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Popular Calculus Problems

tangent of f(x)=x^4-5x^2+4,\at x=-1	tangent\:f(x)=x^{4}-5x^{2}+4,\at\:x=-1
limit as x approaches 2 of cos(1/(x-2))	\lim\:_{x\to\:2}(\cos(\frac{1}{x-2}))
limit as x approaches pi of 3sin(x)	\lim\:_{x\to\:π}(3\sin(x))
integral of cos(3x)cos(4x)	\int\:\cos(3x)\cos(4x)dx
inverse oflaplace 1/((s+3)^2+25)	inverselaplace\:\frac{1}{(s+3)^{2}+25}
derivative of g(x)=(1-x^2)^{-x}	derivative\:g(x)=(1-x^{2})^{-x}
limit as x approaches 0 of 2xln(x^2)	\lim\:_{x\to\:0}(2x\ln(x^{2}))
7xy^'-2y=-(x^2)/(y^6)	7xy^{\prime\:}-2y=-\frac{x^{2}}{y^{6}}
integral of cos(t^2)	\int\:\cos(t^{2})dt
taylor 1/(x-1),8	taylor\:\frac{1}{x-1},8
integral of 1/(x(ln(x)))	\int\:\frac{1}{x(\ln(x))}dx
derivative of x^2-3x-5	derivative\:x^{2}-3x-5
integral from-14 to 7 of 7e^x	\int\:_{-14}^{7}7e^{x}dx
derivative of (x^3-3x^2/((x-1)^3))	\frac{d}{dx}(\frac{x^{3}-3x^{2}}{(x-1)^{3}})
derivative of y=(8x)/(8+sqrt(x))	derivative\:y=\frac{8x}{8+\sqrt{x}}
y^{''}-y^'=5sin(2x)	y^{\prime\:\prime\:}-y^{\prime\:}=5\sin(2x)
(\partial)/(\partial x)(yze^{xz}-8)	\frac{\partial\:}{\partial\:x}(yze^{xz}-8)
integral of 150x+7500	\int\:150x+7500dx
(\partial)/(\partial y)(2x+3)	\frac{\partial\:}{\partial\:y}(2x+3)
integral from 0 to 0.6 of 8000x	\int\:_{0}^{0.6}8000xdx
tangent of sqrt(3x+4)	tangent\:\sqrt{3x+4}
tangent of f(x)=7x-4sqrt(x),(1,3)	tangent\:f(x)=7x-4\sqrt{x},(1,3)
y^'-2y=-(2y)/x	y^{\prime\:}-2y=-\frac{2y}{x}
integral of x/((x-3)(x+1)^2)	\int\:\frac{x}{(x-3)(x+1)^{2}}dx
(e^{x-1})^'	(e^{x-1})^{\prime\:}
derivative of 390x^2-3120x^3	\frac{d}{dx}(390x^{2}-3120x^{3})
integral from 0 to pi of x^5cos(x)	\int\:_{0}^{π}x^{5}\cos(x)dx
(dy)/(dx)=(sqrt(x))/(sqrt(y))	\frac{dy}{dx}=\frac{\sqrt{x}}{\sqrt{y}}
y^'-8/x y=(y^4)/(x^{13)}	y^{\prime\:}-\frac{8}{x}y=\frac{y^{4}}{x^{13}}
derivative of 10x	derivative\:10x
integral of 5/(2-4x)	\int\:\frac{5}{2-4x}dx
integral of 2x+3x^2	\int\:2x+3x^{2}dx
derivative of y=(x-4)/(x+2)	derivative\:y=\frac{x-4}{x+2}
integral of 5/((x^2+1)^{3/2)}	\int\:\frac{5}{(x^{2}+1)^{\frac{3}{2}}}dx
integral of (e^{8x})/(e^{8x)+2}	\int\:\frac{e^{8x}}{e^{8x}+2}dx
inverse oflaplace 2/(s^2+4)	inverselaplace\:\frac{2}{s^{2}+4}
derivative of In(x+sqrt(a^2+x^2))	\frac{d}{dx}(In(x+\sqrt{a^{2}+x^{2}}))
derivative of sqrt((x^2+1/(x^2-1)))	\frac{d}{dx}(\sqrt{\frac{x^{2}+1}{x^{2}-1}})
y^'+4y=e^{-4t}	y^{\prime\:}+4y=e^{-4t}
derivative of (7x/(x^2+1))	\frac{d}{dx}(\frac{7x}{x^{2}+1})
integral of 1/(sqrt(x^2+5))	\int\:\frac{1}{\sqrt{x^{2}+5}}dx
sin(y)dx+cos(x)dy=0	\sin(y)dx+\cos(x)dy=0
area sqrt(x),-3,16,1	area\:\sqrt{x},-3,16,1
integral of y^2z+2xz^3	\int\:y^{2}z+2xz^{3}dx
derivative of 2(16e^{4x}x+8e^{4x})	\frac{d}{dx}(2(16e^{4x}x+8e^{4x}))
integral of 3/(sqrt(x^2-6x-7))	\int\:\frac{3}{\sqrt{x^{2}-6x-7}}dx
area-x^2+16,-1/4 x-1,x-6.6	area\:-x^{2}+16,-\frac{1}{4}x-1,x-6.6
derivative of sqrt(7x+5)	\frac{d}{dx}(\sqrt{7x+5})
y'=y^3-4y	y\prime\:=y^{3}-4y
limit as x approaches 0+of (3x)^{5x}	\lim\:_{x\to\:0+}((3x)^{5x})
integral of 1/(1-y^2)	\int\:\frac{1}{1-y^{2}}dy
derivative of f(x)= 1/(-3+(2x+1)^2)	derivative\:f(x)=\frac{1}{-3+(2x+1)^{2}}
