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Popular Calculus Problems

sum from n=0 to infinity of 1/((2^n))	\sum\:_{n=0}^{\infty\:}\frac{1}{(2^{n})}
P-P^2=(dP)/(dt)	P-P^{2}=\frac{dP}{dt}
(\partial}{\partial x}(e^{\frac{-y)/x})	\frac{\partial\:}{\partial\:x}(e^{\frac{-y}{x}})
x^2y^'-2xy=3y^4	x^{2}y^{\prime\:}-2xy=3y^{4}
integral of x/8 sqrt(64+x^2)	\int\:\frac{x}{8}\sqrt{64+x^{2}}dx
tangent of y=x^2+2,(1,3)	tangent\:y=x^{2}+2,(1,3)
integral of (\sqrt[5]{x}+\sqrt[6]{x})	\int\:(\sqrt[5]{x}+\sqrt[6]{x})dx
limit as x approaches 0 of 1/(x^2(x-7))	\lim\:_{x\to\:0}(\frac{1}{x^{2}(x-7)})
derivative of ln(y+y^2+cos(x))	\frac{d}{dx}(\ln(y)+y^{2}+\cos(x))
y^{''}+2y^'+y=sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(2t)
integral from-infinity to 6 of xe^{x/2}	\int\:_{-\infty\:}^{6}xe^{\frac{x}{2}}dx
y^'= 1/(1+y)	y^{\prime\:}=\frac{1}{1+y}
derivative of x^2(1-3x)	derivative\:x^{2}(1-3x)
limit as x approaches 1 of-(3)	\lim\:_{x\to\:1}(-(3))
derivative of ln(xx)	\frac{d}{dx}(\ln(x)x)
integral from 0 to infinity of 1/(2^x)	\int\:_{0}^{\infty\:}\frac{1}{2^{x}}dx
limit as x approaches 0 of x^6cos(5/x)	\lim\:_{x\to\:0}(x^{6}\cos(\frac{5}{x}))
sum from n=1 to infinity of (9/10)^n	\sum\:_{n=1}^{\infty\:}(\frac{9}{10})^{n}
derivative of sqrt(3x^2+1)(3x^4+1^3)	\frac{d}{dx}(\sqrt{3x^{2}+1}(3x^{4}+1)^{3})
integral of x^3cos(x^4-5)	\int\:x^{3}\cos(x^{4}-5)dx
limit as t approaches infinity of e^{-t}	\lim\:_{t\to\:\infty\:}(e^{-t})
derivative of 2x^{1/3}	derivative\:2x^{\frac{1}{3}}
integral of (2x+1)sin(x)	\int\:(2x+1)\sin(x)dx
integral of x/(x^3+x^2+x+1)	\int\:\frac{x}{x^{3}+x^{2}+x+1}dx
derivative of a^2x+a^2y+b^2x+b^2y	\frac{d}{dx}(a^{2}x+a^{2}y+b^{2}x+b^{2}y)
derivative of 2/3 (5-2x^2^3)	\frac{d}{dx}(\frac{2}{3}(5-2x^{2})^{3})
y=-3cot(2x)sec(2x)	y=-3\cot(2x)\sec(2x)
(\partial)/(\partial t)(Pe^{rt})	\frac{\partial\:}{\partial\:t}(Pe^{rt})
limit as x approaches-0.01 of (3^x-1)/x	\lim\:_{x\to\:-0.01}(\frac{3^{x}-1}{x})
y^{''}+y^'-30y=0	y^{\prime\:\prime\:}+y^{\prime\:}-30y=0
integral of 0.5x^3	\int\:0.5x^{3}dx
derivative of R^3	derivative\:R^{3}
(\partial)/(\partial x)((x-y)^3)	\frac{\partial\:}{\partial\:x}((x-y)^{3})
integral of (3x-2)/(sqrt(3+2x-x^2))	\int\:\frac{3x-2}{\sqrt{3+2x-x^{2}}}dx
integral of 4x^2cos(6x)	\int\:4x^{2}\cos(6x)dx
derivative of (2x^3/(2x^4-5x^3+x^2))	\frac{d}{dx}(\frac{2x^{3}}{2x^{4}-5x^{3}+x^{2}})
derivative of f(x)=4e^x	derivative\:f(x)=4e^{x}
derivative of sqrt(x)(x-10)	derivative\:\sqrt{x}(x-10)
derivative of (2x^2/(3x-1))	\frac{d}{dx}(\frac{2x^{2}}{3x-1})
integral of (sqrt(x)+3)^3	\int\:(\sqrt{x}+3)^{3}dx
limit as x approaches-4 of x^3+4x^2-8x	\lim\:_{x\to\:-4}(x^{3}+4x^{2}-8x)
yln(y)dx+(x-ln(y))dy=0	y\ln(y)dx+(x-\ln(y))dy=0
(\partial)/(\partial x)(x^3y+e^{xy^2})	\frac{\partial\:}{\partial\:x}(x^{3}y+e^{xy^{2}})
(dy)/(dx)=1-2y	\frac{dy}{dx}=1-2y
integral of tan^5(8x)sec^4(8x)	\int\:\tan^{5}(8x)\sec^{4}(8x)dx
f(x)= 1/(3x)	f(x)=\frac{1}{3x}
derivative of (4x)^{10x^3}	derivative\:(4x)^{10x^{3}}
derivative of 1/(sinh(x))	\frac{d}{dx}(\frac{1}{\sinh(x)})
(x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=6	(x^{2}+1)\frac{dy}{dx}+3x(y-1)=0,y(0)=6
derivative of (d^2/(dx^2)(1/x)-ln(x))	\frac{d}{dx}(\frac{d^{2}}{dx^{2}}(\frac{1}{x})-\ln(x))
