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Popular Calculus Problems

4t*(dy)/(dt)-y=sqrt(t)	4t\cdot\:\frac{dy}{dt}-y=\sqrt{t}
limit as x approaches 0 of tan(5x)	\lim\:_{x\to\:0}(\tan(5x))
limit as x approaches 1-of 3x-1	\lim\:_{x\to\:1-}(3x-1)
area y=x^2-x^3,(0,1)	area\:y=x^{2}-x^{3},(0,1)
(\partial)/(\partial x)(sec^2(x))	\frac{\partial\:}{\partial\:x}(\sec^{2}(x))
(\partial)/(\partial x)(-2e^{2y}sin(2x))	\frac{\partial\:}{\partial\:x}(-2e^{2y}\sin(2x))
(\partial)/(\partial x)(e^{-y}+x^2)	\frac{\partial\:}{\partial\:x}(e^{-y}+x^{2})
derivative of {f}(x(-x))	\frac{d}{dx}({f}(x)(-x))
derivative of 20x^{7/5}-6x^{2/13}	derivative\:20x^{\frac{7}{5}}-6x^{\frac{2}{13}}
integral of 2e^{-2t}	\int\:2e^{-2t}dt
tangent of x^5	tangent\:x^{5}
integral of csc^2(x/3)	\int\:\csc^{2}(\frac{x}{3})dx
(\partial)/(\partial y)(5y^2e^{5xy})	\frac{\partial\:}{\partial\:y}(5y^{2}e^{5xy})
integral of sin(wt)	\int\:\sin(wt)dt
xy^'= 1/(y^3)	xy^{\prime\:}=\frac{1}{y^{3}}
integral from-1 to 2 of (-x^2+x+2)^2	\int\:_{-1}^{2}(-x^{2}+x+2)^{2}dx
limit as x approaches infinity of x/0	\lim\:_{x\to\:\infty\:}(\frac{x}{0})
(t^2+x^2)dt+txdx=0	(t^{2}+x^{2})dt+txdx=0
integral of (5x\sqrt[3]{5x^2+1})/3	\int\:\frac{5x\sqrt[3]{5x^{2}+1}}{3}dx
derivative of-cos^2(x)	derivative\:-\cos^{2}(x)
derivative of 8/(x-2)	derivative\:\frac{8}{x-2}
integral of 6sin(3x)-cos(2x)	\int\:6\sin(3x)-\cos(2x)dx
derivative of ln(sin(x^2+1))	\frac{d}{dx}(\ln(\sin(x^{2})+1))
integral of 4x^6-2x^3+7x-4	\int\:4x^{6}-2x^{3}+7x-4dx
integral from 2 to 5 of 1/(x^2)	\int\:_{2}^{5}\frac{1}{x^{2}}dx
integral from 0 to 2 of ((4x+3))/(x^4)	\int\:_{0}^{2}\frac{(4x+3)}{x^{4}}dx
derivative of asin^3(x/3)	\frac{d}{dx}(a\sin^{3}(\frac{x}{3}))
y^'+y/x =(e^x)/x	y^{\prime\:}+\frac{y}{x}=\frac{e^{x}}{x}
tangent of sqrt(5x+4),\at x=9	tangent\:\sqrt{5x+4},\at\:x=9
derivative of 2arccos(x)	\frac{d}{dx}(2\arccos(x))
limit as x approaches-2 of sqrt(4x^2)-3	\lim\:_{x\to\:-2}(\sqrt{4x^{2}}-3)
f(x)=2-x^2	f(x)=2-x^{2}
limit as x approaches 1 of f(x)(x^2-2x)	\lim\:_{x\to\:1}(f(x)(x^{2}-2x))
derivative of 3x-ln(3x+1)	\frac{d}{dx}(3x-\ln(3x+1))
area 2sqrt(x),x	area\:2\sqrt{x},x
limit as x approaches 0 of 6	\lim\:_{x\to\:0}(6)
derivative of 10-10e^{-2x}	\frac{d}{dx}(10-10e^{-2x})
limit as x approaches 1+of 1/(x+1)	\lim\:_{x\to\:1+}(\frac{1}{x+1})
derivative of x^2sin^8(x)+xcos^{-5}(x)	derivative\:x^{2}\sin^{8}(x)+x\cos^{-5}(x)
derivative of 1/3 (e^{3-x})	\frac{d}{dx}(\frac{1}{3}(e^{3-x}))
(\partial)/(\partial x)((3x-3z)/(2y+3z))	\frac{\partial\:}{\partial\:x}(\frac{3x-3z}{2y+3z})
sum from n=0 to infinity of sqrt(n+1)	\sum\:_{n=0}^{\infty\:}\sqrt{n+1}
integral of (6x^2-6x+2)	\int\:(6x^{2}-6x+2)dx
derivative of (e^x)/(7+e^x)	derivative\:\frac{e^{x}}{7+e^{x}}
(d^2)/(dx^2)(1/(x-1))	\frac{d^{2}}{dx^{2}}(\frac{1}{x-1})
integral of+x^6ln(x)	\int\:+x^{6}\ln(x)dx
derivative of (y^4)/(x^{12)}+8e^x	derivative\:\frac{y^{4}}{x^{12}}+8e^{x}
integral from 0 to 5 of (xe^{-x})	\int\:_{0}^{5}(xe^{-x})dx
derivative of 2+xsqrt(x)	\frac{d}{dx}(2+x\sqrt{x})
derivative of y=(x^5+1)^7	derivative\:y=(x^{5}+1)^{7}
(dy)/(dx)-y=2e^xy^2	\frac{dy}{dx}-y=2e^{x}y^{2}
