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Popular Calculus Problems

(\partial)/(\partial x)(mx+b)	\frac{\partial\:}{\partial\:x}(mx+b)
integral from-infinity to 0 of e^{4y}	\int\:_{-\infty\:}^{0}e^{4y}dy
sum from n=1 to infinity of ((x-2)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(x-2)^{n}}{n}
(dy)/(dx)=(y-x+5)/(2y-2x+6)	\frac{dy}{dx}=\frac{y-x+5}{2y-2x+6}
integral of 1/(xsqrt(x^6-4))	\int\:\frac{1}{x\sqrt{x^{6}-4}}dx
x(dy)/(dx)=y+sqrt(x^2+y^2),x>0	x\frac{dy}{dx}=y+\sqrt{x^{2}+y^{2}},x>0
integral of (-2)	\int\:(-2)dx
integral from 0 to 2 of (4-x)^2	\int\:_{0}^{2}(4-x)^{2}dx
derivative of (-2x-y)/(x+3y^2)	derivative\:\frac{-2x-y}{x+3y^{2}}
(dy)/(dx)=((x-3))/((y-3))	\frac{dy}{dx}=\frac{(x-3)}{(y-3)}
integral of (x+4)(x-2)	\int\:(x+4)(x-2)dx
tangent of y=3sin(x),\at x= pi/6	tangent\:y=3\sin(x),\at\:x=\frac{π}{6}
implicit (dy)/(dx),e^xy=2	implicit\:\frac{dy}{dx},e^{x}y=2
integral of (2x+5-1/x)	\int\:(2x+5-\frac{1}{x})dx
(\partial)/(\partial y)(6xy)	\frac{\partial\:}{\partial\:y}(6xy)
integral of y/((x^2+y^2))	\int\:\frac{y}{(x^{2}+y^{2})}dy
derivative of (x^3-2/x)	\frac{d}{dx}(\frac{x^{3}-2}{x})
y^'=(y^2-x^2)/(xy)	y^{\prime\:}=\frac{y^{2}-x^{2}}{xy}
derivative of 3x^2+(8x)/3-2	derivative\:3x^{2}+\frac{8x}{3}-2
2y^'+y=8t^2	2y^{\prime\:}+y=8t^{2}
(\partial)/(\partial y)(sqrt(4-x^2-2y))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-2y})
derivative of 3cos(x)	derivative\:3\cos(x)
tangent of 1/(2-3x),\at x=1	tangent\:\frac{1}{2-3x},\at\:x=1
(cosh(t))^'	(\cosh(t))^{\prime\:}
derivative of x/(sqrt(9+x^2))	derivative\:\frac{x}{\sqrt{9+x^{2}}}
(dy)/(dx)=-1/(x+2)	\frac{dy}{dx}=-\frac{1}{x+2}
limit as x approaches 3 of x(x-1)	\lim\:_{x\to\:3}(x(x-1))
integral of (5e^x)/(e^{2x)+4e^x+4}	\int\:\frac{5e^{x}}{e^{2x}+4e^{x}+4}dx
derivative of cos(pi/2+1/x)	\frac{d}{dx}(\cos(\frac{π}{2}+\frac{1}{x}))
tangent of 1/(x+4)	tangent\:\frac{1}{x+4}
integral of (3x^2+6)	\int\:(3x^{2}+6)dx
integral from 0 to t of t^2e^{-t}	\int\:_{0}^{t}t^{2}e^{-t}dt
integral of (t-3)cos(t-3)	\int\:(t-3)\cos(t-3)dt
(\partial)/(\partial x)(xe^{xy})	\frac{\partial\:}{\partial\:x}(xe^{xy})
integral from-6 to 6 of 1/(sqrt(36-x^2))	\int\:_{-6}^{6}\frac{1}{\sqrt{36-x^{2}}}dx
integral of 1/((3x+1))	\int\:\frac{1}{(3x+1)}dx
limit as x approaches 3+of (x+4)/(x-3)	\lim\:_{x\to\:3+}(\frac{x+4}{x-3})
derivative of f(x)=cot^2(cos(θ))	derivative\:f(x)=\cot^{2}(\cos(θ))
integral of ((2sqrt(x)-5)^2)/3	\int\:\frac{(2\sqrt{x}-5)^{2}}{3}dx
integral from 0 to pi/6 of 3cos^5(3x)	\int\:_{0}^{\frac{π}{6}}3\cos^{5}(3x)dx
d/(dy)(x^2+xy+y^2)	\frac{d}{dy}(x^{2}+xy+y^{2})
integral from 0 to 4 of 2sqrt(x)-x	\int\:_{0}^{4}2\sqrt{x}-xdx
limit as x approaches 0 of 1/(x^3-1)+1	\lim\:_{x\to\:0}(\frac{1}{x^{3}-1}+1)
limit as x approaches 0 of (x^2-5)/x	\lim\:_{x\to\:0}(\frac{x^{2}-5}{x})
limit as t approaches-2 of t^2+5t+7	\lim\:_{t\to\:-2}(t^{2}+5t+7)
integral of tan^3(x/2)sec^3(x/2)	\int\:\tan^{3}(\frac{x}{2})\sec^{3}(\frac{x}{2})dx
f^'(x)=(2x^2-9x+8)/(6x+5)	f^{\prime\:}(x)=\frac{2x^{2}-9x+8}{6x+5}
integral of r^3+2r	\int\:r^{3}+2rdr
d/(dt)(2cos^2(t))	\frac{d}{dt}(2\cos^{2}(t))
integral of x(3x^2-5)^{10}	\int\:x(3x^{2}-5)^{10}dx
integral of x^4e^{5x}	\int\:x^{4}e^{5x}dx
