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Popular Calculus Problems

limit as x approaches 10 of 12x	\lim\:_{x\to\:10}(12x)
derivative of (sqrt(x)/(1+x^{3/2)})	\frac{d}{dx}(\frac{\sqrt{x}}{1+x^{\frac{3}{2}}})
(\partial)/(\partial x)(sqrt(y/x))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{y}{x}})
integral from 0 to x of sqrt(t^2+t^4)	\int\:_{0}^{x}\sqrt{t^{2}+t^{4}}dt
(dy)/(dx)=y^2-4	\frac{dy}{dx}=y^{2}-4
(\partial)/(\partial x)(sin(5pix+2y))	\frac{\partial\:}{\partial\:x}(\sin(5πx+2y))
derivative of (xy(x^2-y^2)/(x^2+y^2))	\frac{d}{dx}(\frac{xy(x^{2}-y^{2})}{x^{2}+y^{2}})
derivative of 1/(2sqrt(r))+1/(6r^{5/6)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{6r^{\frac{5}{6}}}
derivative of ((x+2)(2x+4))/(-x^2-x-2)	derivative\:\frac{(x+2)(2x+4)}{-x^{2}-x-2}
derivative of x+x^2	\frac{d}{dx}(x+x^{2})
derivative of ln(((2x+9^3)/(x^2)))	\frac{d}{dx}(\ln(\frac{(2x+9)^{3}}{x^{2}}))
derivative of (arcsin(5x)^{2x})	\frac{d}{dx}((\arcsin(5x))^{2x})
(d^2)/(dx^2)((x^2)/(x-3))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{x-3})
tangent of f(x)=6+5x^2-2x^3,\at x=a	tangent\:f(x)=6+5x^{2}-2x^{3},\at\:x=a
d/(dt)(e^{-8t})	\frac{d}{dt}(e^{-8t})
inverse oflaplace 5/((s+1)(s+2)^2)	inverselaplace\:\frac{5}{(s+1)(s+2)^{2}}
derivative of cos(3x)cos(5*x)	derivative\:\cos(3\cdot\:x)\cdot\:\cos(5\cdot\:x)
(\partial)/(\partial y)(e^{(x/y)})	\frac{\partial\:}{\partial\:y}(e^{(\frac{x}{y})})
derivative of 7^{9x}	\frac{d}{dx}(7^{9x})
integral of x^3*sqrt(x^2+1)	\int\:x^{3}\cdot\:\sqrt{x^{2}+1}dx
derivative of x^3-8x^2+5x+8	derivative\:x^{3}-8x^{2}+5x+8
inverse oflaplace 1/(2s^2)	inverselaplace\:\frac{1}{2s^{2}}
(dy)/(dx)+xy=e^xy	\frac{dy}{dx}+xy=e^{x}y
tangent of f(x)=x^2+4,\at x=1	tangent\:f(x)=x^{2}+4,\at\:x=1
tangent of f(x)=x^5-3(x)^3+6	tangent\:f(x)=x^{5}-3(x)^{3}+6
derivative of 6x^5(x^4-8)	derivative\:6x^{5}(x^{4}-8)
inverse oflaplace ((2s+13))/(s^2+4s+13)	inverselaplace\:\frac{(2s+13)}{s^{2}+4s+13}
integral from 0 to 4 of 1	\int\:_{0}^{4}1
derivative of 7x^{-1}	\frac{d}{dx}(7x^{-1})
integral of 2xsin(3xy)	\int\:2x\sin(3xy)dx
limit as x approaches-4 of x^3+x^2	\lim\:_{x\to\:-4}(x^{3}+x^{2})
integral from 2 to 5 of f(x)	\int\:_{2}^{5}f(x)dx
