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Popular Calculus Problems

derivative of (9-x)^{1/2}	derivative\:(9-x)^{\frac{1}{2}}
derivative of y= 1/(3x^2)-5/(2x)	derivative\:y=\frac{1}{3x^{2}}-\frac{5}{2x}
derivative of f(x)=(2-ln(x))/(2xsqrt(x))	derivative\:f(x)=\frac{2-\ln(x)}{2x\sqrt{x}}
y^{'''}-2y^{''}-4y^'+8y=0	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:\prime\:}-4y^{\prime\:}+8y=0
(\partial)/(\partial y)(-4x^3+4x)	\frac{\partial\:}{\partial\:y}(-4x^{3}+4x)
integral from 0 to pi/(28) of tan(14x)	\int\:_{0}^{\frac{π}{28}}\tan(14x)dx
derivative of (3x/(5y))	\frac{d}{dx}(\frac{3x}{5y})
derivative of (mx)/(bx+c)	derivative\:\frac{mx}{bx+c}
integral of (x+5)sqrt(8-x)	\int\:(x+5)\sqrt{8-x}dx
(\partial)/(\partial x)(2+3xsqrt(y))	\frac{\partial\:}{\partial\:x}(2+3x\sqrt{y})
sum from n=0 to infinity of (4x^2)^n	\sum\:_{n=0}^{\infty\:}(4x^{2})^{n}
limit as x approaches pi of 9sin(sin(x))	\lim\:_{x\to\:π}(9\sin(\sin(x)))
integral of 4/(x+2)	\int\:\frac{4}{x+2}dx
y^{''}-4y^'-5y=0,y(0)=3,y^'(0)=9	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(0)=3,y^{\prime\:}(0)=9
integral of s/((s^2+16)^2)	\int\:\frac{s}{(s^{2}+16)^{2}}ds
derivative of 100(y-x^2^2+(1-x)^2)	\frac{d}{dx}(100(y-x^{2})^{2}+(1-x)^{2})
derivative of (24x/(2x+3))	\frac{d}{dx}(\frac{24x}{2x+3})
limit as x approaches 0 of x/(-x)	\lim\:_{x\to\:0}(\frac{x}{-x})
derivative of t^{3/2}	derivative\:t^{\frac{3}{2}}
integral of (x^2+1/4 y^2+3)	\int\:(x^{2}+\frac{1}{4}y^{2}+3)dx
(dy)/(dt)=0.03y+3600	\frac{dy}{dt}=0.03y+3600
(\partial)/(\partial x)(x^{3/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{3}{2}})
integral of e^{bx}	\int\:e^{bx}dx
laplacetransform 3cos(t)	laplacetransform\:3\cos(t)
y^{''}-2y^'+y=0,y(0)=-1,y^'(0)=-2	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0,y(0)=-1,y^{\prime\:}(0)=-2
derivative of cy^{-3}	derivative\:cy^{-3}
derivative of f(x)=ln(x+5)	derivative\:f(x)=\ln(x+5)
tangent of (70)/x	tangent\:\frac{70}{x}
integral of sin(30x)	\int\:\sin(30x)dx
sum from n=1 to infinity of 1/(n+3)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+3}
integral from 0 to 5 of ln(x)	\int\:_{0}^{5}\ln(x)dx
tangent of f(x)=x^2-6,\at x=-5	tangent\:f(x)=x^{2}-6,\at\:x=-5
limit as x approaches 0 of (3^x-1)/(x^2)	\lim\:_{x\to\:0}(\frac{3^{x}-1}{x^{2}})
d/(dt)(9t)	\frac{d}{dt}(9t)
(\partial)/(\partial x)(9xe^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(9xe^{\sqrt{xy}})
derivative of arctan((3x/2))	\frac{d}{dx}(\arctan(\frac{3x}{2}))
integral of (tan(x))^{-1}	\int\:(\tan(x))^{-1}dx
(\partial)/(\partial x)(log_{10}(x))	\frac{\partial\:}{\partial\:x}(\log_{10}(x))
x^'=x-4	x^{\prime\:}=x-4
limit as x approaches infinity of-cos(x)	\lim\:_{x\to\:\infty\:}(-\cos(x))
derivative of cos(x+1/(sqrt(x)))	\frac{d}{dx}(\cos(x)+\frac{1}{\sqrt{x}})
(\partial)/(\partial x)(2cos(pix))	\frac{\partial\:}{\partial\:x}(2\cos(πx))
integral of (x^2-3x+7)/(x+5)	\int\:\frac{x^{2}-3x+7}{x+5}dx
derivative of log_{2}(x^2+1)	derivative\:\log_{2}(x^{2}+1)
derivative of f(x)=sqrt(x/(x+5))	derivative\:f(x)=\sqrt{\frac{x}{x+5}}
tangent of y=sqrt(9-4x),\at x=-1	tangent\:y=\sqrt{9-4x},\at\:x=-1
integral from 0 to pi/4 of 9tan^3(x)	\int\:_{0}^{\frac{π}{4}}9\tan^{3}(x)dx
derivative of (5x^4+3x^3/(4x-9))	\frac{d}{dx}(\frac{5x^{4}+3x^{3}}{4x-9})
