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Popular Calculus Problems

derivative of sqrt(y/4)	derivative\:\sqrt{\frac{y}{4}}
(\partial)/(\partial x)((x-a/(y^3))(b-x))	\frac{\partial\:}{\partial\:x}((x-\frac{a}{y^{3}})(b-x))
(dP)/(dt)=7sqrt(Pt),P(1)=5	\frac{dP}{dt}=7\sqrt{Pt},P(1)=5
sum from n=1 to infinity of 1/n (-1)^n	\sum\:_{n=1}^{\infty\:}\frac{1}{n}(-1)^{n}
-y^{''}+3y^'=0	-y^{\prime\:\prime\:}+3y^{\prime\:}=0
tangent of y=2x^2-6x+6,(1,2)	tangent\:y=2x^{2}-6x+6,(1,2)
integral of a^{4x}	\int\:a^{4x}dx
derivative of sin(3x^2-1)	\frac{d}{dx}(\sin(3x^{2}-1))
limit as x approaches 0 of (1+x)^{1/(3x)}	\lim\:_{x\to\:0}((1+x)^{\frac{1}{3x}})
derivative of y=sqrt(3x)+3sqrt(x)	derivative\:y=\sqrt{3x}+3\sqrt{x}
(dy)/(dx)+y=e^xy^{-2}	\frac{dy}{dx}+y=e^{x}y^{-2}
tangent of y=x^3,\at x=-4	tangent\:y=x^{3},\at\:x=-4
integral from-4 to 0 of (4+sqrt(16-x^2))	\int\:_{-4}^{0}(4+\sqrt{16-x^{2}})dx
integral of-5e^{6x}	\int\:-5e^{6x}dx
integral of 1/(x^2sqrt(100-x^2))	\int\:\frac{1}{x^{2}\sqrt{100-x^{2}}}dx
limit as x approaches-infinity of sin(x)	\lim\:_{x\to\:-\infty\:}(\sin(x))
derivative of sqrt(arctan(x))	derivative\:\sqrt{\arctan(x)}
integral of 2/3 x(a^2+x^2)^{3/2}	\int\:\frac{2}{3}x(a^{2}+x^{2})^{\frac{3}{2}}dx
derivative of (sqrt(s)-1)/(sqrt(s)+7)	derivative\:\frac{\sqrt{s}-1}{\sqrt{s}+7}
integral of ln(1+t)	\int\:\ln(1+t)dt
integral of e^{-x/(100)}	\int\:e^{-\frac{x}{100}}dx
integral of 15x^2e^{5x^3-6}	\int\:15x^{2}e^{5x^{3}-6}dx
limit as s approaches 0 of (-1/s}{1+(3+\frac{13)/s)(7/(xs+1))}	\lim\:_{s\to\:0}(\frac{-\frac{1}{s}}{1+(3+\frac{13}{s})(\frac{7}{xs+1})})
limit as x approaches 1+of 3/(\|x-1\|)	\lim\:_{x\to\:1+}(\frac{3}{\left\|x-1\right\|})
maclaurin x^3	maclaurin\:x^{3}
(\partial)/(\partial x)((x^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{x^{2}+y^{2}})
limit as x approaches 0 of xln(5x)	\lim\:_{x\to\:0}(x\ln(5x))
integral of x/(2+x^4)	\int\:\frac{x}{2+x^{4}}dx
d/(dy)((1/(y^2)-7/(y^4))(y+5y^3))	\frac{d}{dy}((\frac{1}{y^{2}}-\frac{7}{y^{4}})(y+5y^{3}))
inverse oflaplace 1/((s^2-2s))	inverselaplace\:\frac{1}{(s^{2}-2s)}
integral from 0 to 5 of 1/(x^2-6x+5)	\int\:_{0}^{5}\frac{1}{x^{2}-6x+5}dx
limit as x approaches 3+of ln\|x^2-9\|	\lim\:_{x\to\:3+}(\ln\left\|x^{2}-9\right\|)
