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Popular Calculus Problems

derivative of (xcos(x+pi)/(x-pi))	\frac{d}{dx}(\frac{x\cos(x)+π}{x-π})
limit as x approaches 4 of 7x+12x	\lim\:_{x\to\:4}(7x+12x)
limit as x approaches 0 of (1-e^{4x})^x	\lim\:_{x\to\:0}((1-e^{4x})^{x})
sum from n=1 to infinity of n^{-1/6}	\sum\:_{n=1}^{\infty\:}n^{-\frac{1}{6}}
derivative of sin^3(cos(2x))	\frac{d}{dx}(\sin^{3}(\cos(2x)))
integral of 1/(25+x^2)	\int\:\frac{1}{25+x^{2}}dx
derivative of (x^2y^2/2-2xy-y^2)	\frac{d}{dx}(\frac{x^{2}y^{2}}{2}-2xy-y^{2})
(1+y)dy=2tdt	(1+y)dy=2tdt
integral of (x^2)/(sqrt(16-x^2))	\int\:\frac{x^{2}}{\sqrt{16-x^{2}}}dx
derivative of \sqrt[3]{1+x}	derivative\:\sqrt[3]{1+x}
derivative of (x-1)^{1/2}	derivative\:(x-1)^{\frac{1}{2}}
derivative of sqrt(x)+sqrt(y)	derivative\:\sqrt{x}+\sqrt{y}
integral of x/(\sqrt[3]{x-2)}	\int\:\frac{x}{\sqrt[3]{x-2}}dx
limit as x approaches (3pi)/2 of cos(x)	\lim\:_{x\to\:\frac{3π}{2}}(\cos(x))
integral of 1/(9-(3x+5)^2)	\int\:\frac{1}{9-(3x+5)^{2}}dx
y^{'''}-4y^{''}+y^'+6y=36	y^{\prime\:\prime\:\prime\:}-4y^{\prime\:\prime\:}+y^{\prime\:}+6y=36
limit as x approaches-1 of x^2+x	\lim\:_{x\to\:-1}(x^{2}+x)
integral from 2 to 5 of 1/(x-2)	\int\:_{2}^{5}\frac{1}{x-2}dx
integral of e^{4x}cos(x)	\int\:e^{4x}\cos(x)dx
tangent of f(x)=-2x^2-1,\at x=1	tangent\:f(x)=-2x^{2}-1,\at\:x=1
(dx}{dy}=\frac{x+y)/y	\frac{dx}{dy}=\frac{x+y}{y}
integral of-3x^4+x^3+5-5e^x	\int\:-3x^{4}+x^{3}+5-5e^{x}dx
limit as x approaches (9pi)/2-of tan(x)	\lim\:_{x\to\:\frac{9π}{2}-}(\tan(x))
integral of sin^3(a)x	\int\:\sin^{3}(a)xdx
integral of (1/(2x+1))	\int\:(\frac{1}{2x+1})dx
tangent of f(x)=3x^2-1,\at x=-2	tangent\:f(x)=3x^{2}-1,\at\:x=-2
integral of 5cos(5x)-4	\int\:5\cos(5x)-4dx
7y^{''}+30y=0	7y^{\prime\:\prime\:}+30y=0
(d^2)/(dx^2)(sqrt(x)+\sqrt[9]{x})	\frac{d^{2}}{dx^{2}}(\sqrt{x}+\sqrt[9]{x})
derivative of ycos(x-y)	\frac{d}{dx}(y\cos(x-y))
derivative of f(x)=2x^2-x-3	derivative\:f(x)=2x^{2}-x-3
integral of 3t^{-1}	\int\:3t^{-1}dt
derivative of arccos(x/5)	\frac{d}{dx}(\arccos(\frac{x}{5}))
derivative of x/(x^2+13x+40)	derivative\:\frac{x}{x^{2}+13x+40}
integral of (sec^2(1/(x^7)))/(x^8)	\int\:\frac{\sec^{2}(\frac{1}{x^{7}})}{x^{8}}dx
integral of (2x^2-x+3)/(x(x^2+1))	\int\:\frac{2x^{2}-x+3}{x(x^{2}+1)}dx
integral of sqrt(16+x^2)	\int\:\sqrt{16+x^{2}}dx
y^{''}+2y^'=3+4sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}=3+4\sin(2t)
integral from 1 to 22 of 1	\int\:_{1}^{22}1dx
integral of 8x^2cos(5x)	\int\:8x^{2}\cos(5x)dx
derivative of f(x)= x/(x^2+10)	derivative\:f(x)=\frac{x}{x^{2}+10}
integral of 10sin(sqrt(x))	\int\:10\sin(\sqrt{x})dx
limit as x approaches 2+of x/(\|x\|)	\lim\:_{x\to\:2+}(\frac{x}{\left\|x\right\|})
slope of (-45)(-4-8)	slope\:(-45)(-4-8)
derivative of f(x)=-3/(e^{3x)},x=0	derivative\:f(x)=-\frac{3}{e^{3x}},x=0
integral of e^{5x}sin(7x)	\int\:e^{5x}\sin(7x)dx
(\partial)/(\partial x)(1/x+1/y+xy)	\frac{\partial\:}{\partial\:x}(\frac{1}{x}+\frac{1}{y}+xy)
y^'-1/t y=te^{-t}	y^{\prime\:}-\frac{1}{t}y=te^{-t}
limit as x approaches 9 of x^2+2	\lim\:_{x\to\:9}(x^{2}+2)
derivative of y=7x^{-3}	derivative\:y=7x^{-3}
d/(dy)(ln(3x^2-y^3-3))	\frac{d}{dy}(\ln(3x^{2}-y^{3}-3))
