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Popular Calculus Problems

tangent of f(x)=-3x^2+3x+1,\at x=1	tangent\:f(x)=-3x^{2}+3x+1,\at\:x=1
derivative of y= 2/(1-9x^2)	derivative\:y=\frac{2}{1-9x^{2}}
integral from 0 to pi/2 of xcos(x/3)	\int\:_{0}^{\frac{π}{2}}x\cos(\frac{x}{3})dx
derivative of (2ln(x))/x	derivative\:\frac{2\ln(x)}{x}
(dy)/(dx)=2y(9-y)	\frac{dy}{dx}=2y(9-y)
(dx)/(dt)=x(1-1/2500 x)	\frac{dx}{dt}=x(1-\frac{1}{2500}x)
integral of (x+4)sqrt(8x+x^2)	\int\:(x+4)\sqrt{8x+x^{2}}dx
derivative of sqrt(r^2-7x^2)	\frac{d}{dx}(\sqrt{r^{2}-7x^{2}})
derivative of 2sec^2(xtan(x))	\frac{d}{dx}(2\sec^{2}(x)\tan(x))
limit as x approaches 0 of 5/(x-1)	\lim\:_{x\to\:0}(\frac{5}{x-1})
laplacetransform sin(2t+3)	laplacetransform\:\sin(2t+3)
area y=x,x>= 0	area\:y=x,x\ge\:0
integral of 1/(xsqrt(5x^2-3))	\int\:\frac{1}{x\sqrt{5x^{2}-3}}dx
maclaurin 6sin(2x)	maclaurin\:6\sin(2x)
integral of x^5sin(2x)	\int\:x^{5}\sin(2x)dx
derivative of 1/(1+ce^{-x})	\frac{d}{dx}(\frac{1}{1+ce^{-x}})
t(dy)/(dt)+30y= 1/t	t\frac{dy}{dt}+30y=\frac{1}{t}
integral of xe^{x/2}	\int\:xe^{\frac{x}{2}}dx
slope of (8.4)(5.2)	slope\:(8.4)(5.2)
integral of-(3000)/(x^2)	\int\:-\frac{3000}{x^{2}}dx
integral of (10x)/(sqrt(4x^2-4))	\int\:\frac{10x}{\sqrt{4x^{2}-4}}dx
inverse oflaplace ((s+3))/((s+7))	inverselaplace\:\frac{(s+3)}{(s+7)}
y^'+(2y)/t =(2cos(t^2))/t	y^{\prime\:}+\frac{2y}{t}=\frac{2\cos(t^{2})}{t}
integral of x*ln(x+1)	\int\:x\cdot\:\ln(x+1)dx
derivative of 3sin(3x)	derivative\:3\sin(3x)
integral of (x^4-6x^3+12x^2+6)/(x^3-6x^2+12x-8)	\int\:\frac{x^{4}-6x^{3}+12x^{2}+6}{x^{3}-6x^{2}+12x-8}dx
derivative of ((x+4(x^2-4x+16))/(x^3))	\frac{d}{dx}(\frac{(x+4)(x^{2}-4x+16)}{x^{3}})
derivative of 5sqrt(x)sin(x)	derivative\:5\sqrt{x}\sin(x)
integral of e^{-x}-1	\int\:e^{-x}-1dx
(\partial)/(\partial x)(-x^2)	\frac{\partial\:}{\partial\:x}(-x^{2})
(\partial ^2)/(\partial r\partial θ)(r(θ)*sin(θ))	\frac{\partial\:^{2}}{\partial\:r\partial\:θ}(r(θ)\cdot\:\sin(θ))
tangent of y=2x^4,(-2,32)	tangent\:y=2x^{4},(-2,32)
limit as x approaches 2 of-x	\lim\:_{x\to\:2}(-x)
derivative of (5x^2+25x/(5x))	\frac{d}{dx}(\frac{5x^{2}+25x}{5x})
integral of sqrt(10-x^2)	\int\:\sqrt{10-x^{2}}dx
integral of (xe^{-x^2})	\int\:(xe^{-x^{2}})dx
integral of (5cos(x)-4sin(x))	\int\:(5\cos(x)-4\sin(x))dx
maclaurin 1/(x-2)	maclaurin\:\frac{1}{x-2}
derivative of f(x)=e^{4x}	derivative\:f(x)=e^{4x}
(d^2)/(dx^2)(x^{8/9}+5x)	\frac{d^{2}}{dx^{2}}(x^{\frac{8}{9}}+5x)
integral from 3 to infinity of 1/x	\int\:_{3}^{\infty\:}\frac{1}{x}dx
integral from 0 to 4 of (x^2-4x)	\int\:_{0}^{4}(x^{2}-4x)dx
derivative of y=ln(-7x^6)	derivative\:y=\ln(-7x^{6})
(\partial)/(\partial x)(xsqrt(1+y^5))	\frac{\partial\:}{\partial\:x}(x\sqrt{1+y^{5}})
slope ofintercept (50,5119),(80,7219)	slopeintercept\:(50,5119),(80,7219)
integral of e^{2x}*cos(3x)	\int\:e^{2x}\cdot\:\cos(3x)dx
(\partial)/(\partial x)((1-x)^{1/2})	\frac{\partial\:}{\partial\:x}((1-x)^{\frac{1}{2}})
(\partial)/(\partial x)(4y^3sin(6x))	\frac{\partial\:}{\partial\:x}(4y^{3}\sin(6x))
(dy)/(dx)=-x^4-4x^3+5x^2	\frac{dy}{dx}=-x^{4}-4x^{3}+5x^{2}
derivative of 3x^2+8x+5	\frac{d}{dx}(3x^{2}+8x+5)
derivative of \sqrt[3]{x+sqrt(x)}	\frac{d}{dx}(\sqrt[3]{x+\sqrt{x}})