(d^3)/(dx^3)(sqrt(6x+8))	\frac{d^{3}}{dx^{3}}(\sqrt{6x+8})
laplacetransform (1-e^t+3e^{-4t})cos(5t)	laplacetransform\:(1-e^{t}+3e^{-4t})\cos(5t)
integral of (xsin(x)+cos(x)-1)/(x^2)	\int\:\frac{x\sin(x)+\cos(x)-1}{x^{2}}dx
(\partial)/(\partial x)(ln(x^2+3xy+2y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+3xy+2y^{2}))
7x^2y+(dy)/(dx)=4x^2	7x^{2}y+\frac{dy}{dx}=4x^{2}
derivative of y^2-2xy+6x	\frac{d}{dx}(y^{2}-2xy+6x)
sum from k=0 to infinity of (1)^k	\sum\:_{k=0}^{\infty\:}(1)^{k}
integral of 1/(sqrt(2x^3))	\int\:\frac{1}{\sqrt{2x^{3}}}dx
derivative of f(x)=\sqrt[3]{-(-27)}	derivative\:f(x)=\sqrt[3]{-(-27)}
y^{''}+16y=tsin(4t)	y^{\prime\:\prime\:}+16y=t\sin(4t)
derivative of f(x)=(2x^2-1)^2(3x^2)	derivative\:f(x)=(2x^{2}-1)^{2}(3x^{2})
derivative of e^{2x}	derivative\:e^{2x}
derivative of 2sin(θ)	derivative\:2\sin(θ)
(\partial)/(\partial x)(x^2+2xy+2y^2-8x+8y)	\frac{\partial\:}{\partial\:x}(x^{2}+2xy+2y^{2}-8x+8y)
integral from 1 to infinity of 1/(x^2+3)	\int\:_{1}^{\infty\:}\frac{1}{x^{2}+3}dx
derivative of y=\sqrt[3]{1.6x^2+4.9}	derivative\:y=\sqrt[3]{1.6x^{2}+4.9}
derivative of f(t)= 1/2 (9t^2+t)^{-3}	derivative\:f(t)=\frac{1}{2}(9t^{2}+t)^{-3}
limit as x approaches infinity of 21^x	\lim\:_{x\to\:\infty\:}(21^{x})
(\partial)/(\partial y)(cos(12x)sin(2y))	\frac{\partial\:}{\partial\:y}(\cos(12x)\sin(2y))
integral of 9/(xln(3x))	\int\:\frac{9}{x\ln(3x)}dx
derivative of f(x)=-247	derivative\:f(x)=-247
integral of 1/(sqrt(121+x^2))	\int\:\frac{1}{\sqrt{121+x^{2}}}dx
limit as x approaches 2+of (x-3)/(x-2)	\lim\:_{x\to\:2+}(\frac{x-3}{x-2})
integral of 2/(sin(x))	\int\:\frac{2}{\sin(x)}dx
(\partial)/(\partial x)(x^{0.25}y^{0.75})	\frac{\partial\:}{\partial\:x}(x^{0.25}y^{0.75})
y^'+sin(t)y=sin(t),y(0)=3	y^{\prime\:}+\sin(t)y=\sin(t),y(0)=3
integral of (-2y)	\int\:(-2y)dy
(dy)/(dx)= 4/(x^2e^{3y+9)}	\frac{dy}{dx}=\frac{4}{x^{2}e^{3y+9}}
(\partial)/(\partial x)(x^4y^3)	\frac{\partial\:}{\partial\:x}(x^{4}y^{3})
integral of (x/((x^2+y^2)^{3/2)})	\int\:(\frac{x}{(x^{2}+y^{2})^{\frac{3}{2}}})dy
integral from 1 to 5 of 1/((5-x)^{5/2)}	\int\:_{1}^{5}\frac{1}{(5-x)^{\frac{5}{2}}}dx
(\partial)/(\partial x)(y^3-3x^2y)	\frac{\partial\:}{\partial\:x}(y^{3}-3x^{2}y)
