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Popular Calculus Problems

d/(dt)(1/6 t^3)	\frac{d}{dt}(\frac{1}{6}t^{3})
integral of (xsqrt(x^2+3))	\int\:(x\sqrt{x^{2}+3})dx
y^{''}+36y=-60sec(6t)	y^{\prime\:\prime\:}+36y=-60\sec(6t)
integral of 12(y^4+4y^2+8)^2(y^3+2y)	\int\:12(y^{4}+4y^{2}+8)^{2}(y^{3}+2y)dy
integral of x-10	\int\:x-10dx
integral of sec^5(θ)	\int\:\sec^{5}(θ)dθ
derivative of C(x)=-0.01x^2+7.2x-163	derivative\:C(x)=-0.01x^{2}+7.2x-163
integral of sin(-4x)	\int\:\sin(-4x)dx
integral of 6x+3	\int\:6x+3dx
integral of 1-x	\int\:1-xdx
derivative of (x-1)^4	derivative\:(x-1)^{4}
integral of sec^4(xta)n^5x	\int\:\sec^{4}(xta)n^{5}xdx
sum from n=1 to infinity of 4/(n(n+7))	\sum\:_{n=1}^{\infty\:}\frac{4}{n(n+7)}
sum from n=2 to infinity of n/(n+2)	\sum\:_{n=2}^{\infty\:}\frac{n}{n+2}
derivative of f(x)=(x^2+3x-2)/(x^2-5x+6)	derivative\:f(x)=\frac{x^{2}+3x-2}{x^{2}-5x+6}
derivative of f(x)=e^x-x^3	derivative\:f(x)=e^{x}-x^{3}
y^{''}+12y^'+36y=0,y(1)=0,y^'(1)=-1	y^{\prime\:\prime\:}+12y^{\prime\:}+36y=0,y(1)=0,y^{\prime\:}(1)=-1
y^'=((x-y))/((x+2y)),y(0)=1	y^{\prime\:}=\frac{(x-y)}{(x+2y)},y(0)=1
derivative of log_{e}(cos(4x))	\frac{d}{dx}(\log_{e}(\cos(4x)))
integral of xln(x^5)	\int\:x\ln(x^{5})dx
integral from 0 to pi/4 of xsin(2x)	\int\:_{0}^{\frac{π}{4}}x\sin(2x)dx
integral from 0 to 9 of (sqrt(x)-1/3 x)	\int\:_{0}^{9}(\sqrt{x}-\frac{1}{3}x)dx
integral of e^{2x}cos(7x)	\int\:e^{2x}\cos(7x)dx
limit as z approaches 1-i of x+i(2x+y)	\lim\:_{z\to\:1-i}(x+i(2x+y))
(\partial)/(\partial x)(sin(pi(2x-y)))	\frac{\partial\:}{\partial\:x}(\sin(π(2x-y)))
integral of sqrt(x^7)	\int\:\sqrt{x^{7}}dx
derivative of (1-cos(x)/(1+cos(x)))	\frac{d}{dx}(\frac{1-\cos(x)}{1+\cos(x)})
integral of 1/(sqrt((25-y^2)-x^2))	\int\:\frac{1}{\sqrt{(25-y^{2})-x^{2}}}dx
laplacetransform sin(2t)+2cos(2t)+e^{-t}sin(2t)	laplacetransform\:\sin(2t)+2\cos(2t)+e^{-t}\sin(2t)
y^'=3y^2	y^{\prime\:}=3y^{2}
sum from n=1 to infinity of 8^nx^nn!	\sum\:_{n=1}^{\infty\:}8^{n}x^{n}n!
(\partial)/(\partial x)((x^2+y^2)^{-1})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{-1})
x*(dy)/(dx)=xtan(y/x)+y	x\cdot\:\frac{dy}{dx}=x\tan(\frac{y}{x})+y
integral of x(x+8)^5	\int\:x(x+8)^{5}dx
derivative of-3cos^2(x)	\frac{d}{dx}(-3\cos^{2}(x))
derivative of y=x^3+1	derivative\:y=x^{3}+1
derivative of (6x+8x^2)/((3+8x)^2)	derivative\:\frac{6x+8x^{2}}{(3+8x)^{2}}
(dx)/(dt)=-2x+t	\frac{dx}{dt}=-2x+t
taylor sqrt(x),\at 4	taylor\:\sqrt{x},\at\:4
limit as x approaches 0 of (1-5x)^{3/x}	\lim\:_{x\to\:0}((1-5x)^{\frac{3}{x}})
derivative of x^3csc(x)	derivative\:x^{3}\csc(x)
derivative of ln((ln(x)^2))	\frac{d}{dx}(\ln((\ln(x))^{2}))
integral of (1-sin^3(x))/(sin^2(x))	\int\:\frac{1-\sin^{3}(x)}{\sin^{2}(x)}dx
derivative of (2x^2-3x+1/x)	\frac{d}{dx}(\frac{2x^{2}-3x+1}{x})
slope of x^2+xy+2y^2=28,(2,3)	slope\:x^{2}+xy+2y^{2}=28,(2,3)
t^2y^{''}+7ty^'+10y=0	t^{2}y^{\prime\:\prime\:}+7ty^{\prime\:}+10y=0
integral of tan(4x)sec^5(4x)	\int\:\tan(4x)\sec^{5}(4x)dx
limit as x approaches 7-of 1/(x-7)	\lim\:_{x\to\:7-}(\frac{1}{x-7})
derivative of sqrt(x^2+6)	derivative\:\sqrt{x^{2}+6}
tangent of arcsin(x/7)	tangent\:\arcsin(\frac{x}{7})
y^'=(x^2+2y^2)/(xy)	y^{\prime\:}=\frac{x^{2}+2\cdot\:y^{2}}{x\cdot\:y}
