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Popular Calculus Problems

limit as x approaches 9-of (5x)/(x-9)	\lim\:_{x\to\:9-}(\frac{5x}{x-9})
derivative of-4x^4+8x^3	\frac{d}{dx}(-4x^{4}+8x^{3})
inverse oflaplace ((3s+1))/(s(s+2))	inverselaplace\:\frac{(3s+1)}{s(s+2)}
y^'-6/x y=((y^5))/(x^{18)},y(1)=1	y^{\prime\:}-\frac{6}{x}y=\frac{(y^{5})}{x^{18}},y(1)=1
derivative of g(x)=3(5-7x)^5	derivative\:g(x)=3(5-7x)^{5}
(dx)/(dy)=7sin(x)+3cos(x)	\frac{dx}{dy}=7\sin(x)+3\cos(x)
derivative of sin(pi/4)	\frac{d}{dx}(\sin(\frac{π}{4}))
integral of (7e^{2t})/(1+e^{4t)}	\int\:\frac{7e^{2t}}{1+e^{4t}}dt
derivative of x^3-2x+4	\frac{d}{dx}(x^{3}-2x+4)
derivative of 3x^{4/3}	derivative\:3x^{\frac{4}{3}}
limit as x approaches 1 of (x^2-1)/(x-3)	\lim\:_{x\to\:1}(\frac{x^{2}-1}{x-3})
laplacetransform cos(ax+b)	laplacetransform\:\cos(ax+b)
derivative of ((x^2)/(7+6x))	\frac{d}{dx}(\frac{(x^{2})}{7+6x})
integral of 5(1-x)^4	\int\:5(1-x)^{4}dx
integral of (24)/(x^3)	\int\:\frac{24}{x^{3}}dx
limit as x approaches 1 of (x-3)/(x^2+4)	\lim\:_{x\to\:1}(\frac{x-3}{x^{2}+4})
(dy)/(dx)=x+y,y(0)=3	\frac{dy}{dx}=x+y,y(0)=3
derivative of 2/(sqrt(65+4t))	derivative\:\frac{2}{\sqrt{65+4t}}
(x^2+y^2)dx=xydy	(x^{2}+y^{2})dx=xydy
derivative of ((4x^2/(4-x))^3)	\frac{d}{dx}((\frac{4x^{2}}{4-x})^{3})
integral of (4x^3)	\int\:(4x^{3})dx
integral from 1 to sqrt(3 of)arctan(x)	\int\:_{1}^{\sqrt{3}}\arctan(x)dx
integral of (x+1)/(x^2+16)	\int\:\frac{x+1}{x^{2}+16}dx
derivative of f(x)=sqrt(x)(x-4)	derivative\:f(x)=\sqrt{x}(x-4)
y^{''}+2y^'+y=10e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=10e^{-t}
derivative of-2xe^{-2x}	\frac{d}{dx}(-2xe^{-2x})
integral of (x^2+x-1)/(x^3+2x^2+x)	\int\:\frac{x^{2}+x-1}{x^{3}+2x^{2}+x}dx
integral of 1/(sqrt(x^2+y^2))	\int\:\frac{1}{\sqrt{x^{2}+y^{2}}}dx
inverse oflaplace 9/(s^2+9s+9)*1/s	inverselaplace\:\frac{9}{s^{2}+9s+9}\cdot\:\frac{1}{s}
tangent of f(x)=x^4+9x^2-x,\at x=1	tangent\:f(x)=x^{4}+9x^{2}-x,\at\:x=1
sum from n=3 to infinity of (4/7)^n	\sum\:_{n=3}^{\infty\:}(\frac{4}{7})^{n}
integral of 1/(cos^2(4x))	\int\:\frac{1}{\cos^{2}(4x)}dx
derivative of e^x-4	\frac{d}{dx}(e^{x}-4)
