(sqrt(7)/x)	\frac{d}{dx}(\sqrt{5x}+\frac{\sqrt{7}}{x})
integral from 1 to 5 of (ln(x))/(x^5)	\int\:_{1}^{5}\frac{\ln(x)}{x^{5}}dx
derivative of f(x)=4x^3-11x^2-14x+19	derivative\:f(x)=4x^{3}-11x^{2}-14x+19
limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))}	\lim\:_{x\to\:0}((\frac{1+\tan(x)}{1+\sin(x)})^{\frac{1}{\sin(x)}})
derivative of (2x-x^2^3)	\frac{d}{dx}((2x-x^{2})^{3})
integral of (x^4)/((x^4-1))	\int\:\frac{x^{4}}{(x^{4}-1)}dx
derivative of y=x^{7/5}+e^{-4x}	derivative\:y=x^{\frac{7}{5}}+e^{-4x}
d/(dt)(sqrt(t+1))	\frac{d}{dt}(\sqrt{t+1})
derivative of \sqrt[4]{1/x}	\frac{d}{dx}(\sqrt[4]{\frac{1}{x}})
slope of (-4.3)(3.1)	slope\:(-4.3)(3.1)
(\partial)/(\partial x)(arcsec(-x))	\frac{\partial\:}{\partial\:x}(\arcsec(-x))
(\partial)/(\partial y)(ycos(x-y))	\frac{\partial\:}{\partial\:y}(y\cos(x-y))
derivative of 4/((x+2^2))	\frac{d}{dx}(\frac{4}{(x+2)^{2}})
integral of (x^4+9x^2+x+2)/(x^2+9)	\int\:\frac{x^{4}+9x^{2}+x+2}{x^{2}+9}dx
limit as x approaches-2 of (2-x)/(2+x)	\lim\:_{x\to\:-2}(\frac{2-x}{2+x})
normal of y=(x-2)^{2/3},(3,1)	normal\:y=(x-2)^{\frac{2}{3}},(3,1)
integral of e^{-1/3 x}	\int\:e^{-\frac{1}{3}x}dx
derivative of cot(e^x)	\frac{d}{dx}(\cot(e^{x}))
sum from n=3 to infinity of (4/10)^n	\sum\:_{n=3}^{\infty\:}(\frac{4}{10})^{n}
(\partial)/(\partial x)(x^2y+10xy)	\frac{\partial\:}{\partial\:x}(x^{2}y+10xy)
derivative of y=ln(8)x^2	derivative\:y=\ln(8)x^{2}
derivative of (2x-9)^2	derivative\:(2x-9)^{2}
integral of x^3e^{x^2-1}	\int\:x^{3}e^{x^{2}-1}dx
tangent of y=sqrt(x),(16,4)	tangent\:y=\sqrt{x},(16,4)
y^'+y/x = 7/(x^2)+3	y^{\prime\:}+\frac{y}{x}=\frac{7}{x^{2}}+3
integral of (ex^2+pi)	\int\:(ex^{2}+π)dx
limit as x approaches 0 of ((2\|x\|))/(3x)	\lim\:_{x\to\:0}(\frac{(2\left\|x\right\|)}{3x})
(\partial)/(\partial x)(x^2+y^2-ycos(x))	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-y\cos(x))
integral of-(x^2)/((-x+1)(x+1))	\int\:-\frac{x^{2}}{(-x+1)(x+1)}dx
xy^'=((1-x)y+x^2+x^3),y(3)=2	xy^{\prime\:}=((1-x)y+x^{2}+x^{3}),y(3)=2
limit as x approaches 3-of x/(\|x\|)	\lim\:_{x\to\:3-}(\frac{x}{\left\|x\right\|})
(\partial)/(\partial x)(2y^7+7y^9x^6)	\frac{\partial\:}{\partial\:x}(2y^{7}+7y^{9}x^{6})
integral of 2x(x+1)	\int\:2x(x+1)dx
limit as x approaches 2 of x^3+8	\lim\:_{x\to\:2}(x^{3}+8)
derivative of (200t)/(t+2)	derivative\:\frac{200t}{t+2}
integral of 1/((ln(x))^3x)	\int\:\frac{1}{(\ln(x))^{3}x}dx
derivative of 3/(4x)	derivative\:\frac{3}{4x}
integral of sin^2(3θ)	\int\:\sin^{2}(3θ)dθ
integral of-3/x+3e^x	\int\:-\frac{3}{x}+3e^{x}dx
integral of ((sin(x))/(2e^x))	\int\:(\frac{\sin(x)}{2e^{x}})dx
y^'=5y^2+xy^2	y^{\prime\:}=5y^{2}+xy^{2}
derivative of 1/2 ln(1+x^2)	derivative\:\frac{1}{2}\ln(1+x^{2})
limit as n approaches infinity of n^{-2}e^{3n}	\lim\:_{n\to\:\infty\:}(n^{-2}e^{3n})
slope of (-2,-4),(2,2)	slope\:(-2,-4),(2,2)
slope of 2x^2+4x-7	slope\:2x^{2}+4x-7
integral of 1/(4u^2+9)	\int\:\frac{1}{4u^{2}+9}du
limit as x approaches pi/3 of 1/(cot(x))	\lim\:_{x\to\:\frac{π}{3}}(\frac{1}{\cot(x)})
