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Popular Calculus Problems

derivative of (x^2+y^2^{2/3})	\frac{d}{dx}((x^{2}+y^{2})^{\frac{2}{3}})
derivative of f(x)=ln(x^3+5x+3)	derivative\:f(x)=\ln(x^{3}+5x+3)
(2x+3)(dy)/(dx)=y+(2x+3)^{1/2}	(2x+3)\frac{dy}{dx}=y+(2x+3)^{\frac{1}{2}}
derivative of y=-4/(5x^5)+(15)/(4x^4)	derivative\:y=-\frac{4}{5x^{5}}+\frac{15}{4x^{4}}
derivative of f(x)=sqrt(x^2+21)	derivative\:f(x)=\sqrt{x^{2}+21}
integral of 1/((x+3)^2(x-2))	\int\:\frac{1}{(x+3)^{2}(x-2)}dx
derivative of x^22^x	\frac{d}{dx}(x^{2}2^{x})
(d^3)/(dx^3)((1-3x)/(1+3x))	\frac{d^{3}}{dx^{3}}(\frac{1-3x}{1+3x})
limit as x approaches 0 of (sin(4x))/((2x))	\lim\:_{x\to\:0}(\frac{\sin(4x)}{(2x)})
integral from 2 to infinity of ye^{-5y}	\int\:_{2}^{\infty\:}ye^{-5y}dy
area (1/(14x^2)),x,(x/4)	area\:(\frac{1}{14x^{2}}),x,(\frac{x}{4})
derivative of 90x	derivative\:90x
(\partial)/(\partial y)(-ysin(x))	\frac{\partial\:}{\partial\:y}(-y\sin(x))
integral from-2 to 2 of 3/2 x^2	\int\:_{-2}^{2}\frac{3}{2}x^{2}dx
limit as x approaches 1 of-x^2+4x	\lim\:_{x\to\:1}(-x^{2}+4x)
limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6)	\lim\:_{x\to\:2+}(\frac{x^{2}-2x-8}{x^{2}-5x+6})
integral of (x+4)/(x^2+8x+17)	\int\:\frac{x+4}{x^{2}+8x+17}dx
derivative of 2+1/x	\frac{d}{dx}(2+\frac{1}{x})
derivative of f(x)=x(x+1)^2	derivative\:f(x)=x(x+1)^{2}
(\partial)/(\partial x)(2x^2+3y^2-z^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}-z^{2})
tangent of y=4+xsqrt(x),(1,5)	tangent\:y=4+x\sqrt{x},(1,5)
limit as x approaches 2 of sqrt(x^4)-8	\lim\:_{x\to\:2}(\sqrt{x^{4}}-8)
y^{''}+y^'-6y=12x-50sin(x)	y^{\prime\:\prime\:}+y^{\prime\:}-6y=12x-50\sin(x)
(d^2)/(dx^2)(cos(7x))	\frac{d^{2}}{dx^{2}}(\cos(7x))
y^'=3x(y+4)^2	y^{\prime\:}=3x(y+4)^{2}
f(t)=t-4	f(t)=t-4
integral of (6x^2-5x+8)/(x^3+4x)	\int\:\frac{6x^{2}-5x+8}{x^{3}+4x}dx
integral from 0 to 4 of 16x^2-x^4	\int\:_{0}^{4}16x^{2}-x^{4}dx
(\partial)/(\partial x)(x^2sin(6t))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(6t))
derivative of-(e^{-x}(x^3+3(x^2+2x+2))/(x^4))	\frac{d}{dx}(-\frac{e^{-x}(x^{3}+3(x^{2}+2x+2))}{x^{4}})
tangent of f(x)=(x^2+8)/(x+28),(5,1)	tangent\:f(x)=\frac{x^{2}+8}{x+28},(5,1)
slope ofintercept (4,-9),(2,-2)	slopeintercept\:(4,-9),(2,-2)
integral of x^{m-1}	\int\:x^{m-1}dx
y^'= 1/(sqrt(1-x^2))	y^{\prime\:}=\frac{1}{\sqrt{1-x^{2}}}
integral of ye^{3y^2}	\int\:ye^{3y^{2}}dy
derivative of Inx^2	\frac{d}{dx}(Inx^{2})
derivative of ln(x^2-3x+2)	\frac{d}{dx}(\ln(x^{2}-3x+2))
derivative of x/(4+x)	\frac{d}{dx}(\frac{x}{4+x})
3y^{''}+8y^'-16y=0	3y^{\prime\:\prime\:}+8y^{\prime\:}-16y=0
y^{''}+4y=e^{-x}	y^{\prime\:\prime\:}+4y=e^{-x}
(\partial)/(\partial x)(t^2e^{-x})	\frac{\partial\:}{\partial\:x}(t^{2}e^{-x})
integral of 2x(x^2+1)^5	\int\:2x(x^{2}+1)^{5}dx
(\partial)/(\partial x)(ln(5x))	\frac{\partial\:}{\partial\:x}(\ln(5x))
derivative of (x^3-4arcsin(x))	\frac{d}{dx}((x^{3}-4)\arcsin(x))
(dy)/(dx)+xe^{x+y}=0	\frac{dy}{dx}+xe^{x+y}=0
integral of (22)/(xln(7x))	\int\:\frac{22}{x\ln(7x)}dx
derivative of x-2y	\frac{d}{dx}(x-2y)
integral of xsin^3(x^2)cos^2(x^2)	\int\:x\sin^{3}(x^{2})\cos^{2}(x^{2})dx
ty^'+2y=sin(t),y(pi/2)=9	ty^{\prime\:}+2y=\sin(t),y(\frac{π}{2})=9
integral of x^2ln(x)	\int\:x^{2}\ln(x)dx
