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Popular Calculus Problems

derivative of arctan(sec(x+tan(x)))	\frac{d}{dx}(\arctan(\sec(x)+\tan(x)))
derivative of y=(sin(x))/(x^2)	derivative\:y=\frac{\sin(x)}{x^{2}}
derivative of 5/(sqrt(x+1))	\frac{d}{dx}(\frac{5}{\sqrt{x+1}})
y^'xy=x^2+2y^2	y^{\prime\:}xy=x^{2}+2y^{2}
derivative of ((1-2x/(1+3x))^4)	\frac{d}{dx}((\frac{1-2x}{1+3x})^{4})
integral from-9 to 9 of sqrt(1+x^2)	\int\:_{-9}^{9}\sqrt{1+x^{2}}dx
derivative of 2/(1+x^2)	derivative\:\frac{2}{1+x^{2}}
integral of 1/(x^2+12x+85)	\int\:\frac{1}{x^{2}+12x+85}dx
area y= 1/2 x^3+2,y=-x+1,x=0,x=2	area\:y=\frac{1}{2}x^{3}+2,y=-x+1,x=0,x=2
derivative of te^{-3t}	derivative\:te^{-3t}
laplacetransform 2e^{3t}sin(4t)	laplacetransform\:2e^{3t}\sin(4t)
derivative of ln(xcsch(7x))	\frac{d}{dx}(\ln(x)\csch(7x))
(\partial)/(\partial x)(y/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{x^{2}+y^{2}})
integral of sin(x)+y	\int\:\sin(x)+ydx
(\partial)/(\partial y)((2xy^2)/(3+x^2y^2))	\frac{\partial\:}{\partial\:y}(\frac{2xy^{2}}{3+x^{2}y^{2}})
integral of x^7arctan(x^4)	\int\:x^{7}\arctan(x^{4})dx
derivative of 4x^2+1/(x^2+3x^4)	\frac{d}{dx}(4x^{2}+\frac{1}{x^{2}}+3x^{4})
integral from 9 to 16 of 1/(1-sqrt(x))	\int\:_{9}^{16}\frac{1}{1-\sqrt{x}}dx
integral of sqrt(x^2+3)	\int\:\sqrt{x^{2}+3}dx
derivative of 8x-5	\frac{d}{dx}(8x-5)
(\partial)/(\partial x)(ln(x^4+1)+y^2)	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+1)+y^{2})
derivative of tan(x^x)	\frac{d}{dx}(\tan(x^{x}))
3x(xy-2)dx+(x^3+2y)dy=0	3x(xy-2)dx+(x^{3}+2y)dy=0
derivative of x+x^2+sqrt(x)+6/(7x^3)	\frac{d}{dx}(x+x^{2}+\sqrt{x}+\frac{6}{7x^{3}})
integral of ((1+x))/(x^2)	\int\:\frac{(1+x)}{x^{2}}dx
integral of cos^5(4x)sin(4x)	\int\:\cos^{5}(4x)\sin(4x)dx
derivative of ln(6x^2+2x+2)	\frac{d}{dx}(\ln(6x^{2}+2x+2))
d/(dt)(e^{t/7}cos(t/7))	\frac{d}{dt}(e^{\frac{t}{7}}\cos(\frac{t}{7}))
derivative of (2^x/(e^x))	\frac{d}{dx}(\frac{2^{x}}{e^{x}})
y^'=y(y-1)	y^{\prime\:}=y(y-1)
tangent of f(x)=(4x+3)/(x+1),\at x=3	tangent\:f(x)=\frac{4x+3}{x+1},\at\:x=3
derivative of (arcsec((x^2/2))^{3x})	\frac{d}{dx}((\arcsec(\frac{x^{2}}{2}))^{3x})
f(x)=-x/2	f(x)=-\frac{x}{2}
derivative of x+5	derivative\:x+5
area y=3x,y=4x^2	area\:y=3x,y=4x^{2}
y^'=((x+y))/x	y^{\prime\:}=\frac{(x+y)}{x}
integral of e^{sin(x)}sin(2x)	\int\:e^{\sin(x)}\sin(2x)dx
limit as x approaches 5 of g(x)	\lim\:_{x\to\:5}(g(x))
tangent of f(x)=4x^3-24x^2,\at x=-1	tangent\:f(x)=4x^{3}-24x^{2},\at\:x=-1
derivative of 100e^{-x-2y}	\frac{d}{dx}(100e^{-x-2y})
integral of 8sin^2(x)cos^2(x)	\int\:8\sin^{2}(x)\cos^{2}(x)dx
tangent of y= 1/(x^6),(2, 1/64)	tangent\:y=\frac{1}{x^{6}},(2,\frac{1}{64})
integral of 1x^3	\int\:1x^{3}dx
tangent of f(x)=(6x)/(x^2+1),(0,0)	tangent\:f(x)=\frac{6x}{x^{2}+1},(0,0)
integral of 1/48 x	\int\:\frac{1}{48}xdx
tangent of f(x)=(x-1)^2+1,\at x=0	tangent\:f(x)=(x-1)^{2}+1,\at\:x=0
taylor (1+x^2)^{1/4}	taylor\:(1+x^{2})^{\frac{1}{4}}
derivative of (10x+8x^2)/((5+8x)^2)	derivative\:\frac{10x+8x^{2}}{(5+8x)^{2}}
integral of (6x^2)(2x^3+1)^2	\int\:(6x^{2})(2x^{3}+1)^{2}dx
derivative of 2sec(θ)	derivative\:2\sec(θ)
(dy)/(dx)=-5y	\frac{dy}{dx}=-5y
integral from 0 to 9 of \|sqrt(4x+5)-x\|	\int\:_{0}^{9}\left\|\sqrt{4x+5}-x\right\|dx
