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Popular Calculus Problems

(\partial)/(\partial x)((2x)/(x^2+y))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}+y})
integral of (x^2+1)^{3/2}	\int\:(x^{2}+1)^{\frac{3}{2}}dx
integral of-15x^4(-3x^5-1)^5	\int\:-15x^{4}(-3x^{5}-1)^{5}dx
derivative of sqrt(x)ln(4x)	\frac{d}{dx}(\sqrt{x}\ln(4x))
area 4-x,0,-2,6	area\:4-x,0,-2,6
area y=1,x=y^{5/2},[0,1]	area\:y=1,x=y^{\frac{5}{2}},[0,1]
integral of 6e^{-6x}	\int\:6e^{-6x}dx
limit as x approaches 1 of ln(x)-ln(x-1)	\lim\:_{x\to\:1}(\ln(x)-\ln(x-1))
limit as x approaches 0 of x/(x^2+y^2)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+y^{2}})
integral of 1/(x^2+8)	\int\:\frac{1}{x^{2}+8}dx
integral of 1/(xsqrt(9x^2+1))	\int\:\frac{1}{x\sqrt{9x^{2}+1}}dx
integral of (x^8)	\int\:(x^{8})dx
limit as x approaches 3 of 3sqrt(9x-3)	\lim\:_{x\to\:3}(3\sqrt{9x-3})
derivative of 4x^2-5x-50	derivative\:4x^{2}-5x-50
taylor 1/(sqrt(1+x)),0	taylor\:\frac{1}{\sqrt{1+x}},0
limit as x approaches-3 of x^2+x-6	\lim\:_{x\to\:-3}(x^{2}+x-6)
tangent of f(x)=x^3-9x,(3,0)	tangent\:f(x)=x^{3}-9x,(3,0)
t(dy)/(dt)=t^3+4t^3y	t\frac{dy}{dt}=t^{3}+4t^{3}y
integral of (x^2+3)5x	\int\:(x^{2}+3)5xdx
derivative of f(x)=(3x^3+2)(x^4-2x)	derivative\:f(x)=(3x^{3}+2)(x^{4}-2x)
(dy)/(dx)x+y=(xy)^{3/2}	\frac{dy}{dx}x+y=(xy)^{\frac{3}{2}}
integral of 1/(1+8x)	\int\:\frac{1}{1+8x}dx
derivative of 6^{sin(pix})	\frac{d}{dx}(6^{\sin(πx)})
(\partial)/(\partial x)(ln(7ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(7ye^{xy}))
tangent of f(x)=(4x)/(x+2),(6,3)	tangent\:f(x)=\frac{4x}{x+2},(6,3)
integral of (-3/x+3e^x)	\int\:(-\frac{3}{x}+3e^{x})dx
slope of (-10)(-13.3)	slope\:(-10)(-13.3)
inverse oflaplace 1/(s^2+220)	inverselaplace\:\frac{1}{s^{2}+220}
limit as x approaches+4 of (x^2-1)/(x-4)	\lim\:_{x\to\:+4}(\frac{x^{2}-1}{x-4})
derivative of f(x)=sqrt(x^2+5x)	derivative\:f(x)=\sqrt{x^{2}+5x}
derivative of e^{sqrt(ln(x^2+1+x)})	\frac{d}{dx}(e^{\sqrt{\ln(x^{2}+1)+x}})
integral of (x^4+2x+4)/(x^5+x^4)	\int\:\frac{x^{4}+2x+4}{x^{5}+x^{4}}dx
integral from-1 to 6 of (9y)/(y^2-5y-14)	\int\:_{-1}^{6}\frac{9y}{y^{2}-5y-14}dy
x^{''}=kx	x^{\prime\:\prime\:}=kx
integral of (sin^5(x))/(cos^3(x))	\int\:\frac{\sin^{5}(x)}{\cos^{3}(x)}dx
