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Popular Calculus Problems

d/(dt)(e^{-at}cos(xt))	\frac{d}{dt}(e^{-at}\cos(xt))
y^'=(2x^5e^{y/x}+x^3y^2)/(x^4y)	y^{\prime\:}=\frac{2x^{5}e^{\frac{y}{x}}+x^{3}y^{2}}{x^{4}y}
tangent of f(x)=-2x^2+4x-4,\at x=3	tangent\:f(x)=-2x^{2}+4x-4,\at\:x=3
(\partial)/(\partial x)(sqrt(x+3y))	\frac{\partial\:}{\partial\:x}(\sqrt{x+3y})
(log_{e}(x))^'	(\log_{e}(x))^{\prime\:}
slope of (-3,5),(3,5)	slope\:(-3,5),(3,5)
y^'=2x+3	y^{\prime\:}=2x+3
64y^{''}-48y^'+34y=0	64y^{\prime\:\prime\:}-48y^{\prime\:}+34y=0
derivative of ln((x^2+1^{20}))	\frac{d}{dx}(\ln((x^{2}+1)^{20}))
integral of (x^2)/((x+1)(x-1)^2)	\int\:\frac{x^{2}}{(x+1)(x-1)^{2}}dx
integral from 1 to 2 of x^{-3}	\int\:_{1}^{2}x^{-3}dx
ty^'+(t+1)y=t	ty^{\prime\:}+(t+1)y=t
integral of 6x(3x^2-2)^4	\int\:6x(3x^{2}-2)^{4}dx
integral from 0 to 1/5 of 4arcsin(5y)	\int\:_{0}^{\frac{1}{5}}4\arcsin(5y)dy
tangent of y=3x-4x^2,(-2,-22)	tangent\:y=3x-4x^{2},(-2,-22)
(\partial)/(\partial x)(e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(e^{-xy}\cos(y))
inverse oflaplace 1/(s^2(s^2+3s+10))	inverselaplace\:\frac{1}{s^{2}(s^{2}+3s+10)}
derivative of (4e^{2x}-2e^x+1/(2e^{2x)})	\frac{d}{dx}(\frac{4e^{2x}-2e^{x}+1}{2e^{2x}})
integral of 3x^2e^x	\int\:3x^{2}e^{x}dx
(\partial)/(\partial x)(-2ycsc^3(x))	\frac{\partial\:}{\partial\:x}(-2y\csc^{3}(x))
derivative of 2cos^2(x^2+2)	\frac{d}{dx}(2\cos^{2}(x^{2}+2))
integral of 3/2 xe^{-6x}	\int\:\frac{3}{2}xe^{-6x}dx
derivative of 6+1/5 sin(6pit)	derivative\:6+\frac{1}{5}\sin(6πt)
limit as x approaches 0 of (1+3x)^{2/x}	\lim\:_{x\to\:0}((1+3x)^{\frac{2}{x}})
integral of (x^3)/(sqrt(x^2+144))	\int\:\frac{x^{3}}{\sqrt{x^{2}+144}}dx
(\partial)/(\partial x)(ln(2x^2))	\frac{\partial\:}{\partial\:x}(\ln(2x^{2}))
derivative of ((x^3)/3)	\frac{d}{dx}(\frac{(x^{3})}{3})
integral of v/(g-kv^2)	\int\:\frac{v}{g-kv^{2}}dv
integral of 4sin^3(x)cos^7(x)	\int\:4\sin^{3}(x)\cos^{7}(x)dx
integral of (x^2-y^2)	\int\:(x^{2}-y^{2})dx
limit as x approaches 1 of ln(5x)+e^x	\lim\:_{x\to\:1}(\ln(5x)+e^{x})
integral of (1/(x^2-1))	\int\:(\frac{1}{x^{2}-1})dx
y^{''}-36y=0	y^{\prime\:\prime\:}-36y=0
d/(dt)((2t)/(1+t^2))	\frac{d}{dt}(\frac{2t}{1+t^{2}})
integral from-3 to 3 of 6/(x^2+9)	\int\:_{-3}^{3}\frac{6}{x^{2}+9}dx
integral of x^9*e^{x^{10}-9}	\int\:x^{9}\cdot\:e^{x^{10}-9}dx
normal of y= x/(1+x^2),(2, 2/5)	normal\:y=\frac{x}{1+x^{2}},(2,\frac{2}{5})
sum from n=0 to infinity of e^{-(9n)/2}	\sum\:_{n=0}^{\infty\:}e^{-\frac{9n}{2}}
integral of u^{-3}	\int\:u^{-3}du
d/(dt)(t^{3/2})	\frac{d}{dt}(t^{\frac{3}{2}})
(dy)/(dx)=(x-3)e^{-2y}	\frac{dy}{dx}=(x-3)e^{-2y}
expand (xsinh(x)+cos(x))^5	expand\:(x\sinh(x)+\cos(x))^{5}
integral of ln(t+1)	\int\:\ln(t+1)dt
integral of (-5)/(sqrt(4-2x-x^2))	\int\:\frac{-5}{\sqrt{4-2x-x^{2}}}dx
derivative of (sin(x)/(x^5))	\frac{d}{dx}(\frac{\sin(x)}{x^{5}})
derivative of x^4-2x^2+3	\frac{d}{dx}(x^{4}-2x^{2}+3)
tangent of x^3-2x+1	tangent\:x^{3}-2x+1
tangent of y=(x^3-9x)^{10},(3,0)	tangent\:y=(x^{3}-9x)^{10},(3,0)
tangent of y=3x^3-3x,(-4,0)	tangent\:y=3x^{3}-3x,(-4,0)
integral from 0 to 3 of (5-5/3 x)^2	\int\:_{0}^{3}(5-\frac{5}{3}x)^{2}dx
slope of (-10.6)(-5.8)	slope\:(-10.6)(-5.8)
