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Popular Calculus Problems

derivative of ln(sqrt(3x+4))	\frac{d}{dx}(\ln(\sqrt{3x+4}))
limit as x approaches 6+of xsqrt(6-x)	\lim\:_{x\to\:6+}(x\sqrt{6-x})
limit as x approaches 0 of (x)sin(1/x)	\lim\:_{x\to\:0}((x)\sin(\frac{1}{x}))
limit as x approaches-7 of (x^2-3)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-3}{7-x})
derivative of 8(x-1/x)^3	derivative\:8(x-\frac{1}{x})^{3}
integral of 6x^2-8x+3	\int\:6x^{2}-8x+3dx
derivative of x^3(3-x)^4	derivative\:x^{3}(3-x)^{4}
integral of sqrt(1+(1/(x^{1/3)))^2}	\int\:\sqrt{1+(\frac{1}{x^{\frac{1}{3}}})^{2}}dx
derivative of sqrt(100+x^2)	\frac{d}{dx}(\sqrt{100+x^{2}})
derivative of y=x6^x	derivative\:y=x6^{x}
x(x+y)((dy)/(dx))+y(3x+y)=0	x(x+y)(\frac{dy}{dx})+y(3x+y)=0
derivative of y=ln(arctan(4x))	derivative\:y=\ln(\arctan(4x))
integral from 1 to 3 of 5r^3ln(r)	\int\:_{1}^{3}5r^{3}\ln(r)dr
y^{''}-y^'-2y=2e^{-t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=2e^{-t}
integral of tan^3(x)sec^{1/2}(x)	\int\:\tan^{3}(x)\sec^{\frac{1}{2}}(x)dx
limit as x approaches 0 of 1/(e^x)	\lim\:_{x\to\:0}(\frac{1}{e^{x}})
limit as x approaches 6 of x/(x^2-36)	\lim\:_{x\to\:6}(\frac{x}{x^{2}-36})
(dx)/(dt)+x=-e^t	\frac{dx}{dt}+x=-e^{t}
derivative of (3t^2-t+a^2^{101})	\frac{d}{dx}((3t^{2}-t+a^{2})^{101})
limit as x approaches+3+of 7/(x-3)	\lim\:_{x\to\:+3+}(\frac{7}{x-3})
(\partial)/(\partial x)(-2y)	\frac{\partial\:}{\partial\:x}(-2y)
integral of (sqrt(a^2+x^2))/(x^4)	\int\:\frac{\sqrt{a^{2}+x^{2}}}{x^{4}}dx
integral of (7x^2)/((x+1)(x^2+1))	\int\:\frac{7x^{2}}{(x+1)(x^{2}+1)}dx
derivative of sin(x^2)	\frac{d}{dx}(\sin(x^{2}))
(\partial)/(\partial y)(arcsin(x/y))	\frac{\partial\:}{\partial\:y}(\arcsin(\frac{x}{y}))
derivative of \sqrt[5]{2-x^2}	\frac{d}{dx}(\sqrt[5]{2-x^{2}})
taylor e^{x^2+x}	taylor\:e^{x^{2}+x}
derivative of sqrt(y^2-x)	\frac{d}{dx}(\sqrt{y^{2}-x})
simplify e^{ln(sin(x^2))}sqrt(2x+1)	simplify\:e^{\ln(\sin(x^{2}))}\sqrt{2x+1}
limit as x approaches 0 of (ln(x+1))/x	\lim\:_{x\to\:0}(\frac{\ln(x+1)}{x})
integral of cos^2(10x)	\int\:\cos^{2}(10x)dx
derivative of (x^4+2^{cos(x)})	\frac{d}{dx}((x^{4}+2)^{\cos(x)})
y^{''}+9y=2sec(3t)	y^{\prime\:\prime\:}+9y=2\sec(3t)
derivative of i/x	\frac{d}{dx}(\frac{i}{x})
derivative of 6(sec(x+tan(x))^{3/2})	\frac{d}{dx}(6(\sec(x)+\tan(x))^{\frac{3}{2}})
(\partial)/(\partial x)(x^5sin(y))	\frac{\partial\:}{\partial\:x}(x^{5}\sin(y))
integral of xcos(7x^2)	\int\:x\cos(7x^{2})dx
derivative of x/x	\frac{d}{dx}(\frac{x}{x})
integral from 0 to 1 of sqrt(3+9x^2)	\int\:_{0}^{1}\sqrt{3+9x^{2}}dx
derivative of (e^x/(9x))	\frac{d}{dx}(\frac{e^{x}}{9x})
integral from 0 to 1 of (2x-3)(5x+1)	\int\:_{0}^{1}(2x-3)(5x+1)dx
integral of 1/2 sin(x)	\int\:\frac{1}{2}\sin(x)dx
limit as x approaches 8+of log_{5}(x-8)	\lim\:_{x\to\:8+}(\log_{5}(x-8))
integral from 0 to 2 of x/(x+1)	\int\:_{0}^{2}\frac{x}{x+1}dx
derivative of log_{5}((6x^3+4/(2x^3-3)))	\frac{d}{dx}(\log_{5}(\frac{6x^{3}+4}{2x^{3}-3}))
slope ofintercept (4,-3),(12,0)	slopeintercept\:(4,-3),(12,0)
integral from 2 to 3 of (25)/(sqrt(3-x))	\int\:_{2}^{3}\frac{25}{\sqrt{3-x}}dx
integral of (3ln(x))/(x^3)	\int\:\frac{3\ln(x)}{x^{3}}dx
derivative of arcsin(x/7)	\frac{d}{dx}(\arcsin(\frac{x}{7}))