derivative of 10^{tan(piθ)}	derivative\:10^{\tan(πθ)}
derivative of f(x)=tan(2x)	derivative\:f(x)=\tan(2x)
integral of-4sin^3(x)cos^5(x)	\int\:-4\sin^{3}(x)\cos^{5}(x)dx
area y=x^2-4x+1,y=x+1	area\:y=x^{2}-4x+1,y=x+1
limit as x approaches 0 of (-x^{-x}-1)/x	\lim\:_{x\to\:0}(\frac{-x^{-x}-1}{x})
derivative of (e^{-x}/(x-5)+1)	\frac{d}{dx}(\frac{e^{-x}}{x-5}+1)
limit as x approaches 0+of (1+2x)^{4/x}	\lim\:_{x\to\:0+}((1+2x)^{\frac{4}{x}})
x^3(d^3y)/(dx^3)+2x^2(d^2y)/(dx^2)-x(dy)/(dx)+y=12x^2	x^{3}\frac{d^{3}y}{dx^{3}}+2x^{2}\frac{d^{2}y}{dx^{2}}-x\frac{dy}{dx}+y=12x^{2}
(d^3)/(dt^3)((t^2-1)^3)	\frac{d^{3}}{dt^{3}}((t^{2}-1)^{3})
integral of z(ln(z))^2	\int\:z(\ln(z))^{2}dz
(\partial)/(\partial x)((x^2y+4y)e^{2xy})	\frac{\partial\:}{\partial\:x}((x^{2}y+4y)e^{2xy})
integral of ((x^2+1))/(5cosh^2(x^3+3x))	\int\:\frac{(x^{2}+1)}{5\cosh^{2}(x^{3}+3x)}dx
(\partial)/(\partial y)(x^2+y^2-z)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-z)
(\partial)/(\partial y)(cos(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\cos(x^{2}+y^{2}))
integral of (3x+5)cos(x/4)	\int\:(3x+5)\cos(\frac{x}{4})dx
(\partial)/(\partial y)(3xz+y^2)	\frac{\partial\:}{\partial\:y}(3xz+y^{2})
derivative of e^{x/y}	derivative\:e^{\frac{x}{y}}
derivative of 3(e^xcos(x)-e^xsin(x))	derivative\:3(e^{x}\cos(x)-e^{x}\sin(x))
limit as x approaches 0 of (sqrt(6x+4)-2)/x	\lim\:_{x\to\:0}(\frac{\sqrt{6x+4}-2}{x})
derivative of 5e^{-6x}	derivative\:5e^{-6x}
integral of ((x^4+1))/(x^3+2x^2+x)	\int\:\frac{(x^{4}+1)}{x^{3}+2x^{2}+x}dx
derivative of-6/((x+1^4))	\frac{d}{dx}(-\frac{6}{(x+1)^{4}})
limit as x approaches infinity of x*x/x	\lim\:_{x\to\:\infty\:}(x\cdot\:\frac{x}{x})
d/(dt)((3t^2-3)/(2t))	\frac{d}{dt}(\frac{3t^{2}-3}{2t})
derivative of x^2+2x+6	\frac{d}{dx}(x^{2}+2x+6)
integral from 0 to 1 of (27)/(4y-1)	\int\:_{0}^{1}\frac{27}{4y-1}dy
(d^2)/(dx^2)(sin(9x^2))	\frac{d^{2}}{dx^{2}}(\sin(9x^{2}))
sum from n=1 to infinity of 10^nx^nn!	\sum\:_{n=1}^{\infty\:}10^{n}x^{n}n!
derivative of 2sqrt(x)+5	derivative\:2\sqrt{x}+5
integral of (1+x^3)	\int\:(1+x^{3})dx
integral from-1 to 1 of 3x^2sqrt(x^3+1)	\int\:_{-1}^{1}3x^{2}\sqrt{x^{3}+1}dx
derivative of (1+x^4^{2/3})	\frac{d}{dx}((1+x^{4})^{\frac{2}{3}})
slope ofintercept (4)(8.6)	slopeintercept\:(4)(8.6)
derivative of f(x)=(4x+1)	derivative\:f(x)=(4x+1)
(\partial)/(\partial x)(ln(3x+5y))	\frac{\partial\:}{\partial\:x}(\ln(3x+5y))
derivative of (2x^2)	\frac{d}{dx}((2x)^{2})
f(x)=e^{2x}	f(x)=e^{2x}
(\partial)/(\partial x)(x^2+4)	\frac{\partial\:}{\partial\:x}(x^{2}+4)
derivative of ln(3x^2+1ln(2x^3+1))	\frac{d}{dx}(\ln(3x^{2}+1)\ln(2x^{3}+1))
integral of (x^5+x+1)/(x^3-8)	\int\:\frac{x^{5}+x+1}{x^{3}-8}dx
derivative of y=(x^2+3)((2x+5)^6)	derivative\:y=(x^{2}+3)((2x+5)^{6})
derivative of 5+1/(x^2)	\frac{d}{dx}(5+\frac{1}{x^{2}})
integral from 0 to 3 of \|x^2-4\|	\int\:_{0}^{3}\left\|x^{2}-4\right\|dx
integral of 29x^{28}	\int\:29x^{28}dx
limit as x approaches 1/3 of 5x-7	\lim\:_{x\to\:\frac{1}{3}}(5x-7)
integral from-2 to 3 of (x^2+3x-5)	\int\:_{-2}^{3}(x^{2}+3x-5)dx
taylor (2-x)^{-1}	taylor\:(2-x)^{-1}
derivative of 4xe^xcsc(x)	derivative\:4xe^{x}\csc(x)

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