integral from 1 to 2 of (4/x-(16)/(x^2))	\int\:_{1}^{2}(\frac{4}{x}-\frac{16}{x^{2}})dx
y^'-2ty=t	y^{\prime\:}-2ty=t
integral of (5cos^2(x))/(sin(x))	\int\:\frac{5\cos^{2}(x)}{\sin(x)}dx
tangent of y=(8x)/((x^2+1)),\at	tangent\:y=\frac{8x}{(x^{2}+1)},\at\:
y^'=y(1-y/(6200))	y^{\prime\:}=y(1-\frac{y}{6200})
integral of (cos(pi/(x^{35)}))/(x^{36)}	\int\:\frac{\cos(\frac{π}{x^{35}})}{x^{36}}dx
integral of sec(6x)tan(6x)	\int\:\sec(6x)\tan(6x)dx
limit as x approaches 1000 of x^{8/3}	\lim\:_{x\to\:1000}(x^{\frac{8}{3}})
(\partial)/(\partial x)(1/(sqrt(1+x^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{1+x^{2}}})
derivative of ((x-3/(x+2))^{12})	\frac{d}{dx}((\frac{x-3}{x+2})^{12})
derivative of 1/16 e^{2x^2}	\frac{d}{dx}(\frac{1}{16}e^{2x^{2}})
d/(dy)(sqrt(y-y^2))	\frac{d}{dy}(\sqrt{y-y^{2}})
y^'=(3y-4x)/(2x-3x)	y^{\prime\:}=\frac{3y-4x}{2x-3x}
derivative of x+ln(x^2+1)	\frac{d}{dx}(x+\ln(x^{2}+1))
area y=2x+2,y=x^2+2,x=-1,x=3	area\:y=2x+2,y=x^{2}+2,x=-1,x=3
limit as x approaches-pi of (sin(x))/x	\lim\:_{x\to\:-π}(\frac{\sin(x)}{x})
derivative of-x^2+2x+3	\frac{d}{dx}(-x^{2}+2x+3)
integral of 2t+1	\int\:2t+1dt
derivative of y=ln(sqrt(1-x^2))	derivative\:y=\ln(\sqrt{1-x^{2}})
integral from 0 to y of 0.5	\int\:_{0}^{y}0.5dx
derivative of sqrt(4-x^2)	derivative\:\sqrt{4-x^{2}}
derivative of f(x)=cos(sqrt(sin(tan(pix))))	derivative\:f(x)=\cos(\sqrt{\sin(\tan(πx))})
(dy}{dx}= 1/x y-\frac{x^2)/3 y^4	\frac{dy}{dx}=\frac{1}{x}y-\frac{x^{2}}{3}y^{4}
tangent of y=(2x)/(1+x^2),(4, 8/17)	tangent\:y=\frac{2x}{1+x^{2}},(4,\frac{8}{17})
integral of 1/(1-sin(x)+cos(x))	\int\:\frac{1}{1-\sin(x)+\cos(x)}dx
limit as x approaches 4 of ln\|x-4\|	\lim\:_{x\to\:4}(\ln\left\|x-4\right\|)
derivative of (8t)/(t+7)	derivative\:\frac{8t}{t+7}
(dy)/(dt)=2y+1	\frac{dy}{dt}=2y+1
integral of (4x-5)/((x-2)(x+3))	\int\:\frac{4x-5}{(x-2)(x+3)}dx
derivative of 1/(sin(x-sin(x)))	\frac{d}{dx}(\frac{1}{\sin(x-\sin(x))})
derivative of y=(8x^2+4x+2)/(sqrt(x))	derivative\:y=\frac{8x^{2}+4x+2}{\sqrt{x}}
(\partial)/(\partial x)((4x+y)^3(x-y)^2)	\frac{\partial\:}{\partial\:x}((4x+y)^{3}(x-y)^{2})
(dy)/(dx)=14x^{-8}	\frac{dy}{dx}=14x^{-8}
derivative of x^3-3x^2-9x+15	\frac{d}{dx}(x^{3}-3x^{2}-9x+15)
x^3+3y-xy^'=0	x^{3}+3y-xy^{\prime\:}=0