derivative of x^2+4x+8	derivative\:x^{2}+4x+8
(\partial)/(\partial x)(x^2+yz)	\frac{\partial\:}{\partial\:x}(x^{2}+yz)
x(dy}{dx}+\frac{y^2)/x =y	x\frac{dy}{dx}+\frac{y^{2}}{x}=y
(\partial)/(\partial y)(3x^2y^2-3)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}-3)
integral from 1 to 7 of 3x^2+1/(12x^2)	\int\:_{1}^{7}3x^{2}+\frac{1}{12x^{2}}dx
y^'=2y-1	y^{\prime\:}=2y-1
derivative of x^{4/3}(2-x^3)	\frac{d}{dx}(x^{\frac{4}{3}}(2-x)^{3})
integral of (sqrt(49-x^2))/(x^4)	\int\:\frac{\sqrt{49-x^{2}}}{x^{4}}dx
(d^3)/(dx^3)(x^6e^x)	\frac{d^{3}}{dx^{3}}(x^{6}e^{x})
tangent of f(x)=(6x+5)/(x-1),\at x=2	tangent\:f(x)=\frac{6x+5}{x-1},\at\:x=2
limit as t approaches 2 of (t-2)/(t^2-4)	\lim\:_{t\to\:2}(\frac{t-2}{t^{2}-4})
integral of 19tan^2(x)sec^3(x)	\int\:19\tan^{2}(x)\sec^{3}(x)dx
(\partial)/(\partial x)(4x^3+2xy+1)	\frac{\partial\:}{\partial\:x}(4x^{3}+2xy+1)
integral of x^2csc^2(x^3)	\int\:x^{2}\csc^{2}(x^{3})dx
limit as x approaches infinity of (an+1)/(an)	\lim\:_{x\to\:\infty\:}(\frac{an+1}{an})
integral from 0 to 1 of y-y^2	\int\:_{0}^{1}y-y^{2}dy
(\partial)/(\partial x)(y+sin(x))	\frac{\partial\:}{\partial\:x}(y+\sin(x))
derivative of 8e^{3x}	derivative\:8e^{3x}
integral of+(2x+1)/((x+5)^3)	\int\:+\frac{2x+1}{(x+5)^{3}}dx
derivative of 1/(\sqrt[3]{x^2+x+3})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x^{2}+x+3}})
d/(dy)(x-y^3+y^2sin(x))	\frac{d}{dy}(x-y^{3}+y^{2}\sin(x))
derivative of x^3+5	derivative\:x^{3}+5
limit as y approaches-3 of (5-y)^{4/3}	\lim\:_{y\to\:-3}((5-y)^{\frac{4}{3}})
f(x)=sqrt((x^2+1)/(x^2+4))	f(x)=\sqrt{\frac{x^{2}+1}{x^{2}+4}}
derivative of sqrt(1+9x)	\frac{d}{dx}(\sqrt{1+9x})
derivative of a^8+cos^8(x)	derivative\:a^{8}+\cos^{8}(x)
integral of (3x^5-2x^3+5x^2-2)/(x^3+1)	\int\:\frac{3x^{5}-2x^{3}+5x^{2}-2}{x^{3}+1}dx
limit as x approaches 4 of (3x)/4+2	\lim\:_{x\to\:4}(\frac{3x}{4}+2)
derivative of (x^2-3^3)	\frac{d}{dx}((x^{2}-3)^{3})
derivative of f(x)=(x-2)(5x+3)	derivative\:f(x)=(x-2)(5x+3)
tangent of f(x)= 1/x ,\at x=-1	tangent\:f(x)=\frac{1}{x},\at\:x=-1
limit as x approaches 0+of (x)^{sqrt(x)}	\lim\:_{x\to\:0+}((x)^{\sqrt{x}})
limit as x approaches 3 of-9	\lim\:_{x\to\:3}(-9)
derivative of f(x)= 8/(x^2)	derivative\:f(x)=\frac{8}{x^{2}}
integral from 0 to 80 of (317)/(903*80)	\int\:_{0}^{80}\frac{317}{903\cdot\:80}
integral of 1/(y+2)	\int\:\frac{1}{y+2}dy
(\partial)/(\partial y)(-2xysin(x^2y))	\frac{\partial\:}{\partial\:y}(-2xy\sin(x^{2}y))
integral from 0 to 4 of (2v+5)(3v-1)	\int\:_{0}^{4}(2v+5)(3v-1)dv
integral of (x^2)/(sqrt(6x^2-49))	\int\:\frac{x^{2}}{\sqrt{6x^{2}-49}}dx
tangent of f(x)=x^2-6,(-4,10)	tangent\:f(x)=x^{2}-6,(-4,10)
integral of (x^{-3})	\int\:(x^{-3})dx
(dy)/(dt)=t^2e^{-4t}-4y	\frac{dy}{dt}=t^{2}e^{-4t}-4y
tangent of 7xy^3+5xy=12,\at x=1	tangent\:7xy^{3}+5xy=12,\at\:x=1
integral of x^2sqrt(x-3)	\int\:x^{2}\sqrt{x-3}dx
limit as x approaches 0 of (3sin(x))/x	\lim\:_{x\to\:0}(\frac{3\sin(x)}{x})

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