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Popular Calculus Problems

tangent of f(x)=sqrt(1-6x),\at x=-1	tangent\:f(x)=\sqrt{1-6x},\at\:x=-1
derivative of (9x)/(sqrt(x))	derivative\:\frac{9x}{\sqrt{x}}
integral of (x^2-2x-5)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-2x-5}{(x-1)^{2}(x^{2}+1)}dx
limit as x approaches 1 of (3x-2)/(2x-1)	\lim\:_{x\to\:1}(\frac{3x-2}{2x-1})
derivative of arctanh(3x)	\frac{d}{dx}(\arctanh(3x))
limit as x approaches 1-of 8/(x^3-1)	\lim\:_{x\to\:1-}(\frac{8}{x^{3}-1})
integral of e^{1.2t}	\int\:e^{1.2t}dt
derivative of x^2sin^2(x)	\frac{d}{dx}(x^{2}\sin^{2}(x))
integral of+x^3sin(2x)	\int\:+x^{3}\sin(2x)dx
(dy)/(dt)=ty^2+2y^2	\frac{dy}{dt}=ty^{2}+2y^{2}
y^'-3y=2sin(3x)-cos(3x)	y^{\prime\:}-3y=2\sin(3x)-\cos(3x)
integral of (6x+7)/(x^2+4x+29)	\int\:\frac{6x+7}{x^{2}+4x+29}dx
derivative of (sin^2(x)/(cos(x)))	\frac{d}{dx}(\frac{\sin^{2}(x)}{\cos(x)})
area (-x+2),(-x^2-2x),-2,-1	area\:(-x+2),(-x^{2}-2x),-2,-1
maclaurin (1+x)^{-2/3}	maclaurin\:(1+x)^{-\frac{2}{3}}
tangent of y=(1+2x)^{10},(0,1)	tangent\:y=(1+2x)^{10},(0,1)
derivative of 5xarcsin(x)	derivative\:5x\arcsin(x)
integral of (1-2y)/(y^2)	\int\:\frac{1-2y}{y^{2}}dy
derivative of e^{x+y}-x	\frac{d}{dx}(e^{x+y}-x)
derivative of cos(sin(6x))	\frac{d}{dx}(\cos(\sin(6x)))
(\partial)/(\partial y)((1+t^2)/(3y-y^2))	\frac{\partial\:}{\partial\:y}(\frac{1+t^{2}}{3y-y^{2}})
derivative of (4x^2+6x+6)/(sqrt(x))	derivative\:\frac{4x^{2}+6x+6}{\sqrt{x}}
limit as x approaches pi/2 of 1/(cos(x))	\lim\:_{x\to\:\frac{π}{2}}(\frac{1}{\cos(x)})
derivative of (cos(3x^6)/(2x))	\frac{d}{dx}(\frac{\cos(3)x^{6}}{2x})
limit as x approaches infinity+of 2+1/x	\lim\:_{x\to\:\infty\:+}(2+\frac{1}{x})
integral of (2x^3-x)/(x^4-x^2-25)	\int\:\frac{2x^{3}-x}{x^{4}-x^{2}-25}dx
derivative of 5/(x^3+1/(e^{2x)})	\frac{d}{dx}(\frac{5}{x^{3}}+\frac{1}{e^{2x}})
maclaurin e^{3x}cos(2x)	maclaurin\:e^{3x}\cos(2x)
derivative of (5x^2-7xe^x)	\frac{d}{dx}((5x^{2}-7x)e^{x})
inverse oflaplace (0.5)/(s^2)	inverselaplace\:\frac{0.5}{s^{2}}
integral of (tan^3(9/z))/(z^2)	\int\:\frac{\tan^{3}(\frac{9}{z})}{z^{2}}
derivative of (log_{2}(x)^2)	\frac{d}{dx}((\log_{2}(x))^{2})
limit as x approaches 1-of (-3x-1)/(x-1)	\lim\:_{x\to\:1-}(\frac{-3x-1}{x-1})
limit as x approaches pi/2 of x-pi/2	\lim\:_{x\to\:\frac{π}{2}}(x-\frac{π}{2})
(\partial)/(\partial z)(x^2+yz)	\frac{\partial\:}{\partial\:z}(x^{2}+yz)
tangent of f(x)=x^2+2x,\at x=1	tangent\:f(x)=x^{2}+2x,\at\:x=1
integral of 1/(by^2+b^3)	\int\:\frac{1}{by^{2}+b^{3}}dy
integral of 1/(xsqrt(9x^2+64))	\int\:\frac{1}{x\sqrt{9x^{2}+64}}dx
integral of sqrt(x)(3+10x)	\int\:\sqrt{x}(3+10x)dx
(d^2y)/(dx^2)=4y	\frac{d^{2}y}{dx^{2}}=4y
(dv)/(dt)=v^2+5v+1	\frac{dv}{dt}=v^{2}+5v+1
integral of sqrt(tan(x))sec^2(x)	\int\:\sqrt{\tan(x)}\sec^{2}(x)dx
derivative of (2x+3)(3x-4)	derivative\:(2x+3)(3x-4)
derivative of 5/(x^3)	derivative\:\frac{5}{x^{3}}
integral from pi/9 to infinity of 5/x	\int\:_{\frac{π}{9}}^{\infty\:}\frac{5}{x}dx
derivative of x^2-10x	\frac{d}{dx}(x^{2}-10x)
area y=2x^2,y=2x+6,x=-2	area\:y=2x^{2},y=2x+6,x=-2
derivative of f(x)=(3x-2)^2(x^5-x^2)^3	derivative\:f(x)=(3x-2)^{2}(x^{5}-x^{2})^{3}
area x^2-3x,3x+7	area\:x^{2}-3x,3x+7
limit as x approaches-4 of (x-4)^2+2	\lim\:_{x\to\:-4}((x-4)^{2}+2)