integral of (x^2+2x+5)/((x+1)(x^2+1))	\int\:\frac{x^{2}+2x+5}{(x+1)(x^{2}+1)}dx
integral from 0 to 1 of (12)/(x^2-4)	\int\:_{0}^{1}\frac{12}{x^{2}-4}dx
derivative of 1/(5+x)	\frac{d}{dx}(\frac{1}{5+x})
area (64)/(16+x^2),1	area\:\frac{64}{16+x^{2}},1
(\partial)/(\partial x)(e^{3x}cos(5y))	\frac{\partial\:}{\partial\:x}(e^{3x}\cos(5y))
inverse oflaplace 1/(t^2)	inverselaplace\:\frac{1}{t^{2}}
integral of (3x^2-8x+13)/((x+3)(x-1)^2)	\int\:\frac{3x^{2}-8x+13}{(x+3)(x-1)^{2}}dx
(\partial)/(\partial y)(4x^2+3cos(y))	\frac{\partial\:}{\partial\:y}(4x^{2}+3\cos(y))
derivative of x^2+4/x	\frac{d}{dx}(x^{2}+\frac{4}{x})
(\partial)/(\partial x)(ln(3x+3cy))	\frac{\partial\:}{\partial\:x}(\ln(3x+3cy))
derivative of cos(5pix)	derivative\:\cos(5πx)
derivative of (5-x^2)/(5+x^2)	derivative\:\frac{5-x^{2}}{5+x^{2}}
integral of 7x^2ln(x)	\int\:7x^{2}\ln(x)dx
implicit (dy)/(dx),arctan(xy)=arcsin(4x+4y),(0,0)	implicit\:\frac{dy}{dx},\arctan(xy)=\arcsin(4x+4y),(0,0)
laplacetransform e^{7t}sin^2(t)	laplacetransform\:e^{7t}\sin^{2}(t)
(dP)/(dt)=kP^{1.01}	\frac{dP}{dt}=kP^{1.01}
integral of ((x-3))/(x^3+x^2)	\int\:\frac{(x-3)}{x^{3}+x^{2}}dx
integral of 4x^2-sin(x)	\int\:4x^{2}-\sin(x)dx
integral of 1/(x^2-36)	\int\:\frac{1}{x^{2}-36}dx
derivative of ((x^2+2x+1)/((x^2-2x+1)))	\frac{d}{dx}(\frac{(x^{2}+2x+1)}{(x^{2}-2x+1)})
y^'=-a*y^2	y^{\prime\:}=-a\cdot\:y^{2}
d/(dt)(t^9e^t)	\frac{d}{dt}(t^{9}e^{t})
4^'	4^{\prime\:}
derivative of sin(4x^2+3x)	\frac{d}{dx}(\sin(4x^{2}+3x))
integral of 8/(xsqrt(64-(ln(x))^2))	\int\:\frac{8}{x\sqrt{64-(\ln(x))^{2}}}dx
integral of sec^6(5x)tan(5x)	\int\:\sec^{6}(5x)\tan(5x)dx
(sqrt(1-x^2))^'	(\sqrt{1-x^{2}})^{\prime\:}
y^'+xy+4=0	y^{\prime\:}+xy+4=0
integral of 1/(sqrt(x^2-36))	\int\:\frac{1}{\sqrt{x^{2}-36}}dx
integral of 1/(sqrt(8+6x-9x^2))	\int\:\frac{1}{\sqrt{8+6x-9x^{2}}}dx
derivative of {f}(h,x({g}(h,x)(h(x))))	\frac{d}{dx}({f}(h,x)({g}(h,x)(h(x))))
integral of sqrt(x^2+1-1/2+1/(16x^2))	\int\:\sqrt{x^{2}+1-\frac{1}{2}+\frac{1}{16x^{2}}}dx
integral of (cos(2x))/(cos(x)-sin(x))	\int\:\frac{\cos(2x)}{\cos(x)-\sin(x)}dx
derivative of 5cos^{-4}(x)	\frac{d}{dx}(5\cos^{-4}(x))