f(x)=(4x+5)^3(x^2-6x+5)^4	f(x)=(4x+5)^{3}(x^{2}-6x+5)^{4}
integral of (36)/((1-x^2)^{3/2)}	\int\:\frac{36}{(1-x^{2})^{\frac{3}{2}}}dx
slope of (-5)(-5.1)	slope\:(-5)(-5.1)
derivative of cos^{7/4}(4x^3)	\frac{d}{dx}(\cos^{\frac{7}{4}}(4x^{3}))
integral from 1 to 8 of sqrt(x+1)	\int\:_{1}^{8}\sqrt{x+1}dx
derivative of f(x)=x^{3/2}+sqrt(x+4)	derivative\:f(x)=x^{\frac{3}{2}}+\sqrt{x+4}
tangent of xe^x	tangent\:xe^{x}
limit as x approaches 0 of tan(4x)	\lim\:_{x\to\:0}(\tan(4x))
y^{''}-4y^'-5y=0,y(-1)=3,y^'(-1)=9	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(-1)=3,y^{\prime\:}(-1)=9
derivative of 4e^{4e^x+x}	\frac{d}{dx}(4e^{4e^{x}+x})
derivative of f(x)=(-x^2-4)/((x^2-4)^2)	derivative\:f(x)=\frac{-x^{2}-4}{(x^{2}-4)^{2}}
(d^2)/(dx^2)(x^3)	\frac{d^{2}}{dx^{2}}(x^{3})
derivative of x^2arctan(x)	derivative\:x^{2}\arctan(x)
integral of 3sin^3(xco)s^5x	\int\:3\sin^{3}(xco)s^{5}xdx
integral of 1/((x^2+4)^3)	\int\:\frac{1}{(x^{2}+4)^{3}}dx
derivative of cos(tan(x)e^{-(x/8)^2})	\frac{d}{dx}(\cos(\tan(x))e^{-(\frac{x}{8})^{2}})
integral of (x^3)/(x^8+1)	\int\:\frac{x^{3}}{x^{8}+1}dx
d/(d{y)}({x}{y}{z}^2)	\frac{d}{d{y}}({x}{y}{z}^{2})
derivative of f(w)=((2w^4-5w))/(9w)	derivative\:f(w)=\frac{(2w^{4}-5w)}{9w}
derivative of (x^2-1/(x^2+1))	\frac{d}{dx}(\frac{x^{2}-1}{x^{2}+1})
integral of 2t-4	\int\:2t-4dt
laplacetransform f(t)=2e^{-t}cos(4t)1(t)	laplacetransform\:f(t)=2e^{-t}\cos(4t)1(t)
(dy)/(dx)=(2sqrt(y+1)cos(x))	\frac{dy}{dx}=(2\sqrt{y+1}\cos(x))
(d^2)/(dx^2)(x^3)	\frac{d^{2}}{dx^{2}}(x^{3})
integral of-6/(x^4)	\int\:-\frac{6}{x^{4}}dx
integral from 0 to 1 of (x^2+y^2+z^2)	\int\:_{0}^{1}(x^{2}+y^{2}+z^{2})dx
integral of t^2e^{-6t}	\int\:t^{2}e^{-6t}dt
sum from n=1 to infinity of n!	\sum\:_{n=1}^{\infty\:}n!
derivative of 12x^3+6x^2+2x	\frac{d}{dx}(12x^{3}+6x^{2}+2x)
derivative of y=cos(a^5+x^5)	derivative\:y=\cos(a^{5}+x^{5})
derivative of f(x)=sqrt(3x^2+2)	derivative\:f(x)=\sqrt{3x^{2}+2}
inverse oflaplace 7/(s^4)	inverselaplace\:\frac{7}{s^{4}}
integral of xtan^3(x^2)	\int\:x\tan^{3}(x^{2})dx
y^{''}+6y^'+6y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+6y=0
y^'=2t,y(0)=1	y^{\prime\:}=2t,y(0)=1
integral of (2x)/((x^2+x+1))	\int\:\frac{2x}{(x^{2}+x+1)}dx

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