limit as x approaches 0 of (4/x-1)x	\lim\:_{x\to\:0}((\frac{4}{x}-1)x)
derivative of sqrt(5x+x^2)	derivative\:\sqrt{5x+x^{2}}
derivative of x(x-4^{1/3})	\frac{d}{dx}(x(x-4)^{\frac{1}{3}})
(dy)/(dt)=3t^2	\frac{dy}{dt}=3t^{2}
(\partial)/(\partial x)(x^7y^6+4x^6y)	\frac{\partial\:}{\partial\:x}(x^{7}y^{6}+4x^{6}y)
integral of 8x^{1/2}	\int\:8x^{\frac{1}{2}}dx
limit as x approaches 2 of e^{1/0}	\lim\:_{x\to\:2}(e^{\frac{1}{0}})
tangent of y=3tan(x),\at x= pi/6	tangent\:y=3\tan(x),\at\:x=\frac{π}{6}
integral of 8^3sqrt(x)	\int\:8^{3}\sqrt{x}dx
y^'-6/x y=(y^5)/(x^7)	y^{\prime\:}-\frac{6}{x}y=\frac{y^{5}}{x^{7}}
integral of 1/(sqrt(x^2-2x+17))	\int\:\frac{1}{\sqrt{x^{2}-2x+17}}dx
limit as x approaches 0 of ln(x^2)	\lim\:_{x\to\:0}(\ln(x^{2}))
derivative of ln(3x^2+7y^2)	derivative\:\ln(3x^{2}+7y^{2})
(dy)/(dx)=5sqrt(yx)	\frac{dy}{dx}=5\sqrt{yx}
limit as x approaches 3 of tan((pix)/4)	\lim\:_{x\to\:3}(\tan(\frac{πx}{4}))
laplacetransform (t^4)/7	laplacetransform\:\frac{t^{4}}{7}
derivative of (\sqrt[3]{x}/(x-3))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x-3})
integral of 1/(e^{5y)}	\int\:\frac{1}{e^{5y}}dy
derivative of \sqrt[3]{(t^3-3)}	derivative\:\sqrt[3]{(t^{3}-3)}
inverse oflaplace (4s+1)/(s^3-3s^2+3s-1)	inverselaplace\:\frac{4s+1}{s^{3}-3s^{2}+3s-1}
inverse oflaplace ((10s-3))/(s^2-4s-29)	inverselaplace\:\frac{(10s-3)}{s^{2}-4s-29}
derivative of (ln(x)/(sqrt(x)))	\frac{d}{dx}(\frac{\ln(x)}{\sqrt{x}})
(\partial)/(\partial y)(9x^y+2y^x+11)	\frac{\partial\:}{\partial\:y}(9x^{y}+2y^{x}+11)
integral of (3t-2)/(sqrt(9-t^2))	\int\:\frac{3t-2}{\sqrt{9-t^{2}}}dt
integral of arcsec(x)	\int\:\arcsec(x)dx
derivative of x/(ax^2+b)	\frac{d}{dx}(\frac{x}{ax^{2}+b})
limit as x approaches-4-of x^2+5/(x+4)	\lim\:_{x\to\:-4-}(x^{2}+\frac{5}{x+4})
integral of 1/(1-0.5x)	\int\:\frac{1}{1-0.5x}dx
limit as x approaches 10-of 8-x	\lim\:_{x\to\:10-}(8-x)
(\partial)/(\partial z)(xe^z+xy+z^3-4)	\frac{\partial\:}{\partial\:z}(xe^{z}+xy+z^{3}-4)
integral of e^xsqrt(1-e^{2x)}	\int\:e^{x}\sqrt{1-e^{2x}}dx
derivative of e^{1-x}	derivative\:e^{1-x}
x(dy)/(dx)+y+y^2=0	x\frac{dy}{dx}+y+y^{2}=0
simplify ((1+tan(x))^2)/(sec(x))	simplify\:\frac{(1+\tan(x))^{2}}{\sec(x)}
integral from 1 to 2 of (4x-2/(x^2))	\int\:_{1}^{2}(4x-\frac{2}{x^{2}})dx
integral of sec^7(4x)tan(4x)	\int\:\sec^{7}(4x)\tan(4x)dx
derivative of f(x)=(10)/x	derivative\:f(x)=\frac{10}{x}
derivative of 524288sin(2x)	\frac{d}{dx}(524288\sin(2x))
derivative of 1/(2x^4)	derivative\:\frac{1}{2x^{4}}
integral from 2 to 3 of (37)/(sqrt(3-x))	\int\:_{2}^{3}\frac{37}{\sqrt{3-x}}dx
integral of 7x^{2/5}+5x^{-4/5}	\int\:7x^{\frac{2}{5}}+5x^{-\frac{4}{5}}dx
slope of (0,4),(2,-3)	slope\:(0,4),(2,-3)
integral of e^{2ix}	\int\:e^{2ix}dx
integral from 2 to 3 of (y^2-2y+1)	\int\:_{2}^{3}(y^{2}-2y+1)dy
d/(dt)((3t)/(1+t^3))	\frac{d}{dt}(\frac{3t}{1+t^{3}})
limit as x approaches 0+of ln(4sin(x))	\lim\:_{x\to\:0+}(\ln(4\sin(x)))
derivative of (x^{-1/2})	\frac{d}{dx}((x)^{-\frac{1}{2}})
integral of 1/(sqrt(5-2x))	\int\:\frac{1}{\sqrt{5-2x}}dx
limit as t approaches 0 of sin(7t)	\lim\:_{t\to\:0}(\sin(7t))
derivative of ln(9x^2+5y^2)	derivative\:\ln(9x^{2}+5y^{2})

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