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Popular Calculus Problems
limit as x approaches 0-of e^{4/x}
\lim\:_{x\to\:0-}(e^{\frac{4}{x}})
(\partial)/(\partial y)(x+ye^{y/x})
\frac{\partial\:}{\partial\:y}(x+ye^{\frac{y}{x}})
(\partial)/(\partial y)(e^{-x}+y^2)
\frac{\partial\:}{\partial\:y}(e^{-x}+y^{2})
(\partial)/(\partial x)(9xsin(5x^2y))
\frac{\partial\:}{\partial\:x}(9x\sin(5x^{2}y))
limit as x approaches infinity of 8-e^x
\lim\:_{x\to\:\infty\:}(8-e^{x})
integral of (3(x-3)^2)/(16)
\int\:\frac{3(x-3)^{2}}{16}dx
derivative of ((2e^x))/(x^2)
derivative\:\frac{(2e^{x})}{x^{2}}
integral of (x+7)
\int\:(x+7)dx
derivative of sin(5x+cos(5x))
\frac{d}{dx}(\sin(5x)+\cos(5x))
limit as x approaches 2+of 4/((x-2)^3)
\lim\:_{x\to\:2+}(\frac{4}{(x-2)^{3}})
derivative of 3x^{1/3}+2x^2
\frac{d}{dx}(3x^{\frac{1}{3}}+2x^{2})
integral of e^{3x}sin(e^x)
\int\:e^{3x}\sin(e^{x})dx
derivative of sqrt(x)+1/(\sqrt[3]{x})
\frac{d}{dx}(\sqrt{x}+\frac{1}{\sqrt[3]{x}})
limit as x approaches-infinity of 2^x
\lim\:_{x\to\:-\infty\:}(2^{x})
limit as n approaches infinity of ((-1)^{n+1})/((n+3)*n!)
\lim\:_{n\to\:\infty\:}(\frac{(-1)^{n+1}}{(n+3)\cdot\:n!})
integral of x^3sqrt(x^2-8)
\int\:x^{3}\sqrt{x^{2}-8}dx
integral of e^{3x}sin(2x)
\int\:e^{3x}\sin(2x)dx
sum from n=3 to infinity of e^{3-6n}
\sum\:_{n=3}^{\infty\:}e^{3-6n}
(\partial)/(\partial x)(e^{x+y}-1)
\frac{\partial\:}{\partial\:x}(e^{x+y}-1)
integral of (e^{-2x})/(e^x)
\int\:\frac{e^{-2x}}{e^{x}}dx
derivative of 4x^{5/2}
\frac{d}{dx}(4x^{\frac{5}{2}})
limit as x approaches-2 of (2+|x|)/(2+x)
\lim\:_{x\to\:-2}(\frac{2+\left|x\right|}{2+x})
derivative of (arcsin(x)/(sin(x)))
\frac{d}{dx}(\frac{\arcsin(x)}{\sin(x)})
limit as x approaches 0 of (x^4)/x
\lim\:_{x\to\:0}(\frac{x^{4}}{x})
limit as x approaches 3/7 of (|3-7x|)/(21x^2-9x)
\lim\:_{x\to\:\frac{3}{7}}(\frac{\left|3-7x\right|}{21x^{2}-9x})
limit as x approaches-3-of (2x)/(x+3)
\lim\:_{x\to\:-3-}(\frac{2x}{x+3})
area y=sin^2(x),y=sin^3(x),[0,pi]
area\:y=\sin^{2}(x),y=\sin^{3}(x),[0,π]
derivative of 1/(\sqrt[4]{x})
\frac{d}{dx}(\frac{1}{\sqrt[4]{x}})
sum from n=0 to infinity of (x+1)^n
\sum\:_{n=0}^{\infty\:}(x+1)^{n}
derivative of 2xy^4-3
\frac{d}{dx}(2xy^{4}-3)