derivative of 10xsin(x)	\frac{d}{dx}(10x\sin(x))
9x^2y^2+x^{3/2}y^'=y^2	9x^{2}y^{2}+x^{\frac{3}{2}}y^{\prime\:}=y^{2}
derivative of (x^2-18)(2x+3)	derivative\:(x^{2}-18)(2x+3)
integral of x+1/(x^2)	\int\:x+\frac{1}{x^{2}}dx
(\partial)/(\partial x)(xy-1)	\frac{\partial\:}{\partial\:x}(xy-1)
(\partial)/(\partial y)((x^2-1)(y+2))	\frac{\partial\:}{\partial\:y}((x^{2}-1)(y+2))
tangent of f(x)= 3/(x^2),\at x=1	tangent\:f(x)=\frac{3}{x^{2}},\at\:x=1
integral from 0 to pi/4 of 4sin^2(x)	\int\:_{0}^{\frac{π}{4}}4\sin^{2}(x)dx
limit as h approaches 0 of (1+5h)^{1/h}	\lim\:_{h\to\:0}((1+5h)^{\frac{1}{h}})
derivative of sqrt(y^2-x^2)	\frac{d}{dx}(\sqrt{y^{2}-x^{2}})
integral of e^{5x+e^{5x}}	\int\:e^{5x+e^{5x}}dx
inverse oflaplace s/(2s^2+4s+3)	inverselaplace\:\frac{s}{2s^{2}+4s+3}
(dy)/(dx)=(xsqrt(1-y^2))/(ysqrt(1-x^2))	\frac{dy}{dx}=\frac{x\sqrt{1-y^{2}}}{y\sqrt{1-x^{2}}}
integral of x^3-2x^{-2}+6x	\int\:x^{3}-2x^{-2}+6xdx
taylor sqrt(9+x^2)	taylor\:\sqrt{9+x^{2}}
derivative of ln(4x^3)	derivative\:\ln(4x^{3})
integral of (sqrt(x^5-1))/x	\int\:\frac{\sqrt{x^{5}-1}}{x}dx
integral of 1/(sqrt(x^2-4x+8))	\int\:\frac{1}{\sqrt{x^{2}-4x+8}}dx
derivative of 2x^{sqrt(x)}	\frac{d}{dx}(2x^{\sqrt{x}})
integral of (sqrt(2x-3))/(2x+1)	\int\:\frac{\sqrt{2x-3}}{2x+1}dx
integral of-4sin(5x)sin(x)	\int\:-4\sin(5x)\sin(x)dx
derivative of 1/(1+sin(x))	\frac{d}{dx}(\frac{1}{1+\sin(x)})
integral of 3/4 t+6	\int\:\frac{3}{4}t+6dt
limit as x approaches 3-of sqrt(9-x^2)	\lim\:_{x\to\:3-}(\sqrt{9-x^{2}})
tangent of f(x)=(x+2)/(x^2-9),\at x=1	tangent\:f(x)=\frac{x+2}{x^{2}-9},\at\:x=1
integral of sqrt(3x-12)	\int\:\sqrt{3x-12}dx
derivative of 3/(2x+(4x)/5)	\frac{d}{dx}(\frac{3}{2x}+\frac{4x}{5})
derivative of y=(3x+4)/(sqrt(2x-1))	derivative\:y=\frac{3x+4}{\sqrt{2x-1}}
derivative of f(x)=(x^6-4x^2+2)ln(x)	derivative\:f(x)=(x^{6}-4x^{2}+2)\ln(x)
integral of 2/3 t^{3/2}-8sin(t)+C	\int\:\frac{2}{3}t^{\frac{3}{2}}-8\sin(t)+Cdt
(\partial)/(\partial x)(e^{x^2+y}-2xy)	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y}-2xy)
y^'=xy(y+2)	y^{\prime\:}=xy(y+2)
sum from n=1 to infinity of 9/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{9}{n^{3}}
sum from n=0 to infinity of 4(3/4)^n	\sum\:_{n=0}^{\infty\:}4(\frac{3}{4})^{n}
derivative of (ln(x+2)/(4x^{-2)})	\frac{d}{dx}(\frac{\ln(x+2)}{4x^{-2}})
inverse oflaplace (2s+1)/(s^3)	inverselaplace\:\frac{2s+1}{s^{3}}
derivative of h(x)=(x^2+4x+1)/(3x+5)	derivative\:h(x)=\frac{x^{2}+4x+1}{3x+5}
derivative of 5x^{2x}	\frac{d}{dx}(5x^{2x})
integral of 2x*e^{2x}	\int\:2x\cdot\:e^{2x}dx
integral of (1+1/u)^{-3}(1/(u^2))	\int\:(1+\frac{1}{u})^{-3}(\frac{1}{u^{2}})du
derivative of 4sqrt(x)+8x^{3/8}	\frac{d}{dx}(4\sqrt{x}+8x^{\frac{3}{8}})
derivative of sqrt(((x^2-4^3)/(36)))	\frac{d}{dx}(\sqrt{\frac{(x^{2}-4)^{3}}{36}})
limit as x approaches 1+of 1/(x^3)	\lim\:_{x\to\:1+}(\frac{1}{x^{3}})
slope ofintercept (-5,-1),(0,3)	slopeintercept\:(-5,-1),(0,3)
(dy)/(dx)=(y+1)/(x^3)	\frac{dy}{dx}=\frac{y+1}{x^{3}}
sum from n=1 to infinity of ((3x)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(3x)^{n}}{n}
integral of x-sqrt(x)	\int\:x-\sqrt{x}dx
integral of (5x)/(cos^2(x^2))	\int\:\frac{5x}{\cos^{2}(x^{2})}dx
integral of 21	\int\:21dx

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