f(x)= 3/(x+5)	f(x)=\frac{3}{x+5}
integral of (-2e^x-6/x)	\int\:(-2e^{x}-\frac{6}{x})dx
derivative of y= 3/(x^6)+1/(x^5)-7/(x^2)	derivative\:y=\frac{3}{x^{6}}+\frac{1}{x^{5}}-\frac{7}{x^{2}}
(\partial)/(\partial x)(xsin(4y*z^4))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(4\cdot\:y\cdot\:z^{4}))
limit as x approaches 0+of (7x)^x	\lim\:_{x\to\:0+}((7x)^{x})
tangent of f(x)=2x^2-4x,\at x=-1	tangent\:f(x)=2x^{2}-4x,\at\:x=-1
tangent of f(x)=4x-x^2,(2,5)	tangent\:f(x)=4x-x^{2},(2,5)
integral of (2x-5)^{11}	\int\:(2x-5)^{11}dx
integral from-1 to 2 of x/((x+1)^2)	\int\:_{-1}^{2}\frac{x}{(x+1)^{2}}dx
integral of sin(nt)	\int\:\sin(nt)dt
x^'=6c_{1}-(3x)/5	x^{\prime\:}=6c_{1}-\frac{3x}{5}
integral from 0 to 1 of x(1-x^2)	\int\:_{0}^{1}x(1-x^{2})dx
f(t)=(t^2)/2	f(t)=\frac{t^{2}}{2}
derivative of (x^4+1/(x^2))	\frac{d}{dx}(\frac{x^{4}+1}{x^{2}})
derivative of 5e^{-4x}	\frac{d}{dx}(5e^{-4x})
f^'(x)=x^{(2)}-4	f^{\prime\:}(x)=x^{(2)}-4
derivative of sqrt(x)+\sqrt[3]{x}	derivative\:\sqrt{x}+\sqrt[3]{x}
(\partial)/(\partial x)(sqrt(x^2+5))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+5})
derivative of (5x)/(e^x)	derivative\:\frac{5x}{e^{x}}
x^2y^{''}-4xy^'=x^5	x^{2}y^{\prime\:\prime\:}-4xy^{\prime\:}=x^{5}
derivative of f(x)=(3x^2-x+5)(x^2+3x-9)	derivative\:f(x)=(3x^{2}-x+5)(x^{2}+3x-9)
limit as x approaches 2+of (-2)/(x^2-4)	\lim\:_{x\to\:2+}(\frac{-2}{x^{2}-4})
limit as x approaches 0 of-3/(x^2)	\lim\:_{x\to\:0}(-\frac{3}{x^{2}})
derivative of arctan(sin(4x))	derivative\:\arctan(\sin(4x))
y^{''}+25y=-25sec^2(5x)	y^{\prime\:\prime\:}+25y=-25\sec^{2}(5x)
(\partial)/(\partial x)(2+xln(xy-7))	\frac{\partial\:}{\partial\:x}(2+x\ln(xy-7))
derivative of x^2sqrt(x-1)	\frac{d}{dx}(x^{2}\sqrt{x-1})
integral of (3x^2+8x-12)/(x^3+7x+12x)	\int\:\frac{3x^{2}+8x-12}{x^{3}+7x+12x}dx
integral of (3^{x+2})/(4^{x-1)}	\int\:\frac{3^{x+2}}{4^{x-1}}dx
integral of xcos(6x)	\int\:x\cos(6x)dx
integral of ((26))/((x-1)(x^2+25))	\int\:\frac{(26)}{(x-1)(x^{2}+25)}dx
integral of x^{-2}e^{1/x}	\int\:x^{-2}e^{\frac{1}{x}}dx
derivative of 3x-8	derivative\:3x-8
(5y-2x)y^'-2y=0	(5y-2x)y^{\prime\:}-2y=0
tangent of f(x)=xsqrt(x^2+60),\at x=2	tangent\:f(x)=x\sqrt{x^{2}+60},\at\:x=2
(\partial)/(\partial x)((3-x)(3-y)(x+y-3))	\frac{\partial\:}{\partial\:x}((3-x)(3-y)(x+y-3))
(d^2)/(dx^2)((3+2x)e^{-3x})	\frac{d^{2}}{dx^{2}}((3+2x)e^{-3x})
derivative of x(-3x^{-4})	derivative\:x(-3x^{-4})
integral of-5sin^3(x)cos^2(x)	\int\:-5\sin^{3}(x)\cos^{2}(x)dx
(dy)/(dt)=10^{-21}*y^3	\frac{dy}{dt}=10^{-21}\cdot\:y^{3}
tangent of f(x)=-3x^2+8x+1,\at x=-2	tangent\:f(x)=-3x^{2}+8x+1,\at\:x=-2
derivative of 3^{-x}	derivative\:3^{-x}
limit as x approaches 6 of-x^2+4x-3	\lim\:_{x\to\:6}(-x^{2}+4x-3)
integral of csc(x)sec^2(x)	\int\:\csc(x)\sec^{2}(x)dx
integral of (x^2+1)/(x^2-5x+6)	\int\:\frac{x^{2}+1}{x^{2}-5x+6}dx
(\partial)/(\partial x)(5e^{2x})	\frac{\partial\:}{\partial\:x}(5e^{2x})
derivative of y=(x^4)/4+2/9 x^3-x^2+9x-5	derivative\:y=\frac{x^{4}}{4}+\frac{2}{9}x^{3}-x^{2}+9x-5
maclaurin ((2x))/(1+x^4)	maclaurin\:\frac{(2x)}{1+x^{4}}
derivative of sqrt(7-4x)	derivative\:\sqrt{7-4x}

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