maclaurin e^xsin(x)	maclaurin\:e^{x}\sin(x)
integral of (5-e^x)/(e^{2x)}	\int\:\frac{5-e^{x}}{e^{2x}}dx
integral of 1/((64-x^2)^{3/2)}	\int\:\frac{1}{(64-x^{2})^{\frac{3}{2}}}dx
derivative of (220x)/((x+2)^2)	derivative\:\frac{220x}{(x+2)^{2}}
integral of (1-3/y+x)	\int\:(1-\frac{3}{y}+x)dy
integral from 1 to 4 of (x^3+1/(4x^3))	\int\:_{1}^{4}(x^{3}+\frac{1}{4x^{3}})dx
sum from n=0 to infinity of (n^6)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{6}}{2^{n}}
sum from n=1 to infinity of-1^n	\sum\:_{n=1}^{\infty\:}-1^{n}
derivative of (2x^3-7/(x^2))	\frac{d}{dx}(\frac{2x^{3}-7}{x^{2}})
tangent of y=3x^2-x^3,(1,2)	tangent\:y=3x^{2}-x^{3},(1,2)
integral of (8cos(x)+9sin(x))	\int\:(8\cos(x)+9\sin(x))dx
integral of-1/4 csc(8t)	\int\:-\frac{1}{4}\csc(8t)dt
(\partial)/(\partial x)(x^2+ye^x)	\frac{\partial\:}{\partial\:x}(x^{2}+ye^{x})
integral of (11-2x)/(x^2+9x+14)	\int\:\frac{11-2x}{x^{2}+9x+14}dx
derivative of (2x)/(3-cot(x))	derivative\:\frac{2x}{3-\cot(x)}
limit as x approaches 3 of (x^2-9)^{x-3}	\lim\:_{x\to\:3}((x^{2}-9)^{x-3})
limit as x approaches infinity of x/9	\lim\:_{x\to\:\infty\:}(\frac{x}{9})
(dy)/(dx)= 1/(2y+1)	\frac{dy}{dx}=\frac{1}{2y+1}
integral of 1/136 x^3	\int\:\frac{1}{136}x^{3}dx
derivative of y=(-9e^{4x})/(8x+3)	derivative\:y=\frac{-9e^{4x}}{8x+3}
integral of ((x-2))/(x-1)	\int\:\frac{(x-2)}{x-1}dx
sum from n=0 to infinity of 1/(n^2+n)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+n}
integral of x/(sqrt(x^2-6x))	\int\:\frac{x}{\sqrt{x^{2}-6x}}dx
y^'+y= 1/(1+e^t)	y^{\prime\:}+y=\frac{1}{1+e^{t}}
y^'+7x^6y=x^6	y^{\prime\:}+7x^{6}y=x^{6}
limit as x approaches 0 of x^2	\lim\:_{x\to\:0}(x^{2})
limit as x approaches 1 of 6x	\lim\:_{x\to\:1}(6x)
tangent of y=-4-7x^2,(-4,-16)	tangent\:y=-4-7x^{2},(-4,-16)
derivative of 2x^5ln(x)	derivative\:2x^{5}\ln(x)
derivative of f(x)=(3x+1)/(5+x)	derivative\:f(x)=\frac{3x+1}{5+x}
integral of 7/(x(x^2+4)^2)	\int\:\frac{7}{x(x^{2}+4)^{2}}dx
derivative of e^{x^2-4}	\frac{d}{dx}(e^{x^{2}-4})
derivative of 14(2x+5^6)	\frac{d}{dx}(14(2x+5)^{6})
limit as x approaches 2-of (4x)/(x-2)	\lim\:_{x\to\:2-}(\frac{4x}{x-2})
integral of (x^2sin(x))	\int\:(x^{2}\sin(x))dx
limit as x approaches-8+of (\|x+8\|)/(x+8)	\lim\:_{x\to\:-8+}(\frac{\left\|x+8\right\|}{x+8})
derivative of tan(e^x)	derivative\:\tan(e^{x})
derivative of f(x)=3x^2-3	derivative\:f(x)=3x^{2}-3
xy^'=e^y	xy^{\prime\:}=e^{y}
integral from 0 to 1 of (sqrt(x)-x)	\int\:_{0}^{1}(\sqrt{x}-x)dx
sum from n=1 to infinity of (-1^n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{-1^{n}}{n!}
derivative of x^{8cos(x)}	derivative\:x^{8\cos(x)}
limit as x approaches 1-of 1-x^3	\lim\:_{x\to\:1-}(1-x^{3})
integral of 2/(sqrt(16-25x^2))	\int\:\frac{2}{\sqrt{16-25x^{2}}}dx
derivative of 1/(sqrt(x^2-2))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}-2}})
derivative of f(x)=(x^3)/(x^2-1)	derivative\:f(x)=\frac{x^{3}}{x^{2}-1}
integral of x/(sqrt(x^2-9))	\int\:\frac{x}{\sqrt{x^{2}-9}}dx
derivative of 3^{x^5+2}	\frac{d}{dx}(3^{x^{5}+2})
(\partial)/(\partial x)(2xsin(xy))	\frac{\partial\:}{\partial\:x}(2x\sin(xy))
xv'+2v=0	xv\prime\:+2v=0
xy^'=2y+x^3cos(x)	xy^{\prime\:}=2y+x^{3}\cos(x)
integral of cos^5(x)sin^4(x)	\int\:\cos^{5}(x)\sin^{4}(x)dx

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