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Popular Calculus Problems

y^'=ln(x)y+x^x	y^{\prime\:}=\ln(x)y+x^{x}
derivative of sqrt(sin(x+cos(x)))	\frac{d}{dx}(\sqrt{\sin(x)+\cos(x)})
integral from 0 to 2 of x^2(x^3+1)^{3/2}	\int\:_{0}^{2}x^{2}(x^{3}+1)^{\frac{3}{2}}dx
area 3x^2,x^2+4,-2,2	area\:3x^{2},x^{2}+4,-2,2
derivative of ln(x/(x^2+6))	derivative\:\ln(\frac{x}{x^{2}+6})
integral of (-1)/x	\int\:\frac{-1}{x}dx
y(x+7)+y^'=0	y(x+7)+y^{\prime\:}=0
derivative of tan(5x+2)	\frac{d}{dx}(\tan(5x+2))
derivative of x^3*e^{-x}	\frac{d}{dx}(x^{3}\cdot\:e^{-x})
derivative of x^4-8x^3+22x^2-24x+9	\frac{d}{dx}(x^{4}-8x^{3}+22x^{2}-24x+9)
tangent of x^4+xy^2=5,(1,2)	tangent\:x^{4}+xy^{2}=5,(1,2)
derivative of 4x-2/(x^3)	\frac{d}{dx}(4x-\frac{2}{x^{3}})
(\partial)/(\partial x)(x/(x+y)+e^{xy}x+4y)	\frac{\partial\:}{\partial\:x}(\frac{x}{x+y}+e^{xy}x+4y)
derivative of (x-x^2/(sqrt(x)))	\frac{d}{dx}(\frac{x-x^{2}}{\sqrt{x}})
derivative of 2cos(x/2)	\frac{d}{dx}(2\cos(\frac{x}{2}))
derivative of-4(x-9)^3	derivative\:-4(x-9)^{3}
taylor (sin(x)), pi/2	taylor\:(\sin(x)),\frac{π}{2}
sum from n=1 to infinity of (2n)/(3n)	\sum\:_{n=1}^{\infty\:}\frac{2n}{3n}
derivative of 1+x^2	derivative\:1+x^{2}
integral from 0 to 9 of 4sqrt(x)-(4x)/3	\int\:_{0}^{9}4\sqrt{x}-\frac{4x}{3}dx
(\partial)/(\partial x)(3x^3y^2z)	\frac{\partial\:}{\partial\:x}(3x^{3}y^{2}z)
laplacetransform 0.03(1-cos(2t))	laplacetransform\:0.03(1-\cos(2t))
integral from 0 to infinity of 3e^{2x}	\int\:_{0}^{\infty\:}3e^{2x}dx
limit as y approaches 0 of (4y^5+5y^3)/(y^4-y)	\lim\:_{y\to\:0}(\frac{4y^{5}+5y^{3}}{y^{4}-y})
integral of-x/(1+x)	\int\:-\frac{x}{1+x}dx
area 6-y=x^2,y+8=x^2,x-y+4=0,x-y-6=0	area\:6-y=x^{2},y+8=x^{2},x-y+4=0,x-y-6=0
y^{''}-7y^'+12y=0,y(0)=-2,y^'(0)=4	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=0,y(0)=-2,y^{\prime\:}(0)=4
derivative of 1/(sqrt(x+sin(x)))	\frac{d}{dx}(\frac{1}{\sqrt{x+\sin(x)}})
(dy)/(dx)=(4e^{4x})/(e^y)	\frac{dy}{dx}=\frac{4e^{4x}}{e^{y}}
integral of 2e^{-st}	\int\:2e^{-st}dt
inverse oflaplace ((s-1))/(s^2+2s+2)	inverselaplace\:\frac{(s-1)}{s^{2}+2s+2}
limit as x approaches infinity of 3-f(x)	\lim\:_{x\to\:\infty\:}(3-f(x))
tangent of 8x^3-36x^2-96	tangent\:8x^{3}-36x^{2}-96
derivative of 2arcsec(sqrt(x))	\frac{d}{dx}(2\arcsec(\sqrt{x}))
integral of e^{5x}cos(7x)	\int\:e^{5x}\cos(7x)dx
slope of (3,8),(7,-7)	slope\:(3,8),(7,-7)
limit as x approaches 3+of 1-x	\lim\:_{x\to\:3+}(1-x)
integral from 1 to 4 of 2pix(e^x-ln(x))	\int\:_{1}^{4}2πx(e^{x}-\ln(x))dx
(4arccos(sqrt(1-x^2)))^'	(4\arccos(\sqrt{1-x^{2}}))^{\prime\:}
derivative of sqrt(x^2+y^2-9)	\frac{d}{dx}(\sqrt{x^{2}+y^{2}-9})
derivative of sin^2(x-cos(2x))	\frac{d}{dx}(\sin^{2}(x)-\cos(2x))
limit as x approaches 4+of 5	\lim\:_{x\to\:4+}(5)
integral of sin(ln(14x))	\int\:\sin(\ln(14x))dx
derivative of (x/(2(x^2-1)^2-1))^2	derivative\:(\frac{x}{2(x^{2}-1)^{2}-1})^{2}
integral from 0 to 30 of 4x(30-x)	\int\:_{0}^{30}4x(30-x)dx
(\partial)/(\partial x)(x^3e^{sqrt(4xy)})	\frac{\partial\:}{\partial\:x}(x^{3}e^{\sqrt{4xy}})
y^'= y/t-1/(y/t)	y^{\prime\:}=\frac{y}{t}-\frac{1}{\frac{y}{t}}
tangent of f(x)=x+2/x ,\at x=2	tangent\:f(x)=x+\frac{2}{x},\at\:x=2
integral of (50)/(x^{0.25)}	\int\:\frac{50}{x^{0.25}}dx