derivative of sqrt(5x-x^2)	\frac{d}{dx}(\sqrt{5x-x^{2}})
limit as x approaches 3 of 7	\lim\:_{x\to\:3}(7)
limit as x approaches 1+of (x^2-1)/(x-1)	\lim\:_{x\to\:1+}(\frac{x^{2}-1}{x-1})
y^'=(2-e^x)/(3+2y)	y^{\prime\:}=\frac{2-e^{x}}{3+2y}
limit as x approaches 7 of (x-7)/(sqrt(x-4)-\sqrt{3)}	\lim\:_{x\to\:7}(\frac{x-7}{\sqrt{x-4}-\sqrt{3}})
integral of e^{(-x)/(10)}	\int\:e^{\frac{-x}{10}}dx
tangent of y=2x^3-x^2+6,(2,18)	tangent\:y=2x^{3}-x^{2}+6,(2,18)
y^'= y/x+tan(y/x)	y^{\prime\:}=\frac{y}{x}+\tan(\frac{y}{x})
4y^{''}+9y=0,y(0)=2,y^'(0)=3	4y^{\prime\:\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=3
(\partial)/(\partial x)(xe^{-ax^2})	\frac{\partial\:}{\partial\:x}(xe^{-ax^{2}})
derivative of a(2e^{-3x}x-3e^{-3x}x^2)	\frac{d}{dx}(a(2e^{-3x}x-3e^{-3x}x^{2}))
(\partial)/(\partial x)(-sin(4x))	\frac{\partial\:}{\partial\:x}(-\sin(4x))
derivative of f(x)=sqrt(x^2+2x+3)	derivative\:f(x)=\sqrt{x^{2}+2x+3}
integral of 4 x/((x+2)^{(1/4))}	\int\:4\frac{x}{(x+2)^{(\frac{1}{4})}}dx
limit as x approaches 1-of 3^{1/x}	\lim\:_{x\to\:1-}(3^{\frac{1}{x}})
(\partial)/(\partial y)(e^x+cos(y+z))	\frac{\partial\:}{\partial\:y}(e^{x}+\cos(y+z))
(x^2+4)y^'+3xy=x	(x^{2}+4)y^{\prime\:}+3xy=x
sum from n=1 to infinity of 7/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{4^{n}}
limit as x approaches 0 of (e^{ax}-1)/x	\lim\:_{x\to\:0}(\frac{e^{ax}-1}{x})
derivative of x-asqrt(x)	derivative\:x-a\sqrt{x}
derivative of sin^4(a)cos^9(a)	derivative\:\sin^{4}(a)\cos^{9}(a)
integral of 13e^{-13x}	\int\:13e^{-13x}dx
derivative of-1x	\frac{d}{dx}(-1x)
(\partial)/(\partial y)(xsec(y))	\frac{\partial\:}{\partial\:y}(x\sec(y))
limit as x approaches 8-of 4x-2	\lim\:_{x\to\:8-}(4x-2)
integral of (7/(x^3))	\int\:(\frac{7}{x^{3}})dx
(\partial)/(\partial x)(x^3e^{sqrt(5xy)})	\frac{\partial\:}{\partial\:x}(x^{3}e^{\sqrt{5xy}})
(\partial)/(\partial x)(((7x+4))/(4y+1))	\frac{\partial\:}{\partial\:x}(\frac{(7x+4)}{4y+1})
derivative of (e^{4x})^2	derivative\:(e^{4x})^{2}
y^'+2y=50e^{-10t}	y^{\prime\:}+2y=50e^{-10t}
derivative of (-x/(x^2+1))	\frac{d}{dx}(\frac{-x}{x^{2}+1})
inverse oflaplace 4/(s^2(s+1))	inverselaplace\:\frac{4}{s^{2}(s+1)}
y^{''}+7y^'+10y=13te^{5t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=13te^{5t}
integral of x^3(1-x)	\int\:x^{3}(1-x)dx
integral of cos(x/4)	\int\:\cos(\frac{x}{4})dx
integral of-x^2-4	\int\:-x^{2}-4dx
(\partial)/(\partial x)(sin^3(x))	\frac{\partial\:}{\partial\:x}(\sin^{3}(x))
(x^7)^'	(x^{7})^{\prime\:}
integral of 1/(x*ln(2x))	\int\:\frac{1}{x\cdot\:\ln(2x)}dx
integral of xsqrt(3x+2)	\int\:x\sqrt{3x+2}dx
(dy)/(dx)=(2x+xy^2)/(4y+yx^2)	\frac{dy}{dx}=\frac{2x+xy^{2}}{4y+yx^{2}}
integral from 0 to 1/2 of 6arccos(x)	\int\:_{0}^{\frac{1}{2}}6\arccos(x)dx
limit as x approaches infinity of 55^x	\lim\:_{x\to\:\infty\:}(55^{x})
integral of (2z+1)^3	\int\:(2z+1)^{3}dz
tangent of y=(1+3x)^{10},(0,1)	tangent\:y=(1+3x)^{10},(0,1)
limit as x approaches 0 of 2e^{5x}	\lim\:_{x\to\:0}(2e^{5x})
integral from 0 to 7 of-30x^2+340x	\int\:_{0}^{7}-30x^{2}+340xdx
limit as x approaches+0 of 1/(sqrt(x-1))	\lim\:_{x\to\:+0}(\frac{1}{\sqrt{x-1}})
(x^2-y^2)dx+3xydy=0	(x^{2}-y^{2})dx+3xydy=0

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