(dy}{dx}=\frac{x^4-6y)/x	\frac{dy}{dx}=\frac{x^{4}-6y}{x}
longdivision (x+2)/(3x-4)	longdivision\:\frac{x+2}{3x-4}
integral from 0 to pi of 7sin^4(x)	\int\:_{0}^{π}7\sin^{4}(x)dx
limit as x approaches 0 of (13.5)/x-4.5	\lim\:_{x\to\:0}(\frac{13.5}{x}-4.5)
(\partial)/(\partial y)(e^{y^2}+2x^3)	\frac{\partial\:}{\partial\:y}(e^{y^{2}}+2x^{3})
y^'+2y=20	y^{\prime\:}+2y=20
limit as x approaches 0 of (2x^2)/(x^2)	\lim\:_{x\to\:0}(\frac{2x^{2}}{x^{2}})
derivative of (cos(3x)/(cos(x)))	\frac{d}{dx}(\frac{\cos(3x)}{\cos(x)})
derivative of f(x)=e^{sqrt(3x)}	derivative\:f(x)=e^{\sqrt{3x}}
derivative of (5(2)^2)/(3(2)-1)	derivative\:\frac{5(2)^{2}}{3(2)-1}
limit as x approaches infinity of x/7	\lim\:_{x\to\:\infty\:}(\frac{x}{7})
derivative of (x^{20}-22x+8e^x)	\frac{d}{dx}((x^{20}-22x+8)e^{x})
tx^'+4x=0	tx^{\prime\:}+4x=0
integral from 0 to 64 of 2/(x^{2/3)}	\int\:_{0}^{64}\frac{2}{x^{\frac{2}{3}}}dx
tangent of 3/(sqrt(x))	tangent\:\frac{3}{\sqrt{x}}
derivative of ((x^2+1^3)/((4x-5)^5))	\frac{d}{dx}(\frac{(x^{2}+1)^{3}}{(4x-5)^{5}})
derivative of 2sin(x-2+(2x-1)cos(x-2))	\frac{d}{dx}(2\sin(x-2)+(2x-1)\cos(x-2))
integral of (s^4+81)/(s(s^2+9)^2)	\int\:\frac{s^{4}+81}{s(s^{2}+9)^{2}}ds
sum from n=0 to infinity of (4/9)^{2n+1}	\sum\:_{n=0}^{\infty\:}(\frac{4}{9})^{2n+1}
2xy^'+y=6x,y(4)=24	2xy^{\prime\:}+y=6x,y(4)=24
derivative of 8e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(8e^{x}+\frac{2}{\sqrt[3]{x}})
(dy}{dx}-1/x y=\frac{5x^2e^{2x})/y	\frac{dy}{dx}-\frac{1}{x}y=\frac{5x^{2}e^{2x}}{y}
integral from 5 to 7 of (1/(sqrt(3+x)))	\int\:_{5}^{7}(\frac{1}{\sqrt{3+x}})dx
integral from 0 to 1 of x^2e^{2x}	\int\:_{0}^{1}x^{2}e^{2x}dx
derivative of sqrt(2xy)	\frac{d}{dx}(\sqrt{2xy})
derivative of tan^5(x)	derivative\:\tan^{5}(x)
limit as x approaches 2-of ([x])/x	\lim\:_{x\to\:2-}(\frac{[x]}{x})
integral of 3^x	\int\:3^{x}dx
derivative of 10x-3x^2	derivative\:10x-3x^{2}
tangent of f(x)=3x^2-5x+2,\at x=-1	tangent\:f(x)=3x^{2}-5x+2,\at\:x=-1
integral from 0 to 2pi of e^{i(θ-x)}	\int\:_{0}^{2π}e^{i(θ-x)}dx
integral of (x^4)/(sqrt(x^{10)-2)}	\int\:\frac{x^{4}}{\sqrt{x^{10}-2}}dx
derivative of y*x^2	\frac{d}{dx}(y\cdot\:x^{2})
integral of (4x^2)/(sqrt(4x-x^2))	\int\:\frac{4x^{2}}{\sqrt{4x-x^{2}}}dx
limit as x approaches 5 of x^2-7x+6	\lim\:_{x\to\:5}(x^{2}-7x+6)
derivative of 8xe^{2x}	\frac{d}{dx}(8xe^{2x})
integral of (e^x)/((8-e^x)^2)	\int\:\frac{e^{x}}{(8-e^{x})^{2}}dx
integral of (1-cos(2x^2))/(x^2)	\int\:\frac{1-\cos(2x^{2})}{x^{2}}dx
derivative of y=tan^3(x)	derivative\:y=\tan^{3}(x)
derivative of (-x/(sqrt(16-x^2)))	\frac{d}{dx}(\frac{-x}{\sqrt{16-x^{2}}})
inverse oflaplace 1/(s^2+4s+4)	inverselaplace\:\frac{1}{s^{2}+4s+4}
(\partial)/(\partial x)((x^{-2}+y^{-2})^3)	\frac{\partial\:}{\partial\:x}((x^{-2}+y^{-2})^{3})
derivative of-3\sqrt[4]{2-9x}	derivative\:-3\sqrt[4]{2-9x}
(2/(x^2))^'	(\frac{2}{x^{2}})^{\prime\:}
integral of x^3-3x^{-4}-4	\int\:x^{3}-3x^{-4}-4dx
integral of (1-4x+3x^2)/(x^2)	\int\:\frac{1-4x+3x^{2}}{x^{2}}dx
tangent of f(x)= 3/x ,\at x=5	tangent\:f(x)=\frac{3}{x},\at\:x=5
d/(dt)(1/(sqrt(1+t^{12))})	\frac{d}{dt}(\frac{1}{\sqrt{1+t^{12}}})

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