derivative of (3x^2)/(1-x-x^5)	derivative\:\frac{3x^{2}}{1-x-x^{5}}
limit as x approaches 3 of ln(1/(3-x))-3	\lim\:_{x\to\:3}(\ln(\frac{1}{3-x})-3)
integral of (x^2+6x-5)/(2x^3+3x^2-2x)	\int\:\frac{x^{2}+6x-5}{2x^{3}+3x^{2}-2x}dx
inverse oflaplace (s+1)/(s^2+25)	inverselaplace\:\frac{s+1}{s^{2}+25}
integral of 10xe^{x^2}	\int\:10xe^{x^{2}}dx
f(x)=sqrt(1+2e^{3x)}	f(x)=\sqrt{1+2e^{3x}}
derivative of 8(x-1/x)^2	derivative\:8(x-\frac{1}{x})^{2}
(d^2y)/(dx^2)y+81y=0	\frac{d^{2}y}{dx^{2}}y+81y=0
y^'=kx	y^{\prime\:}=kx
limit as x approaches infinity of 4x+7	\lim\:_{x\to\:\infty\:}(4x+7)
integral of (sqrt(x)+2)(x^2+sqrt(x)-1)	\int\:(\sqrt{x}+2)(x^{2}+\sqrt{x}-1)dx
limit as t approaches 0 of 5/t-5/(t^2+t)	\lim\:_{t\to\:0}(\frac{5}{t}-\frac{5}{t^{2}+t})
limit as n approaches infinity of (n^{100})/(50^n)	\lim\:_{n\to\:\infty\:}(\frac{n^{100}}{50^{n}})
derivative of sec(arctan(x))	\frac{d}{dx}(\sec(\arctan(x)))
derivative of (x^5)/(3-x^4)	derivative\:\frac{x^{5}}{3-x^{4}}
derivative of ln(ln(x/(2-x^2)))	derivative\:\ln(\ln(\frac{x}{2-x^{2}}))
limit as x approaches 5 of x^2-3x-10	\lim\:_{x\to\:5}(x^{2}-3x-10)
derivative of 19^{2x^3+7}	\frac{d}{dx}(19^{2x^{3}+7})
(dy)/(dx)=5xy	\frac{dy}{dx}=5xy
integral of sin(u)	\int\:\sin(u)du
(\partial)/(\partial x)(y^2-2xy-2x^2)	\frac{\partial\:}{\partial\:x}(y^{2}-2xy-2x^{2})
derivative of f(x)=sqrt(5x+7)	derivative\:f(x)=\sqrt{5x+7}
derivative of 1/((1-5x^2))	\frac{d}{dx}(\frac{1}{(1-5x)^{2}})
derivative of \sqrt[3]{0}	\frac{d}{dx}(\sqrt[3]{0})
derivative of 2sin(x+2cos(x))	\frac{d}{dx}(2\sin(x)+2\cos(x))
derivative of log_{7}(x^2+1)	\frac{d}{dx}(\log_{7}(x^{2}+1))
((x^2+1)/(x^2-1))^'	(\frac{x^{2}+1}{x^{2}-1})^{\prime\:}
sum from n=0 to infinity of 1/(n^{1.01)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{1.01}}
limit as x approaches 5 of x^2-3x	\lim\:_{x\to\:5}(x^{2}-3x)
limit as x approaches 2.99 of sqrt(1+x)	\lim\:_{x\to\:2.99}(\sqrt{1+x})
integral of 1/(sqrt(1+\sqrt{1+x))}	\int\:\frac{1}{\sqrt{1+\sqrt{1+x}}}dx
derivative of 3x^2-6	derivative\:3x^{2}-6
integral of (x-1)^2e^x	\int\:(x-1)^{2}e^{x}dx
integral of tan(2θ)	\int\:\tan(2θ)dθ
(y^4-2xy)dx+3x^2dy=0	(y^{4}-2xy)dx+3x^{2}dy=0
(dy)/(dx)=(8e^{4x})/(2cos(2y))	\frac{dy}{dx}=\frac{8e^{4x}}{2\cos(2y)}
derivative of arcsec(x)-6x	derivative\:\arcsec(x)-6x
derivative of \sqrt[3]{x^2}-2sqrt(x)+5	\frac{d}{dx}(\sqrt[3]{x^{2}}-2\sqrt{x}+5)
taylor 1/(3x+5)	taylor\:\frac{1}{3x+5}
integral from 0 to 1 of x^2e^{-x^2}	\int\:_{0}^{1}x^{2}e^{-x^{2}}dx
(\partial ^2)/(\partial x^2)(arctan(y/x))	\frac{\partial\:^{2}}{\partial\:x^{2}}(\arctan(\frac{y}{x}))
integral of (x^2-1)/(sqrt(x))	\int\:\frac{x^{2}-1}{\sqrt{x}}dx
limit as x approaches 2 of 1/(x(x^2-2))	\lim\:_{x\to\:2}(\frac{1}{x(x^{2}-2)})
(dy)/(dx)=(2xy)/(x^2-y^2),y(1)=1	\frac{dy}{dx}=\frac{2xy}{x^{2}-y^{2}},y(1)=1
derivative of 6/((s^3-2)^3)	derivative\:\frac{6}{(s^{3}-2)^{3}}
(\partial)/(\partial y)(x-1/(y^2))	\frac{\partial\:}{\partial\:y}(x-\frac{1}{y^{2}})
area y=-x^2+4,y=-(x^2)/2+2	area\:y=-x^{2}+4,y=-\frac{x^{2}}{2}+2
inverse oflaplace 1/((s^2+s+1))	inverselaplace\:\frac{1}{(s^{2}+s+1)}
limit as x approaches 5 of sqrt(4x-3)	\lim\:_{x\to\:5}(\sqrt{4x-3})

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