(\partial)/(\partial x)(2x^3y+sin(x^3))
\frac{\partial\:}{\partial\:x}(2x^{3}y+\sin(x^{3}))
y^'+4y=sin(3t)
y^{\prime\:}+4y=\sin(3t)
integral of (2x^2+3x)^3
\int\:(2x^{2}+3x)^{3}dx
derivative of y=(f(x))/(x^5)
derivative\:y=\frac{f(x)}{x^{5}}
derivative of 2tan^2(7x)
derivative\:2\tan^{2}(7x)
(2xy+3)dx+(x^2-1)dy=0
(2xy+3)dx+(x^{2}-1)dy=0
3xy^'+7y=0
3xy^{\prime\:}+7y=0
derivative of (e^{10x}+e^{-10x})/x
derivative\:\frac{e^{10x}+e^{-10x}}{x}
derivative of 2(ln(x))
\frac{d}{dx}(2(\ln(x)))
integral from 0 to 1.5 of (3/2-x)^2
\int\:_{0}^{1.5}(\frac{3}{2}-x)^{2}dx
y^{''}-8y^'+16y=t^{-8}e^{4t}
y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-8}e^{4t}
integral of (cos^4(x)sin(x))
\int\:(\cos^{4}(x)\sin(x))dx
integral of (x^2+1)(x^3+3x)^4
\int\:(x^{2}+1)(x^{3}+3x)^{4}dx
integral of (2x+5)/(sqrt(x^2+5x))
\int\:\frac{2x+5}{\sqrt{x^{2}+5x}}dx
derivative of f(x)=sqrt(7+\sqrt{5x)}
derivative\:f(x)=\sqrt{7+\sqrt{5x}}
y^'=k*y
y^{\prime\:}=k\cdot\:y
derivative of ((3t-1))/(sqrt(t)-2)
derivative\:\frac{(3t-1)}{\sqrt{t}-2}
tangent of y=(4x)/(x+2)
tangent\:y=\frac{4x}{x+2}
derivative of ln(4xy)
\frac{d}{dx}(\ln(4xy))
derivative of (18)/(x^4)
derivative\:\frac{18}{x^{4}}
domain of f(x)= x/((1+x^2))
domain\:f(x)=\frac{x}{(1+x^{2})}
derivative of (x^2-3x+2)^5
derivative\:(x^{2}-3x+2)^{5}
integral of x^{12}e^{x^{13}}
\int\:x^{12}e^{x^{13}}dx
tangent of f(x)=x^2-9,(-2,-5)
tangent\:f(x)=x^{2}-9,(-2,-5)
integral of (x^3)/(x^4+5)
\int\:\frac{x^{3}}{x^{4}+5}dx
derivative of 1/(x(8+ln(x)))
\frac{d}{dx}(\frac{1}{x(8+\ln(x))})
limit as x approaches-3 of (x+2)/(x+3)
\lim\:_{x\to\:-3}(\frac{x+2}{x+3})
limit as x approaches-3 of (x-2)/(x+5)
\lim\:_{x\to\:-3}(\frac{x-2}{x+5})
derivative of x^{1/2}y^{1/2}
\frac{d}{dx}(x^{\frac{1}{2}}y^{\frac{1}{2}})
limit as x approaches 8 of x^3-6x+5
\lim\:_{x\to\:8}(x^{3}-6x+5)
tangent of 1/(x^2),\at x=3
tangent\:\frac{1}{x^{2}},\at\:x=3
(dy)/(dx)3x^3+3y^3-5xy=0
\frac{dy}{dx}3x^{3}+3y^{3}-5xy=0
derivative of 4x^6e^x
derivative\:4x^{6}e^{x}
integral of t/(sqrt(at^2+b))
\int\:\frac{t}{\sqrt{at^{2}+b}}dt
(d^2)/(dx^2)(3e^xcos(x))
\frac{d^{2}}{dx^{2}}(3e^{x}\cos(x))
slope of (-3,2),(6,3)
slope\:(-3,2),(6,3)
integral of 30arctan(sqrt(x))
\int\:30\arctan(\sqrt{x})dx
