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Popular Calculus Problems

(dN)/(dt)=0.2(4000-N)	\frac{dN}{dt}=0.2(4000-N)
integral of 2x+9e^x	\int\:2x+9e^{x}dx
derivative of sqrt(16-x^2)	derivative\:\sqrt{16-x^{2}}
(\partial)/(\partial x)(sqrt(x^2+16))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+16})
limit as θ approaches 0 of (sin^2(θ))/θ	\lim\:_{θ\to\:0}(\frac{\sin^{2}(θ)}{θ})
derivative of (5x^6+4x^3^4)	\frac{d}{dx}((5x^{6}+4x^{3})^{4})
derivative of ln(9-x^2)	\frac{d}{dx}(\ln(9-x^{2}))
tangent of f(x)=(9x^9-9)(8-8x^8),\at x=0	tangent\:f(x)=(9x^{9}-9)(8-8x^{8}),\at\:x=0
integral of-1/(sin(x))	\int\:-\frac{1}{\sin(x)}dx
integral from 0 to 4 of xe^{-ax}	\int\:_{0}^{4}xe^{-ax}dx
taylor e^{8x}	taylor\:e^{8x}
integral of x^2sqrt(81-x^2)	\int\:x^{2}\sqrt{81-x^{2}}dx
f(x)=xsqrt(9-x)	f(x)=x\sqrt{9-x}
integral of (3sqrt(x^3)+2\sqrt[3]{x^2})	\int\:(3\sqrt{x^{3}}+2\sqrt[3]{x^{2}})dx
inverse oflaplace 1/((s^2+1)(s^3+1))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{3}+1)}
(\partial}{\partial z}(\frac{(x+y))/z)	\frac{\partial\:}{\partial\:z}(\frac{(x+y)}{z})
derivative of y=(x^2-8x+3)/(x^2+5)	derivative\:y=\frac{x^{2}-8x+3}{x^{2}+5}
derivative of ln(x^{cos(x}))	\frac{d}{dx}(\ln(x^{\cos(x)}))
tangent of xy+1+e=e^{-xy},(1,-1)	tangent\:xy+1+e=e^{-xy},(1,-1)
integral of 6xy^2	\int\:6xy^{2}dy
tangent of f(x)=e^x,\at x=ln(14)	tangent\:f(x)=e^{x},\at\:x=\ln(14)
limit as x approaches 2 of sqrt(2x-4)+8	\lim\:_{x\to\:2}(\sqrt{2x-4}+8)
integral of (cot(x))	\int\:(\cot(x))dx
derivative of 8/(3x^2+3/(2x)+2)	\frac{d}{dx}(\frac{8}{3x^{2}}+\frac{3}{2x}+2)
derivative of 3x+7	derivative\:3x+7
f^'(x)=x^4(x-2)(x+3)	f^{\prime\:}(x)=x^{4}(x-2)(x+3)
integral of 10sqrt(x)+sqrt(11)	\int\:10\sqrt{x}+\sqrt{11}dx
integral of x^2\|8x^3+1\|	\int\:x^{2}\left\|8x^{3}+1\right\|dx
derivative of 2sec(x-7x)	\frac{d}{dx}(2\sec(x)-7x)
slope of (-2,-3),(4,6)	slope\:(-2,-3),(4,6)
integral of 1/(a^2+x^2)	\int\:\frac{1}{a^{2}+x^{2}}dx
derivative of (A-Ax+2Bxe^{-x}cos(2x))	\frac{d}{dx}((A-Ax+2Bx)e^{-x}\cos(2x))
derivative of 32	\frac{d}{dx}(32)
derivative of (5t^2)/2+t+6	derivative\:\frac{5t^{2}}{2}+t+6
d/(dt)(4te^{3t})	\frac{d}{dt}(4te^{3t})
slope of y=x^2-3x-5	slope\:y=x^{2}-3x-5
integral of cos(pi/3 x)	\int\:\cos(\frac{π}{3}x)dx
(d^3)/(dx^3)((1+sqrt(x))^3)	\frac{d^{3}}{dx^{3}}((1+\sqrt{x})^{3})
integral of x/(sqrt(-7-8x-x^2))	\int\:\frac{x}{\sqrt{-7-8x-x^{2}}}dx
integral from 0 to 5 of 5x	\int\:_{0}^{5}5xdx
derivative of x*sin(3x)	\frac{d}{dx}(x\cdot\:\sin(3x))
derivative of x^4+4	\frac{d}{dx}(x^{4}+4)
derivative of x-y+1	\frac{d}{dx}(x-y+1)
(\partial)/(\partial y)(4y^2)	\frac{\partial\:}{\partial\:y}(4y^{2})
derivative of ln(5x^2)	\frac{d}{dx}(\ln(5x^{2}))
slope of (x^2+y^2)^2=4x^2y	slope\:(x^{2}+y^{2})^{2}=4x^{2}y
derivative of \sqrt[3]{x^2}sin(5x)	\frac{d}{dx}(\sqrt[3]{x^{2}}\sin(5x))
derivative of arctanh(x)	\frac{d}{dx}(\arctanh(x))
integral of 5xln(5x)	\int\:5x\ln(5x)dx
integral of 1/(2x^2)	\int\:\frac{1}{2x^{2}}dx
area y=(7t-4),(0,0.5)	area\:y=(7t-4),(0,0.5)
derivative of x^{tan(x})	\frac{d}{dx}(x^{\tan(x)})
integral from 1 to 9 of 2/(sqrt(x))	\int\:_{1}^{9}\frac{2}{\sqrt{x}}dx