d/(dy)(xe^{x-y})	\frac{d}{dy}(xe^{x-y})
integral from 0 to 6 of pi(3x)^2	\int\:_{0}^{6}π(3x)^{2}dx
integral of ((ln(u))^8)/u	\int\:\frac{(\ln(u))^{8}}{u}du
(dy}{dx}=\frac{e^{3x}+3xy+y)/x	\frac{dy}{dx}=\frac{e^{3x}+3xy+y}{x}
(d^2)/(dx^2)((3x-2)/(2x+1))	\frac{d^{2}}{dx^{2}}(\frac{3x-2}{2x+1})
derivative of (log_{3}(x)/(log_{7)(x)})	\frac{d}{dx}(\frac{\log_{3}(x)}{\log_{7}(x)})
integral of x^2-cos(x)	\int\:x^{2}-\cos(x)dx
dx+e^{5x}dy=0	dx+e^{5x}dy=0
laplacetransform s^2+2s+1	laplacetransform\:s^{2}+2s+1
derivative of y=x^2e^x-2xe^x+4e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+4e^{x}
integral of (x-pi)sin(x)	\int\:(x-π)\sin(x)dx
integral from 0 to 5 of 1	\int\:_{0}^{5}1dx
y^{''}+y^'-6y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=1
derivative of 1+2x^2	derivative\:1+2x^{2}
derivative of ln(3+sqrt(x))	derivative\:\ln(3+\sqrt{x})
(dy)/(dx)+y=e^{4x}	\frac{dy}{dx}+y=e^{4x}
derivative of-(2x+3/((x^2+3x+2)^2))	\frac{d}{dx}(-\frac{2x+3}{(x^{2}+3x+2)^{2}})
limit as x approaches 3 of 3x-7	\lim\:_{x\to\:3}(3x-7)
derivative of 1/(x^7)	derivative\:\frac{1}{x^{7}}
limit as x approaches 0+of e^x-(1+x)	\lim\:_{x\to\:0+}(e^{x}-(1+x))
(\partial)/(\partial x)(x*arccsc(x/2))	\frac{\partial\:}{\partial\:x}(x\cdot\:\arccsc(\frac{x}{2}))
integral of sqrt(5x^2+1)	\int\:\sqrt{5x^{2}+1}dx
integral of (ae^x+b)/(ae^x-b)	\int\:\frac{ae^{x}+b}{ae^{x}-b}dx
(9xy^2-4y)+(9x^2y-4x)y^'=0	(9xy^{2}-4y)+(9x^{2}y-4x)y^{\prime\:}=0
integral of (csc(3x)-cot(3x))^2	\int\:(\csc(3x)-\cot(3x))^{2}dx
y^{''}-2y^'=sin(x),y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}=\sin(x),y(0)=1,y^{\prime\:}(0)=2
integral of sqrt(t^2+4)	\int\:\sqrt{t^{2}+4}dt
derivative of sin(x+5/6 cot(x))	\frac{d}{dx}(\sin(x)+\frac{5}{6}\cot(x))
integral from-8 to 0 of (4-9x)^{-0.5}	\int\:_{-8}^{0}(4-9x)^{-0.5}dx
area (x-1)^3,(x-1)	area\:(x-1)^{3},(x-1)
(\partial)/(\partial x)(1/2 ln(x^2d))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(x^{2}d))
derivative of sqrt(csc(x))	\frac{d}{dx}(\sqrt{\csc(x)})
integral of 15cos(15x)	\int\:15\cos(15x)dx
derivative of f(x)=9x-10x^{1/4}	derivative\:f(x)=9x-10x^{\frac{1}{4}}
integral of 1/(cos(y))	\int\:\frac{1}{\cos(y)}dy
integral from 0 to 0.75 of 2x	\int\:_{0}^{0.75}2xdx
derivative of Ax^{-1/2}	\frac{d}{dx}(Ax^{-\frac{1}{2}})
area x=y 1/3 ,x=0,y=64	area\:x=y\frac{1}{3},x=0,y=64
(y^2+yx)dx+x^2dy=0	(y^{2}+yx)dx+x^{2}dy=0
derivative of (4x^5)/(e^{3x)}	derivative\:\frac{4x^{5}}{e^{3x}}
limit as x approaches 0-of (e^x)/(1-e^x)	\lim\:_{x\to\:0-}(\frac{e^{x}}{1-e^{x}})
derivative of f(x)=e^{-x}x-2e^{-x}	derivative\:f(x)=e^{-x}x-2e^{-x}
(\partial)/(\partial x)(cos(8xy))	\frac{\partial\:}{\partial\:x}(\cos(8xy))
derivative of y=2x+8	derivative\:y=2x+8
integral of sqrt(1+36x)	\int\:\sqrt{1+36x}dx
derivative of \sqrt[3]{x^2}(2x-x^2)	\frac{d}{dx}(\sqrt[3]{x^{2}}(2x-x^{2}))
d/(dt)(ae^{bt})	\frac{d}{dt}(ae^{bt})
(\partial)/(\partial x)(e^{-t})	\frac{\partial\:}{\partial\:x}(e^{-t})
derivative of 1/x+1/(x^2)	\frac{d}{dx}(\frac{1}{x}+\frac{1}{x^{2}})
(\partial)/(\partial t)(sech^2(x-t))	\frac{\partial\:}{\partial\:t}(\sech^{2}(x-t))
integral of 6x^4e^{x^5}	\int\:6x^{4}e^{x^{5}}dx

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