laplacetransform 2sin(3t)
laplacetransform\:2\sin(3t)
limit as x approaches 1 of ax+b
\lim\:_{x\to\:1}(ax+b)
derivative of 3x-7
\frac{d}{dx}(3x-7)
integral of 1/(xe^{-x)}
\int\:\frac{1}{xe^{-x}}dx
derivative of (5x^3+3(x^4-2x))
\frac{d}{dx}((5x^{3}+3)(x^{4}-2x))
laplacetransform te^{2t}sin(t)
laplacetransform\:te^{2t}\sin(t)
(dy)/(dx)+2y=e^{-x}
\frac{dy}{dx}+2y=e^{-x}
derivative of (\sqrt[3]{x}/(x-9))
\frac{d}{dx}(\frac{\sqrt[3]{x}}{x-9})
taylor X^3-X^2+4X+5
taylor\:X^{3}-X^{2}+4X+5
tangent of f(x)=(125)/(x^2+24),\at x=-1
tangent\:f(x)=\frac{125}{x^{2}+24},\at\:x=-1
derivative of cos(9x^2)
\frac{d}{dx}(\cos(9x^{2}))
integral of 1/(2x^2-4x+20)
\int\:\frac{1}{2x^{2}-4x+20}dx
(\partial)/(\partial x)(x^2e^{yz^2})
\frac{\partial\:}{\partial\:x}(x^{2}e^{yz^{2}})
limit as x approaches-3.1 of x^2
\lim\:_{x\to\:-3.1}(x^{2})
(dy)/(dx)=(xsqrt(x^2-y^2)+y^2)/(xy)
\frac{dy}{dx}=\frac{x\sqrt{x^{2}-y^{2}}+y^{2}}{xy}
integral of sin((xy)/2)
\int\:\sin(\frac{xy}{2})dy
limit as x approaches 0 of (cos(x))/(5x)
\lim\:_{x\to\:0}(\frac{\cos(x)}{5x})
d/(dt)(3cos(2t))
\frac{d}{dt}(3\cos(2t))
integral of (x^3-(x-1)^2)/x
\int\:\frac{x^{3}-(x-1)^{2}}{x}dx
limit as x approaches 1 of 4x-1
\lim\:_{x\to\:1}(4x-1)
derivative of 100x^2-26xe^x
\frac{d}{dx}(100x^{2}-26xe^{x})
derivative of log_{10}(3x+4)
\frac{d}{dx}(\log_{10}(3x+4))
(\partial)/(\partial x)(tan(xy)+ye^{3x})
\frac{\partial\:}{\partial\:x}(\tan(xy)+ye^{3x})
y^'+y=e^{-t}sin(t)
y^{\prime\:}+y=e^{-t}\sin(t)
derivative of cos(t)
derivative\:\cos(t)
(\partial)/(\partial x)((4x^4y^2+9)^2)
\frac{\partial\:}{\partial\:x}((4x^{4}y^{2}+9)^{2})
sum from n=1 to infinity of (7/10)^n
\sum\:_{n=1}^{\infty\:}(\frac{7}{10})^{n}
integral of (1+e^x)/(1-e^x)
\int\:\frac{1+e^{x}}{1-e^{x}}dx
limit as h approaches 0 of ((7+h)-7)/h
\lim\:_{h\to\:0}(\frac{(7+h)-7}{h})
integral of (x+1)/(sqrt(x+1))
\int\:\frac{x+1}{\sqrt{x+1}}dx
laplacetransform t^2(8e^{2t}-6sin(t))
laplacetransform\:t^{2}(8e^{2t}-6\sin(t))
limit as x approaches 0 of (1+4x)^{4/x}
\lim\:_{x\to\:0}((1+4x)^{\frac{4}{x}})
(\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2))
\frac{\partial\:}{\partial\:x}(\frac{2t}{(1-\frac{0.5(x)}{L})^{2}})
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