limit as x approaches infinity of-(1/x)	\lim\:_{x\to\:\infty\:}(-(\frac{1}{x}))
integral of \sqrt[3]{4-2x^2}(-4x)	\int\:\sqrt[3]{4-2x^{2}}(-4x)dx
(\partial)/(\partial x)(e^{-2x^2-y^2})	\frac{\partial\:}{\partial\:x}(e^{-2x^{2}-y^{2}})
integral of-e^xsin(y)	\int\:-e^{x}\sin(y)dy
(\partial)/(\partial y)(x+2y+z)	\frac{\partial\:}{\partial\:y}(x+2y+z)
integral of x^2e^{-1}	\int\:x^{2}e^{-1}dx
integral of ((x^2-4x+9))/(x^2-6x+9)	\int\:\frac{(x^{2}-4x+9)}{x^{2}-6x+9}dx
inverse oflaplace ((3s+7))/(s^2+2s+4)	inverselaplace\:\frac{(3s+7)}{s^{2}+2s+4}
derivative of f(x)=-3x^2	derivative\:f(x)=-3x^{2}
tangent of x^2+x,\at x=3	tangent\:x^{2}+x,\at\:x=3
integral of 1/(x^2+6x+18)	\int\:\frac{1}{x^{2}+6x+18}dx
derivative of 7/2 x^2-5x+1	\frac{d}{dx}(\frac{7}{2}x^{2}-5x+1)
integral of 1/(3\sqrt[3]{x^2)}	\int\:\frac{1}{3\sqrt[3]{x^{2}}}dx
derivative of y=(x^2-1)/(x^2+x+1)	derivative\:y=\frac{x^{2}-1}{x^{2}+x+1}
derivative of se^{sx}	\frac{d}{dx}(se^{sx})
y^'=(e^y)/(x^3)	y^{\prime\:}=\frac{e^{y}}{x^{3}}
derivative of-tan(2sin(4x))	derivative\:-\tan(2\sin(4x))
integral of ((1+x+x^2))/(sqrt(x))	\int\:\frac{(1+x+x^{2})}{\sqrt{x}}dx
limit as x approaches 2 of 2/(x^2-4)	\lim\:_{x\to\:2}(\frac{2}{x^{2}-4})
integral of (-2sqrt(x))/3	\int\:\frac{-2\sqrt{x}}{3}dx
y^{''}-9y^'=1+3e^{2x}	y^{\prime\:\prime\:}-9y^{\prime\:}=1+3e^{2x}
(dy)/(dx)= y/(x+1)	\frac{dy}{dx}=\frac{y}{x+1}
limit as t approaches 0 of sin(5t)	\lim\:_{t\to\:0}(\sin(5t))
integral of (xsqrt(x))/3	\int\:\frac{x\sqrt{x}}{3}dx
derivative of (e^{2x}+e^{4x}/3)	\frac{d}{dx}(\frac{e^{2x}+e^{4x}}{3})
derivative of f(q)=(500)/(q^2)	derivative\:f(q)=\frac{500}{q^{2}}
limit as x approaches 4 of (x+1)/(x-3)	\lim\:_{x\to\:4}(\frac{x+1}{x-3})
integral of (x^2-3x)	\int\:(x^{2}-3x)dx
(\partial)/(\partial x)(e^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y^{2}})
integral from 0 to 2 of 2/(sqrt(8-x^2))	\int\:_{0}^{2}\frac{2}{\sqrt{8-x^{2}}}dx
derivative of sqrt(cos(x+1))	\frac{d}{dx}(\sqrt{\cos(x)+1})
(d^2)/(dx^2)(5ln(x^5))	\frac{d^{2}}{dx^{2}}(5\ln(x^{5}))
integral of ((2x^3+5x^2-2x)/x)	\int\:(\frac{2x^{3}+5x^{2}-2x}{x})dx
area sin(x),cos(x)-1	area\:\sin(x),\cos(x)-1
integral from 1 to 5 of x^3-10x^2+29x-20	\int\:_{1}^{5}x^{3}-10x^{2}+29x-20dx