(\partial)/(\partial y)(6xy-5y)	\frac{\partial\:}{\partial\:y}(6xy-5y)
area-10x+11,x^2-5x-13,-8,3	area\:-10x+11,x^{2}-5x-13,-8,3
limit as x approaches 0 of 7/x-7cot(x)	\lim\:_{x\to\:0}(\frac{7}{x}-7\cot(x))
derivative of f(x)=(sqrt(x))/(7+x)	derivative\:f(x)=\frac{\sqrt{x}}{7+x}
f(x)=e^x-e^{-x}-2x	f(x)=e^{x}-e^{-x}-2x
limit as x approaches-1 of (ln(x))/x	\lim\:_{x\to\:-1}(\frac{\ln(x)}{x})
laplacetransform 5H	laplacetransform\:5H
derivative of 2x^{5/2}	\frac{d}{dx}(2x^{\frac{5}{2}})
(\partial)/(\partial y)(cos^2(3x-y^2))	\frac{\partial\:}{\partial\:y}(\cos^{2}(3x-y^{2}))
(\partial)/(\partial y)(4x^{0.5}+2y^{0.25})	\frac{\partial\:}{\partial\:y}(4x^{0.5}+2y^{0.25})
(\partial)/(\partial y)(ln(xyz))	\frac{\partial\:}{\partial\:y}(\ln(xyz))
integral of 7^{x^2}	\int\:7^{x^{2}}dx
limit as x approaches infinity of 1/x+1	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+1)
tangent of y^3x+y^2x^2=6,(2,1)	tangent\:y^{3}x+y^{2}x^{2}=6,(2,1)
y^{''}-2y^'+7y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+7y=0
derivative of 1/(10x)	\frac{d}{dx}(\frac{1}{10x})
integral from 0 to ln(2) of 10e^{2t}	\int\:_{0}^{\ln(2)}10e^{2t}dt
integral of (-1/x+7e^x)	\int\:(-\frac{1}{x}+7e^{x})dx
derivative of sqrt(6+x^2)	\frac{d}{dx}(\sqrt{6+x^{2}})
integral of sqrt(2x+1)	\int\:\sqrt{2x+1}dx
integral of 3^xsin(x)	\int\:3^{x}\sin(x)dx
(\partial)/(\partial y)(ycos(xln(y)))	\frac{\partial\:}{\partial\:y}(y\cos(x\ln(y)))
integral from 0 to 2 of sqrt(1+3x^2)	\int\:_{0}^{2}\sqrt{1+3x^{2}}dx
tangent of 6x^{-3},\at x=5	tangent\:6x^{-3},\at\:x=5
derivative of (x^2/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x}})
integral from 0 to 1 of \|2x^2-1\|	\int\:_{0}^{1}\left\|2x^{2}-1\right\|dx
(dx)/(dt)=2x(5-x)	\frac{dx}{dt}=2x(5-x)
y^'=e^{2y+6x}	y^{\prime\:}=e^{2y+6x}
integral of (8x^3+8x^2+8)/(x^2+x)	\int\:\frac{8x^{3}+8x^{2}+8}{x^{2}+x}dx
integral of (xln(x))/x	\int\:\frac{x\ln(x)}{x}dx
tangent of f(x)= 1/(x^5),(2, 1/32)	tangent\:f(x)=\frac{1}{x^{5}},(2,\frac{1}{32})
derivative of f(t)=sqrt(2t^2-t)	derivative\:f(t)=\sqrt{2t^{2}-t}
y^'+1/(x+1)y=x^{-2}	y^{\prime\:}+\frac{1}{x+1}y=x^{-2}
tangent of f(x)=(3x-2)(x+4),(1,5)	tangent\:f(x)=(3x-2)(x+4),(1,5)
(\partial)/(\partial y)(xcos(y)sin(z))	\frac{\partial\:}{\partial\:y}(x\cdot\:\cos(y)\cdot\:\sin(z))
limit as x approaches infinity of (-x)/x	\lim\:_{x\to\:\infty\:}(\frac{-x}{x})
integral of ((3x-5))/(x^2+4x)	\int\:\frac{(3x-5)}{x^{2}+4x}dx
derivative of f(x)=sqrt(3x^2-7)	derivative\:f(x)=\sqrt{3x^{2}-7}
integral of e^xsinh(x)	\int\:e^{x}\sinh(x)dx
(-cos(x))^'	(-\cos(x))^{\prime\:}
(\partial)/(\partial x)(arccos(x))	\frac{\partial\:}{\partial\:x}(\arccos(x))
integral from 3 to infinity of 1/(x^2-4)	\int\:_{3}^{\infty\:}\frac{1}{x^{2}-4}dx
(\partial)/(\partial x)(10x-6xy^3)	\frac{\partial\:}{\partial\:x}(10x-6xy^{3})
integral from 0 to 2pi of cos^2(xsi)n^2x	\int\:_{0}^{2π}\cos^{2}(xsi)n^{2}xdx
integral of ln(1/(x-2))	\int\:\ln(\frac{1}{x-2})dx
integral of 10^{-y}	\int\:10^{-y}dy
derivative of 2x^3-15x^2+36x-10	\frac{d}{dx}(2x^{3}-15x^{2}+36x-10)
integral of (sqrt(t)-1/(sqrt(t)))	\int\:(\sqrt{t}-\frac{1}{\sqrt{t}})dt
derivative of sqrt(sin(7x+ln(5x)))	\frac{d}{dx}(\sqrt{\sin(7x+\ln(5x))})

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