integral of t*sin(t)	\int\:t\cdot\:\sin(t)dt
inverse oflaplace 1/((s+1)^4)	inverselaplace\:\frac{1}{(s+1)^{4}}
(\partial)/(\partial x)(ye^{6x})	\frac{\partial\:}{\partial\:x}(ye^{6x})
derivative of f(x)=(3)e^{-5x}	derivative\:f(x)=(3)e^{-5x}
integral from 0 to 2 of 4t^7	\int\:_{0}^{2}4t^{7}dt
integral of ((x^2-1)/(x^{3/2)})	\int\:(\frac{x^{2}-1}{x^{\frac{3}{2}}})dx
integral from 0 to pi/6 of sin^2(x)	\int\:_{0}^{\frac{π}{6}}\sin^{2}(x)dx
limit as x approaches 0 of (5^x-10^x)/x	\lim\:_{x\to\:0}(\frac{5^{x}-10^{x}}{x})
limit as x approaches 5 of sqrt(x^3+2x)	\lim\:_{x\to\:5}(\sqrt{x^{3}+2x})
integral of 1/(2(x^3+x^2))	\int\:\frac{1}{2(x^{3}+x^{2})}dx
y^{1/2}(dy)/(dx)+y^{3/2}=1,y(0)=9	y^{\frac{1}{2}}\frac{dy}{dx}+y^{\frac{3}{2}}=1,y(0)=9
derivative of 17e^x-ex^e	derivative\:17e^{x}-ex^{e}
(\partial)/(\partial x)(e^{-x}sin(yz))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(yz))
tangent of f(x)=2x^5-6x^3,\at x=1	tangent\:f(x)=2x^{5}-6x^{3},\at\:x=1
integral of ln(x	\int\:\ln(d)xdx
limit as x approaches 3 of (x-1)/(x^2)	\lim\:_{x\to\:3}(\frac{x-1}{x^{2}})
area y=x^2+x-2,y=0	area\:y=x^{2}+x-2,y=0
integral of 1/(sqrt((x-1)(2-x)))	\int\:\frac{1}{\sqrt{(x-1)(2-x)}}dx
integral from-3 to 3 of x^2-3	\int\:_{-3}^{3}x^{2}-3dx
slope of y=x^3-3x	slope\:y=x^{3}-3x
derivative of 2xy	\frac{d}{dx}(2\cdot\:x\cdot\:y)
integral of (e^x)/2	\int\:\frac{e^{x}}{2}dx
d/(dt)(acos(2t)+bsin(2t))	\frac{d}{dt}(a\cos(2t)+b\sin(2t))
integral of sin^2(x-y)	\int\:\sin^{2}(x-y)dy
tangent of y=x^2+2x+10,\at x=6	tangent\:y=x^{2}+2x+10,\at\:x=6
(dy)/(dx)=2y+x^2e^{2x}+5	\frac{dy}{dx}=2y+x^{2}e^{2x}+5
limit as x approaches 0 of 2400x-2x^2	\lim\:_{x\to\:0}(2400x-2x^{2})
limit as x approaches 1 of x/((x-1))	\lim\:_{x\to\:1}(\frac{x}{(x-1)})
derivative of y=6x^3-x^2	derivative\:y=6x^{3}-x^{2}
tangent of f(x)=2x^3+3x^2-12x+6,\at x=0	tangent\:f(x)=2x^{3}+3x^{2}-12x+6,\at\:x=0
derivative of e^x*x	derivative\:e^{x}\cdot\:x
derivative of f(x)=-(12x)/((x^2+2)^{5/2)}	derivative\:f(x)=-\frac{12x}{(x^{2}+2)^{\frac{5}{2}}}
sum from n=1 to infinity of 1/(n!)	\sum\:_{n=1}^{\infty\:}\frac{1}{n!}
derivative of 2xsin(3x)	\frac{d}{dx}(2x\sin(3x))
(\partial)/(\partial x)(5x^4y^7+4x^8y^6)	\frac{\partial\:}{\partial\:x}(5x^{4}y^{7}+4x^{8}y^{6})
derivative of sin(4θ)	derivative\:\sin(4θ)
integral of asqrt(x)	\int\:a\sqrt{x}dx
integral of x*sin((npix)/2)	\int\:x\cdot\:\sin(\frac{nπx}{2})dx
(\partial)/(\partial y)(x^3+y^3)	\frac{\partial\:}{\partial\:y}(x^{3}+y^{3})
integral of 3xsin(x^2)	\int\:3x\sin(x^{2})dx
y^{'''}+6y^{''}+9y^'=0	y^{\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}+9y^{\prime\:}=0
integral from 1 to 6 of 2/(x-11)	\int\:_{1}^{6}\frac{2}{x-11}dx
(dx)/(dt)+410^{-4}x=810^{-5},x(0)=1	\frac{dx}{dt}+4\cdot\:10^{-4}x=8\cdot\:10^{-5},x(0)=1
f(x)=3x^2-5x+1	f(x)=3x^{2}-5x+1
derivative of (4x-3)^{1/2}	derivative\:(4x-3)^{\frac{1}{2}}
taylor ln(1+x),0	taylor\:\ln(1+x),0
y^'+3y=e^{-3t}	y^{\prime\:}+3y=e^{-3t}
integral from 0 to 1 of 3x^3	\int\:_{0}^{1}3x^{3}dx
integral from 0 to 2 of-x^2+4	\int\:_{0}^{2}-x^{2}+4dx

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