(\partial)/(\partial x)(xe^{xy}-x/(y^2))	\frac{\partial\:}{\partial\:x}(xe^{xy}-\frac{x}{y^{2}})
tangent of ((8e^{(9x)}))/((5x-2))	tangent\:\frac{(8e^{(9x)})}{(5x-2)}
derivative of xe^{7x}	\frac{d}{dx}(xe^{7x})
integral of (sqrt(2x+1))	\int\:(\sqrt{2x+1})dx
derivative of 3x^2sin(4x)	\frac{d}{dx}(3x^{2}\sin(4x))
derivative of x^{-2cos(x})	\frac{d}{dx}(x^{-2\cos(x)})
limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x))	\lim\:_{x\to\:0}(\frac{(e^{x}-e^{-x}-2x)}{1-\sin(x)})
limit as x approaches infinity of x*pi	\lim\:_{x\to\:\infty\:}(x\cdot\:π)
limit as x approaches infinity of 1/6	\lim\:_{x\to\:\infty\:}(\frac{1}{6})
derivative of 3/((2x^{-2)})	\frac{d}{dx}(\frac{3}{(2x)^{-2}})
integral of (16x^2)/((x-6)(x+2)^2)	\int\:\frac{16x^{2}}{(x-6)(x+2)^{2}}dx
derivative of ((k^2x^3-6kx+9))/(x-1)	derivative\:\frac{(k^{2}x^{3}-6kx+9)}{x-1}
integral of x/(2x^2+12x+23)	\int\:\frac{x}{2x^{2}+12x+23}dx
x(x+y)y^'=y(x-y)	x(x+y)y^{\prime\:}=y(x-y)
integral of sin(u)cos(u)	\int\:\sin(u)\cos(u)du
f(x)=cos(sqrt(x))	f(x)=\cos(\sqrt{x})
integral of (e^{4x})/x	\int\:\frac{e^{4x}}{x}dx
integral of 2(2x+6)^5	\int\:2(2x+6)^{5}dx
integral of (2x+1)/(sqrt(x+4))	\int\:\frac{2x+1}{\sqrt{x+4}}dx
integral of (12)/(x^3+2x^2-3x)	\int\:\frac{12}{x^{3}+2x^{2}-3x}dx
limit as x approaches infinity of 1/x+x	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+x)
derivative of 4e^t	derivative\:4e^{t}
laplacetransform 3e^{-2t}cos(t)	laplacetransform\:3e^{-2t}\cos(t)
derivative of sqrt(t^2+1)	derivative\:\sqrt{t^{2}+1}
derivative of 5+3sqrt(x)	\frac{d}{dx}(5+3\sqrt{x})
integral of (5x-3)/(x^2+4)	\int\:\frac{5x-3}{x^{2}+4}dx
integral of 1/(x^2+4x+13)	\int\:\frac{1}{x^{2}+4x+13}dx
limit as x approaches pi of ln\|cos(x)-7\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-7\right\|)
integral from 0 to pi/2 of cos^7(x)	\int\:_{0}^{\frac{π}{2}}\cos^{7}(x)dx
6y^{''}+10y^'=0	6y^{\prime\:\prime\:}+10y^{\prime\:}=0
(dy)/(dt)	\frac{dy}{dt}
sum from n=5 to infinity of 0.9^{2(n+1)}	\sum\:_{n=5}^{\infty\:}0.9^{2(n+1)}
integral of (54)/(x^2-81)	\int\:\frac{54}{x^{2}-81}dx
integral of x^3ln(2x)	\int\:x^{3}\ln(2x)dx
derivative of (3x+1/(x-1))	\frac{d}{dx}(\frac{3x+1}{x-1})
(\partial)/(\partial x)(e^xsin(x))	\frac{\partial\:}{\partial\:x}(e^{x}\sin(x))
limit as n approaches infinity of (n^2+3)/(n^3sqrt(n)+n^{5/2)}	\lim\:_{n\to\:\infty\:}(\frac{n^{2}+3}{n^{3}\sqrt{n}+n^{\frac{5}{2}}})
integral of (x^3+3x-2)/(x^2-x)	\int\:\frac{x^{3}+3x-2}{x^{2}-x}dx
derivative of 7/(x^7)	\frac{d}{dx}(\frac{7}{x^{7}})
integral from 1 to 8 of x^{-8/3}	\int\:_{1}^{8}x^{-\frac{8}{3}}dx
area y=x^2+9,y=10+2x	area\:y=x^{2}+9,y=10+2x
limit as x approaches 3 of sqrt(x^2-9)	\lim\:_{x\to\:3}(\sqrt{x^{2}-9})
integral of 3cos(t)-2sin(t)	\int\:3\cos(t)-2\sin(t)dt
laplacetransform e^{4t}(t^2+3t+5)	laplacetransform\:e^{4t}(t^{2}+3t+5)
integral of (-9x^2sec(3x^3+1))	\int\:(-9x^{2}\sec(3x^{3}+1))dx
derivative of (4x^{5x})	\frac{d}{dx}((4x)^{5x})
integral of (3x)^2+sqrt(2)	\int\:(3x)^{2}+\sqrt{2}dx
limit as x approaches 1 of 1-sqrt(2-x)	\lim\:_{x\to\:1}(1-\sqrt{2-x})
derivative of arccos(x^3)	\frac{d}{dx}(\arccos(x^{3}))
derivative of 2*x^2	\frac{d}{dx}(2\cdot\:x^{2})
inverse oflaplace ((s-2))/((s-3)(s+1))	inverselaplace\:\frac{(s-2)}{(s-3)(s+1)}

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