derivative of 9x^3+7^x+20	derivative\:9x^{3}+7^{x}+20
integral of u/((u-1)^2)	\int\:\frac{u}{(u-1)^{2}}du
integral of (x^4)/(x^5-1)	\int\:\frac{x^{4}}{x^{5}-1}dx
limit as x approaches (pi/2)+of 9e^{tan(x)}	\lim\:_{x\to\:(\frac{π}{2})+}(9e^{\tan(x)})
derivative of sqrt(5x^4+x^2)	\frac{d}{dx}(\sqrt{5x^{4}+x^{2}})
integral of (y^2)/((49-y^2)^{3/2)}	\int\:\frac{y^{2}}{(49-y^{2})^{\frac{3}{2}}}dy
integral of (3x-6)e^{x^2-4x}	\int\:(3x-6)e^{x^{2}-4x}dx
derivative of cos^2(x)sin^2(x)	derivative\:\cos^{2}(x)\sin^{2}(x)
sum from n=1 to infinity of (n!)/(105^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{105^{n}}
(\partial)/(\partial x)(x^2-3xy)	\frac{\partial\:}{\partial\:x}(x^{2}-3xy)
xsqrt(1-y^2)dx=dy	x\sqrt{1-y^{2}}dx=dy
limit as x approaches 0+of ln(-x)	\lim\:_{x\to\:0+}(\ln(-x))
sum from n=0 to infinity of n/(n^2+1)x^n	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{2}+1}x^{n}
integral from-2 to 3 of (23)/(x^4)	\int\:_{-2}^{3}\frac{23}{x^{4}}dx
integral of (3x^2+2x-1)/(4e^{3x)}	\int\:\frac{3x^{2}+2x-1}{4e^{3x}}dx
derivative of (1-x^2/5)	\frac{d}{dx}(\frac{1-x^{2}}{5})
derivative of x^2-2x+2	derivative\:x^{2}-2x+2
integral of-x/(x^2+9)	\int\:-\frac{x}{x^{2}+9}dx
derivative of arccos(4x)	derivative\:\arccos(4x)
integral of (x^3)/(x^4+7)	\int\:\frac{x^{3}}{x^{4}+7}dx
limit as x approaches 1 of arctan^2(x)	\lim\:_{x\to\:1}(\arctan^{2}(x))
(\partial)/(\partial x)((sin^2(x))+y)	\frac{\partial\:}{\partial\:x}((\sin^{2}(x))+y)
slope of 3t-t^2	slope\:3t-t^{2}
derivative of cos(ln(sec(e^{-2x})))	\frac{d}{dx}(\cos(\ln(\sec(e^{-2x}))))
derivative of f(x)=(5x-5)(sqrt(x)+3)	derivative\:f(x)=(5x-5)(\sqrt{x}+3)
derivative of x/(1+x^3)	\frac{d}{dx}(\frac{x}{1+x^{3}})
limit as x approaches 0 of (1-4x)^{8/x}	\lim\:_{x\to\:0}((1-4x)^{\frac{8}{x}})
limit as x approaches 4 of 1/(2+sqrt(x))	\lim\:_{x\to\:4}(\frac{1}{2+\sqrt{x}})
derivative of y=sin^2(e^{sin^2(t)})	derivative\:y=\sin^{2}(e^{\sin^{2}(t)})
integral of cos(2x)e^{-x}	\int\:\cos(2x)e^{-x}dx
integral of (3x)/(sqrt(x+4))	\int\:\frac{3x}{\sqrt{x+4}}dx
integral from 0 to t of-5e^ssin(t-s)	\int\:_{0}^{t}-5e^{s}\sin(t-s)ds
integral of (x+2)(x-7)	\int\:(x+2)(x-7)dx
f(x)=e^{x^2-4}+3x+5	f(x)=e^{x^{2}-4}+3x+5
derivative of ae^{4x}	\frac{d}{dx}(ae^{4x})
integral of (2x^2-6)/(x^3+x)	\int\:\frac{2x^{2}-6}{x^{3}+x}dx
integral of (x^2sqrt(x^3+5))	\int\:(x^{2}\sqrt{x^{3}+5})dx
slope of (3,4),(8,-3)	slope\:(3,4),(8,-3)
limit as x approaches 3 of 2x^2+x-7	\lim\:_{x\to\:3}(2x^{2}+x-7)
integral of sqrt(x^2-36)	\int\:\sqrt{x^{2}-36}dx
parity ln(sqrt((1-sin(x))/(1+sin(x))))	parity\:\ln(\sqrt{\frac{1-\sin(x)}{1+\sin(x)}})
derivative of 5^2	\frac{d}{dx}(5^{2})
(\partial)/(\partial x)(rcos(θ))	\frac{\partial\:}{\partial\:x}(r\cos(θ))
integral from 1 to 6 of (5^{ln(x)})/x	\int\:_{1}^{6}\frac{5^{\ln(x)}}{x}dx
sum from n=0 to infinity of 3(3/2)^n	\sum\:_{n=0}^{\infty\:}3(\frac{3}{2})^{n}
integral of (1/x-6/(x^2+1))	\int\:(\frac{1}{x}-\frac{6}{x^{2}+1})dx
integral from 0 to 16 of sqrt(x)-1/4 x	\int\:_{0}^{16}\sqrt{x}-\frac{1}{4}xdx
derivative of (4x+5/8)	\frac{d}{dx}(\frac{4x+5}{8})
slope of y= 3/x ,(5, 3/5)	slope\:y=\frac{3}{x},(5,\frac{3}{5})
inverse oflaplace (s-1)/(s(s+1)(s+2))	inverselaplace\:\frac{s-1}{s(s+1)(s+2)}

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