derivative of g(t)=-3/(2t^{3/2)}	derivative\:g(t)=-\frac{3}{2t^{\frac{3}{2}}}
limit as x approaches pi/2 of tan^2(x)	\lim\:_{x\to\:\frac{π}{2}}(\tan^{2}(x))
y^{''}+2y^'+y=sin(x)+6cos(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(x)+6\cos(2x)
derivative of x/((1+x^2^{1/2)})	\frac{d}{dx}(\frac{x}{(1+x^{2})^{\frac{1}{2}}})
limit as x approaches+4+of 3/(x-4)	\lim\:_{x\to\:+4+}(\frac{3}{x-4})
(\partial)/(\partial x)(-5e^x*cos(yz))	\frac{\partial\:}{\partial\:x}(-5e^{x}\cdot\:\cos(yz))
limit as x approaches-2 of x^3+6x^2-16	\lim\:_{x\to\:-2}(x^{3}+6x^{2}-16)
integral of ((cos^2(x)))/(sin(x))	\int\:\frac{(\cos^{2}(x))}{\sin(x)}dx
integral of 1/((2x+3)^2)	\int\:\frac{1}{(2x+3)^{2}}dx
laplacetransform cos^2(4t)	laplacetransform\:\cos^{2}(4t)
tangent of y=x^2e^x-2xe^x+2e^x,(1,e)	tangent\:y=x^{2}e^{x}-2xe^{x}+2e^{x},(1,e)
y^{''}-y^'-6y=e^{2x}	y^{\prime\:\prime\:}-y^{\prime\:}-6y=e^{2x}
derivative of f(x)=8x^7	derivative\:f(x)=8x^{7}
implicit (dy)/(dx),7x+4y=2	implicit\:\frac{dy}{dx},7x+4y=2
(\partial)/(\partial x)((2y)/(y+cos(x)))	\frac{\partial\:}{\partial\:x}(\frac{2y}{y+\cos(x)})
integral of (x+2)/((x+1)^2)	\int\:\frac{x+2}{(x+1)^{2}}dx
integral from 0 to 10 of 9800pi(10-y)	\int\:_{0}^{10}9800π(10-y)dy
derivative of f(x)=(-x^2)/(200)	derivative\:f(x)=\frac{-x^{2}}{200}
derivative of (x^2+1(x+5+1/x))	\frac{d}{dx}((x^{2}+1)(x+5+\frac{1}{x}))
area y=4x^2,y=24	area\:y=4x^{2},y=24
tangent of f(x)=2x^3-2x,\at x=1	tangent\:f(x)=2x^{3}-2x,\at\:x=1
limit as x approaches 0 of (ln(e^x-x))/x	\lim\:_{x\to\:0}(\frac{\ln(e^{x}-x)}{x})
(\partial)/(\partial x)((8x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{8x}{x^{2}+y^{2}})
(\partial)/(\partial b)((a^3b^4)/(c^2d^4))	\frac{\partial\:}{\partial\:b}(\frac{a^{3}b^{4}}{c^{2}d^{4}})
(\partial)/(\partial x)(-e^{-x-y})	\frac{\partial\:}{\partial\:x}(-e^{-x-y})
integral from 1/2 to 1 of (x^{-3}-24)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-24)dx
y^{''}+2y^'+y=2	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2
limit as x approaches 0 of x*e^x	\lim\:_{x\to\:0}(x\cdot\:e^{x})
derivative of (10log_{4}(x)/x)	\frac{d}{dx}(\frac{10\log_{4}(x)}{x})
limit as x approaches infinity of (6^{x+1})/(7^{x-1)}	\lim\:_{x\to\:\infty\:}(\frac{6^{x+1}}{7^{x-1}})

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