(\partial)/(\partial y)(2x-1)	\frac{\partial\:}{\partial\:y}(2x-1)
y^'=y^3	y^{\prime\:}=y^{3}
limit as x approaches 2 of (x^3-3x^2+4)/(3x^3-18x^2+36x-24)	\lim\:_{x\to\:2}(\frac{x^{3}-3x^{2}+4}{3x^{3}-18x^{2}+36x-24})
integral from 4 to infinity of 9e^{-y/2}	\int\:_{4}^{\infty\:}9e^{-\frac{y}{2}}dy
(\partial)/(\partial x)(ln(xy^4))	\frac{\partial\:}{\partial\:x}(\ln(xy^{4}))
derivative of y=3xe^{2x}	derivative\:y=3xe^{2x}
derivative of f(x)=5x^2-x^3	derivative\:f(x)=5x^{2}-x^{3}
integral from pi/2 to pi of 3x-sin(x)	\int\:_{\frac{π}{2}}^{π}3x-\sin(x)dx
integral of x/((x^2-1)[ln(x^2-1)]^2)	\int\:\frac{x}{(x^{2}-1)[\ln(x^{2}-1)]^{2}}dx
y^'=5y^2sin(x)	y^{\prime\:}=5y^{2}\sin(x)
derivative of x^{cot(x})	\frac{d}{dx}(x^{\cot(x)})
(\partial)/(\partial y)(sin(x/y))	\frac{\partial\:}{\partial\:y}(\sin(\frac{x}{y}))
derivative of csc^3(3-x)	\frac{d}{dx}(\csc^{3}(3-x))
integral of (8x+1)/((4x^2+x)^6)	\int\:\frac{8x+1}{(4x^{2}+x)^{6}}dx
derivative of 8sqrt(7x^2+5)	\frac{d}{dx}(8\sqrt{7x^{2}+5})
derivative of x/(x-10)	\frac{d}{dx}(\frac{x}{x-10})
(dy)/(dx)=(2x-3)/(5y)	\frac{dy}{dx}=\frac{2x-3}{5y}
derivative of ((x^3-x)/(1+x^2))	\frac{d}{dx}(\frac{(x^{3}-x)}{1+x^{2}})
derivative of ln(((1-x)/((x+5)^3)))	\frac{d}{dx}(\ln(\frac{(1-x)}{(x+5)^{3}}))
derivative of cos((pix/2))	\frac{d}{dx}(\cos(\frac{πx}{2}))
(\partial)/(\partial x)(6x+12)	\frac{\partial\:}{\partial\:x}(6x+12)
tangent of f(x)= 8/(7x),\at 1,87	tangent\:f(x)=\frac{8}{7x},\at\:1,87
(\partial)/(\partial x)(x^6-4x^2y^4+3y^2)	\frac{\partial\:}{\partial\:x}(x^{6}-4x^{2}y^{4}+3y^{2})
derivative of (-x^3+1(-2x^2-2x))	\frac{d}{dx}((-x^{3}+1)(-2x^{2}-2x))
integral of (x^3+3x)/((2x-2)(x+2))	\int\:\frac{x^{3}+3x}{(2x-2)(x+2)}dx
simplify ln(10^x)	simplify\:\ln(10^{x})
d/(dy)(x^2y^4)	\frac{d}{dy}(x^{2}y^{4})
(dy)/(dt)t+5y=8t	\frac{dy}{dt}t+5y=8t
d/(dt)((t^2)/(sqrt(t^3+1)))	\frac{d}{dt}(\frac{t^{2}}{\sqrt{t^{3}+1}})
derivative of-x^2sin(x)+4xcos(x)+2sin(x)	derivative\:-x^{2}\sin(x)+4x\cos(x)+2\sin(x)
integral from-2 to 3 of (x^2-12)-(x-6)	\int\:_{-2}^{3}(x^{2}-12)-(x-6)dx
limit as x approaches 1 of sqrt(x)-1	\lim\:_{x\to\:1}(\sqrt{x}-1)
limit as x approaches 1 of 3e^{x-1}	\lim\:_{x\to\:1}(3e^{x-1})

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