derivative of 2/3 x^2(x^3-1)	\frac{d}{dx}(\frac{2}{3}x^{2}(x^{3}-1))
integral of (x^3+x^2-x)	\int\:(x^{3}+x^{2}-x)dx
integral of (cos(x))/(9-sin(x))	\int\:\frac{\cos(x)}{9-\sin(x)}dx
derivative of 3x(10x^3-6/(x+10))	\frac{d}{dx}(3x(10x^{3}-\frac{6}{x+10}))
derivative of-5cos(5x)	\frac{d}{dx}(-5\cos(5x))
limit as x approaches-infinity of 5^x+2	\lim\:_{x\to\:-\infty\:}(5^{x}+2)
integral from 0 to 1/2 of 3arccos(x)	\int\:_{0}^{\frac{1}{2}}3\arccos(x)dx
(\partial)/(\partial y)(x*ln(y-z))	\frac{\partial\:}{\partial\:y}(x\cdot\:\ln(y-z))
integral of (x^3)/(x^4+3x^2+2)	\int\:\frac{x^{3}}{x^{4}+3x^{2}+2}dx
integral from 1 to 7 of 1/(36+(x+5)^2)	\int\:_{1}^{7}\frac{1}{36+(x+5)^{2}}dx
derivative of (x^2-4/(x^2+4))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}+4})
integral of (-2x^4-4x^2-5)	\int\:(-2x^{4}-4x^{2}-5)dx
integral of 2cos(x/2)	\int\:2\cos(\frac{x}{2})dx
(\partial)/(\partial y)(2ln(x)+ln(y))	\frac{\partial\:}{\partial\:y}(2\ln(x)+\ln(y))
(\partial)/(\partial x)(sqrt(x/y))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x}{y}})
integral from-1 to 1 of e^{x^2}	\int\:_{-1}^{1}e^{x^{2}}dx
integral of x^4-2x^2-4x	\int\:x^{4}-2x^{2}-4xdx
expand (e^x-2)/((1-e^{-x))^2}	expand\:\frac{e^{x}-2}{(1-e^{-x})^{2}}
derivative of (x^2-2^{-3})	\frac{d}{dx}((x^{2}-2)^{-3})
(\partial)/(\partial x)(1/(2y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2y})
integral of-xe^{-x^2}	\int\:-xe^{-x^{2}}dx
tangent of f(x)=x^2+x,\at x=-2	tangent\:f(x)=x^{2}+x,\at\:x=-2
2x(dy)/(dx)=y	2x\frac{dy}{dx}=y
limit as x approaches 1/3 of \|3x-1\|-5	\lim\:_{x\to\:\frac{1}{3}}(\left\|3x-1\right\|-5)
3x^2y^2dx+(2y^3x+4y^3)dy=0	3x^{2}y^{2}dx+(2y^{3}x+4y^{3})dy=0
5x^{''}+25x^'+1700x=0	5x^{\prime\:\prime\:}+25x^{\prime\:}+1700x=0
1/(y^{1/3)}dy=1dx	\frac{1}{y^{\frac{1}{3}}}dy=1dx
(\partial)/(\partial x)(300e^{xt})	\frac{\partial\:}{\partial\:x}(300e^{xt})
integral of-4sin(2x)+3cos(3x)	\int\:-4\sin(2x)+3\cos(3x)dx
limit as x approaches 0+of xsin(1/x)	\lim\:_{x\to\:0+}(x\sin(\frac{1}{x}))
derivative of P(t)=0.45t^2-12t+105	derivative\:P(t)=0.45t^{2}-12t+105
derivative of (cos(x)sin(x))	\frac{d}{dx}((\cos(x))\sin(x))
integral of (1/x-5x)	\int\:(\frac{1}{x}-5x)dx
t(dy)/(dt)+(t+1)y=t	t\frac{dy}{dt}+(t+1)y=t
derivative of x^6-4x^5+5x^4-5x^2+4x-1	\frac{d}{dx}(x^{6}-4x^{5}+5x^{4}-5x^{2}+4x-1)
integral from 1 to 5 of 4r^2ln(r)	\int\:_{1}^{5}4r^{2}\ln(r)dr
derivative of f(x)= x/(x^2-x)	derivative\:f(x)=\frac{x}{x^{2}-x}
integral of (x^3-6x-9)	\int\:(x^{3}-6x-9)dx
derivative of f(x)=(4x)/((x-9)^5)	derivative\:f(x)=\frac{4x}{(x-9)^{5}}
(\partial)/(\partial z)(xye^{xz})	\frac{\partial\:}{\partial\:z}(xye^{xz})
taylor ln(4x),1	taylor\:\ln(4x),1
integral of 1/((x^2-64)^2)	\int\:\frac{1}{(x^{2}-64)^{2}}dx
integral of sqrt((2-x)/(2+x))	\int\:\sqrt{\frac{2-x}{2+x}}dx
(\partial)/(\partial x)(xy-xsin(y))	\frac{\partial\:}{\partial\:x}(xy-x\sin(y))
(((t^2+1)^{3/2})/3)^'	(\frac{(t^{2}+1)^{\frac{3}{2}}}{3})^{\prime\:}
derivative of (x+2(x-2)^3)	\frac{d}{dx}((x+2)(x-2)^{3})
derivative of-7(6x^2+7)^{-6}	derivative\:-7(6x^{2}+7)^{-6}

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