integral of (e^{2x})/(e^{2x)-1}	\int\:\frac{e^{2x}}{e^{2x}-1}dx
derivative of sin(x+pi)	\frac{d}{dx}(\sin(x+π))
maclaurin x^2e^x	maclaurin\:x^{2}e^{x}
sum from n=0 to infinity of tan(n)	\sum\:_{n=0}^{\infty\:}\tan(n)
integral of (csc^2(2x))/(cot^5(2x))	\int\:\frac{\csc^{2}(2x)}{\cot^{5}(2x)}dx
limit as x approaches 1 of (8x+1)/(x+3)	\lim\:_{x\to\:1}(\frac{8x+1}{x+3})
integral of (e^{3x})	\int\:(e^{3x})dx
slope ofintercept (-3,2),(-1,-1)	slopeintercept\:(-3,2),(-1,-1)
limit as x approaches 1 of 3x^2-6x+1	\lim\:_{x\to\:1}(3x^{2}-6x+1)
derivative of xsqrt(x^2+9)	derivative\:x\sqrt{x^{2}+9}
derivative of x^4-32x^2	\frac{d}{dx}(x^{4}-32x^{2})
y^{''}+2y^'+10y=0,y(0)=3,y^'(0)=-1	y^{\prime\:\prime\:}+2y^{\prime\:}+10y=0,y(0)=3,y^{\prime\:}(0)=-1
limit as x approaches 2 of 4x^2-8x	\lim\:_{x\to\:2}(4x^{2}-8x)
derivative of (e^{6x}/x)	\frac{d}{dx}(\frac{e^{6x}}{x})
limit as x approaches 3 of x+3	\lim\:_{x\to\:3}(x+3)
derivative of-(18)/(x^3)	derivative\:-\frac{18}{x^{3}}
(dy)/(dx)=(xy+y^2+x^2)/(x^2)	\frac{dy}{dx}=\frac{xy+y^{2}+x^{2}}{x^{2}}
integral from-1 to 3 of \|x-2x^2\|	\int\:_{-1}^{3}\left\|x-2x^{2}\right\|dx
integral of ((e^{2x}))/(1+e^{4x)}	\int\:\frac{(e^{2x})}{1+e^{4x}}dx
integral of 6sin^3(4x)cos^3(4x)	\int\:6\sin^{3}(4x)\cos^{3}(4x)dx
(dy}{dx}=\frac{x^3-2y)/x	\frac{dy}{dx}=\frac{x^{3}-2y}{x}
integral of ((3x+2))/(sqrt(19-5x+x^2))	\int\:\frac{(3x+2)}{\sqrt{19-5x+x^{2}}}dx
derivative of x^3-4x^2	derivative\:x^{3}-4x^{2}
y^'=-ay^2+b	y^{\prime\:}=-ay^{2}+b
derivative of tan(1+e^{2x})	\frac{d}{dx}(\tan(1+e^{2x}))
derivative of-2log_{e}(x)+x^2-4+e^x+x^e	derivative\:-2\log_{e}(x)+x^{2}-4+e^{x}+x^{e}
integral of 2csc^4(x)cot^6(x)	\int\:2\csc^{4}(x)\cot^{6}(x)dx
limit as x approaches-2 of 7-2x	\lim\:_{x\to\:-2}(7-2x)
integral of-2xe^{x^2}	\int\:-2xe^{x^{2}}dx
derivative of 2/(ln(10x^3))	\frac{d}{dx}(\frac{2}{\ln(10)x^{3}})
integral from 4 to 7 of 1/(sqrt(x^2-16))	\int\:_{4}^{7}\frac{1}{\sqrt{x^{2}-16}}dx
derivative of sqrt(2)x	\frac{d}{dx}(\sqrt{2}x)
tangent of f(x)=x^2-2x-6,\at x=-2	tangent\:f(x)=x^{2}-2x-6,\at\:x=-2

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