integral from 2 to 7 of t^4ln(3t)	\int\:_{2}^{7}t^{4}\ln(3t)dt
derivative of x^{-9}	derivative\:x^{-9}
integral of e^{r^2}r	\int\:e^{r^{2}}rdr
derivative of ln(2x^2+y^2)	\frac{d}{dx}(\ln(2x^{2}+y^{2}))
25yy^'-4x=0	25yy^{\prime\:}-4x=0
derivative of ln(-1)	\frac{d}{dx}(\ln(-1))
integral of (x^2-4)^32x	\int\:(x^{2}-4)^{3}2xdx
derivative of (-12)/((1-x)^4)	derivative\:\frac{-12}{(1-x)^{4}}
integral of sinh(8x)	\int\:\sinh(8x)dx
derivative of xsqrt(x^2+36)	\frac{d}{dx}(x\sqrt{x^{2}+36})
derivative of ((x-sqrt(x))/(x^{1/5)})	\frac{d}{dx}(\frac{(x-\sqrt{x})}{x^{\frac{1}{5}}})
derivative of 100-(200)/(sqrt(t^2+4))	derivative\:100-\frac{200}{\sqrt{t^{2}+4}}
derivative of-5/(x^5)	derivative\:-\frac{5}{x^{5}}
y^{''}+25y=cos(4t)	y^{\prime\:\prime\:}+25y=\cos(4t)
limit as x approaches 0 of 2xcot(3x)	\lim\:_{x\to\:0}(2x\cot(3x))
sum from n=1 to infinity of ((n))/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{(n)}{2^{n}}
tangent of (x+2)^2+(y-3)^2=37,(-1,-3)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-1,-3)
derivative of (x^2-2/(x^3+3x^2))	\frac{d}{dx}(\frac{x^{2}-2}{x^{3}+3x^{2}})
derivative of y=(sqrt(x)+x^3)/(x^2)	derivative\:y=\frac{\sqrt{x}+x^{3}}{x^{2}}
derivative of f(x)=7-2x	derivative\:f(x)=7-2x
(\partial)/(\partial x)(2x^3+4y-2z^2)	\frac{\partial\:}{\partial\:x}(2x^{3}+4y-2z^{2})
integral of sqrt(2)xln(4x)	\int\:\sqrt{2}\cdot\:x\cdot\:\ln(4x)dx
integral of yx	\int\:yxdx
integral from 0 to pi of sin^2(tco)s^4t	\int\:_{0}^{π}\sin^{2}(tco)s^{4}tdt
(dy)/(dt)=0.225-y/(200),y(0)=90	\frac{dy}{dt}=0.225-\frac{y}{200},y(0)=90
taylor (x^2+1)*e^{x-1}	taylor\:(x^{2}+1)\cdot\:e^{x-1}
derivative of sqrt(t+2)	derivative\:\sqrt{t+2}
implicit (dy)/(dx),y=x^{15/16}	implicit\:\frac{dy}{dx},y=x^{\frac{15}{16}}
integral of 0.5e^x	\int\:0.5e^{x}dx
integral of e^{-ax}cos(bx)	\int\:e^{-ax}\cos(bx)dx
(\partial)/(\partial y)(x/(sqrt(y+z)))	\frac{\partial\:}{\partial\:y}(\frac{x}{\sqrt{y+z}})
integral from 0 to 1 of 3/(2x-5)	\int\:_{0}^{1}\frac{3}{2x-5}dx
integral from 0 to 1 of 19 1/(x^p)	\int\:_{0}^{1}19\frac{1}{x^{p}}dx
derivative of f(x)=7x^6e^x+e^xx^7	derivative\:f(x)=7x^{6}e^{x}+e^{x}x^{7}
inverse oflaplace 3/(s(6s^2+5s+1))	inverselaplace\:\frac{3}{s(6s^{2}+5s+1)}
(\partial)/(\partial y)(cos(xyz))	\frac{\partial\:}{\partial\:y}(\cos(xyz))
y^{''}+4sqrt(5)y^'+20y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4\sqrt{5}y^{\prime\:}+20y=0,y(0)=1,y^{\prime\:}(0)=0
sum from n=1 to infinity of ne^{3n}	\sum\:_{n=1}^{\infty\:}ne^{3n}
limit as x approaches 0+of 6/(x^2)	\lim\:_{x\to\:0+}(\frac{6}{x^{2}})
integral of x/(sqrt(x^2+2))	\int\:\frac{x}{\sqrt{x^{2}+2}}dx
area 4x,sqrt(64-x^2),[-6.928,0]	area\:4x,\sqrt{64-x^{2}},[-6.928,0]
integral of 2xsin^4(x^2-1)	\int\:2x\sin^{4}(x^{2}-1)dx
limit as x approaches 0 of 2x^2+5	\lim\:_{x\to\:0}(2x^{2}+5)
integral of (x^{1.3}+11x^{4.5})	\int\:(x^{1.3}+11x^{4.5})dx
laplacetransform 1+2t	laplacetransform\:1+2t
integral of u/(u^2+1)	\int\:\frac{u}{u^{2}+1}du
integral of (ln(x)+1)/x	\int\:\frac{\ln(x)+1}{x}dx
integral of ln(x^2)	\int\:\ln(x^{2})dx
integral of 2x(x^2+2)^{-3}	\int\:2x(x^{2}+2)^{-3}dx
sum from i=1 to infinity of 8(5/6)^{i-1}	\sum\:_{i=1}^{\infty\:}8(\frac{5}{6})^{i-1}

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