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Popular Calculus Problems

derivative of f(x)=-x^2	derivative\:f(x)=-x^{2}
derivative of sqrt((x+\sqrt{x))}	derivative\:\sqrt{(x+\sqrt{x})}
limit as x approaches infinity of x^{12}	\lim\:_{x\to\:\infty\:}(x^{12})
integral of p(p+7)^7	\int\:p(p+7)^{7}dp
(\partial)/(\partial x)(y^6sin(6x))	\frac{\partial\:}{\partial\:x}(y^{6}\sin(6x))
integral of 1/(xsqrt(x^2+a^2))	\int\:\frac{1}{x\sqrt{x^{2}+a^{2}}}dx
y^'=x+9y	y^{\prime\:}=x+9y
derivative of x^3cos(x-x^3sin(x))	\frac{d}{dx}(x^{3}\cos(x)-x^{3}\sin(x))
limit as x approaches 2 of (x^2)/(2x-4)	\lim\:_{x\to\:2}(\frac{x^{2}}{2x-4})
derivative of 2t^3-15t^2+24t	derivative\:2t^{3}-15t^{2}+24t
(\partial)/(\partial x)((xy)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{xy}{x-y})
derivative of 450x-90x^2	\frac{d}{dx}(450x-90x^{2})
integral of-sin(y)	\int\:-\sin(y)dy
inverse oflaplace (2s+1)/(s(s+1))	inverselaplace\:\frac{2s+1}{s(s+1)}
limit as x approaches 0 of sqrt(x^3+x^2)	\lim\:_{x\to\:0}(\sqrt{x^{3}+x^{2}})
f(x)=3x*ln(x)	f(x)=3x\cdot\:\ln(x)
limit as n approaches infinity of 3n	\lim\:_{n\to\:\infty\:}(3n)
tangent of f(x)=sqrt(x+1),\at x=3	tangent\:f(x)=\sqrt{x+1},\at\:x=3
derivative of sin(3x^2+5)	derivative\:\sin(3x^{2}+5)
integral from 3 to 5 of x/8	\int\:_{3}^{5}\frac{x}{8}dx
(\partial)/(\partial x)((e^x+e^y)^8)	\frac{\partial\:}{\partial\:x}((e^{x}+e^{y})^{8})
integral of (e^u)/((6-e^u)^2)	\int\:\frac{e^{u}}{(6-e^{u})^{2}}du
integral of 4xsec(x)tan(x)	\int\:4x\sec(x)\tan(x)dx
(\partial)/(\partial x)(x^3y^5+2x^4y)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5}+2x^{4}y)
derivative of-(9x)/y	derivative\:-\frac{9x}{y}
integral of (3x-1)^{-4}	\int\:(3x-1)^{-4}dx
y^'-7/(600+2t)y=6	y^{\prime\:}-\frac{7}{600+2t}y=6
integral from 0 to 2 of 1/(x^2)	\int\:_{0}^{2}\frac{1}{x^{2}}dx
(\partial)/(\partial x)(e^{xy}sin(xyz))	\frac{\partial\:}{\partial\:x}(e^{xy}\sin(xyz))
t^2y^{''}-7ty^'+15y=0	t^{2}y^{\prime\:\prime\:}-7ty^{\prime\:}+15y=0
limit as x approaches infinity of xln(x)	\lim\:_{x\to\:\infty\:}(x\ln(x))
inverse oflaplace (s^2)/(s^3-1)	inverselaplace\:\frac{s^{2}}{s^{3}-1}
integral of x(3x+2)	\int\:x(3x+2)dx
integral of xsinh(x)	\int\:x\sinh(x)dx
integral from 0 to 1 of 6(1+sqrt(x))^5	\int\:_{0}^{1}6(1+\sqrt{x})^{5}dx
derivative of (4x^2)	\frac{d}{dx}((4x)^{2})
(\partial)/(\partial z)(x^2+3yz+4xy)	\frac{\partial\:}{\partial\:z}(x^{2}+3yz+4xy)
sum from n=0 to infinity of 6(0.4)^n	\sum\:_{n=0}^{\infty\:}6(0.4)^{n}
derivative of ky(x^2)	\frac{d}{dx}(ky(x)^{2})
y^{''}-y=3e^x	y^{\prime\:\prime\:}-y=3e^{x}
derivative of (1/(x^2+3)(x^2-1/(x^2)+3))	\frac{d}{dx}((\frac{1}{x^{2}}+3)(x^{2}-\frac{1}{x^{2}}+3))
limit as n approaches infinity of ((-1)^{n+1})/(2n-1)	\lim\:_{n\to\:\infty\:}(\frac{(-1)^{n+1}}{2n-1})
integral from 0 to pi/2 of sin^5(xco)s^{12}x	\int\:_{0}^{\frac{π}{2}}\sin^{5}(xco)s^{12}x
(\partial)/(\partial x)(x^{1/2}*y^{1/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}\cdot\:y^{\frac{1}{2}})
derivative of e^{-x^2}+1	\frac{d}{dx}(e^{-x^{2}}+1)
(\partial)/(\partial x)(z^{x^y})	\frac{\partial\:}{\partial\:x}(z^{x^{y}})
tangent of f(x)= x/(x^2+81)	tangent\:f(x)=\frac{x}{x^{2}+81}
area x=2y^2-5,x=y^2+4	area\:x=2y^{2}-5,x=y^{2}+4
derivative of y=2x-5	derivative\:y=2x-5
integral of x^{-12}	\int\:x^{-12}dx
derivative of f(x)=6x^3-9x+4	derivative\:f(x)=6x^{3}-9x+4
tangent of (sqrt(x)+1)/(sqrt(x)+4)	tangent\:\frac{\sqrt{x}+1}{\sqrt{x}+4}
sum from n=0 to infinity of 5(2/3)^n	\sum\:_{n=0}^{\infty\:}5(\frac{2}{3})^{n}
integral from 1 to 9 of (sqrt(x)-x)	\int\:_{1}^{9}(\sqrt{x}-x)dx
derivative of ln(sqrt((1-x/(1+x))))	\frac{d}{dx}(\ln(\sqrt{\frac{1-x}{1+x}}))
tangent of f(x)=x^4-8x^2+5x+4,\at x=1	tangent\:f(x)=x^{4}-8x^{2}+5x+4,\at\:x=1
inverse oflaplace (3s+4)/(s^2+10s+21)	inverselaplace\:\frac{3s+4}{s^{2}+10s+21}
f^'(x)=16sqrt(x)	f^{\prime\:}(x)=16\sqrt{x}
laplacetransform e^{(-2t)}	laplacetransform\:e^{(-2t)}
integral of-3/(x^4)	\int\:-\frac{3}{x^{4}}dx
integral of (x^2+3x+5)/(x^3+8)	\int\:\frac{x^{2}+3x+5}{x^{3}+8}dx
(d^4)/(dx^4)(e^{2x})	\frac{d^{4}}{dx^{4}}(e^{2x})
area sqrt(2x+8),x,[0,9]	area\:\sqrt{2x+8},x,[0,9]
integral of 5ln(x^2-1)	\int\:5\ln(x^{2}-1)dx
integral of (l-x)^2	\int\:(l-x)^{2}dx
(\partial)/(\partial x)(e^{xy^2}y^2)	\frac{\partial\:}{\partial\:x}(e^{xy^{2}}y^{2})
integral of (7t-3)/(t+1)	\int\:\frac{7t-3}{t+1}dt
limit as x approaches infinity of (3x-7)^{2x-1}	\lim\:_{x\to\:\infty\:}((3x-7)^{2x-1})
integral of [(3x^5-4)^2*5x^4]	\int\:[(3x^{5}-4)^{2}\cdot\:5x^{4}]dx
integral from 0 to 1 of pi(3x^2-3x^6)	\int\:_{0}^{1}π(3x^{2}-3x^{6})dx
(\partial)/(\partial x)(sqrt(8-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{8-x^{2}-y^{2}})
integral of 1/(y^2-4)	\int\:\frac{1}{y^{2}-4}dy
derivative of 3e^{-6x}	\frac{d}{dx}(3e^{-6x})
limit as x approaches-2 of (x^n-1)/(x-1)	\lim\:_{x\to\:-2}(\frac{x^{n}-1}{x-1})
integral of (5x^2+2x+5)/(x^3-1)	\int\:\frac{5x^{2}+2x+5}{x^{3}-1}dx
limit as x approaches 0 of 8^x	\lim\:_{x\to\:0}(8^{x})
derivative of f(x)=sqrt(2)	derivative\:f(x)=\sqrt{2}
integral of (ln(12x)-ln(4x))	\int\:(\ln(12x)-\ln(4x))dx
tangent of f(x)=(-8)/(x-1)	tangent\:f(x)=\frac{-8}{x-1}
y^{''}+2y^'-3y=0,y(0)=6,y^'(0)=-2	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=0,y(0)=6,y^{\prime\:}(0)=-2
y^{''}+5y^'=0	y^{\prime\:\prime\:}+5y^{\prime\:}=0
derivative of-1/((1+x)^2)	derivative\:-\frac{1}{(1+x)^{2}}
tangent of f(x)=x^5,\at x=1	tangent\:f(x)=x^{5},\at\:x=1
derivative of (\sqrt[3]{x}/(x^3+1))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x^{3}+1})
integral of ((x+1))/((x-1)^2)	\int\:\frac{(x+1)}{(x-1)^{2}}dx
integral of (sin^5(x))/(cos^2(x))	\int\:\frac{\sin^{5}(x)}{\cos^{2}(x)}dx
(\partial)/(\partial x)(6ye^{7x})	\frac{\partial\:}{\partial\:x}(6ye^{7x})
(dy)/(dx)=(x/(y-2))^{{3}}ln(2x)	\frac{dy}{dx}=(\frac{x}{y-2})^{\left\{3\right\}}\ln(2x)
integral from 0 to infinity of x^4e^{-x}	\int\:_{0}^{\infty\:}x^{4}e^{-x}dx
derivative of e^{2x}-e^x+1	\frac{d}{dx}(e^{2x}-e^{x}+1)
derivative of x,x^2,x^3	\frac{d}{dx}(x,x^{2},x^{3})
derivative of 1/(sqrt(a^2+x^2))	\frac{d}{dx}(\frac{1}{\sqrt{a^{2}+x^{2}}})
derivative of sin^2(x/(x+1))	\frac{d}{dx}(\sin^{2}(\frac{x}{x+1}))
integral of (x+4)^2	\int\:(x+4)^{2}dx
limit as x approaches 7 of (x-7)/(3x^2-21x)	\lim\:_{x\to\:7}(\frac{x-7}{3x^{2}-21x})
(\partial)/(\partial x)(ln(x)+zln(y))	\frac{\partial\:}{\partial\:x}(\ln(x)+z\ln(y))
y^{''}+7y^'+10y=3e^{4t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=3e^{4t}
derivative of Axe^{x^2}	\frac{d}{dx}(Axe^{x^{2}})
integral of (2sec^2(x)-x^5)	\int\:(2\sec^{2}(x)-x^{5})dx
integral of (xsin(y))	\int\:(x\sin(y))dy

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