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Popular Calculus Problems

integral of 6xcos(x^2)	\int\:6x\cos(x^{2})dx
(\partial)/(\partial x)(x^8+5xy^9)	\frac{\partial\:}{\partial\:x}(x^{8}+5xy^{9})
(\partial)/(\partial y)(xe^{x^2+y^2})	\frac{\partial\:}{\partial\:y}(xe^{x^{2}+y^{2}})
(dy)/(dx)+x^2y=1	\frac{dy}{dx}+x^{2}y=1
limit as x approaches 0 of 8^{-x}	\lim\:_{x\to\:0}(8^{-x})
derivative of 3ln(x)-(x^2)/(24)	derivative\:3\ln(x)-\frac{x^{2}}{24}
y^{''}-3y^'+2y=e^x+e^{2x}+e^{-x}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{x}+e^{2x}+e^{-x}
derivative of (x^2)/(1+2x)	derivative\:\frac{x^{2}}{1+2x}
(6y+2x-7)dx+(8y+6x-1)dy=0	(6y+2x-7)dx+(8y+6x-1)dy=0
limit as x approaches+3 of (6x)/(x-3)	\lim\:_{x\to\:+3}(\frac{6x}{x-3})
tangent of e^{x^2}	tangent\:e^{x^{2}}
integral of 2sin(5x)	\int\:2\sin(5x)dx
laplacetransform e^tcos(5t)	laplacetransform\:e^{t}\cos(5t)
tangent of 2x(x+1)^3(x^2+2x+1)^2	tangent\:2x(x+1)^{3}(x^{2}+2x+1)^{2}
taylor (1+x^2)^{3/2}x	taylor\:(1+x^{2})^{\frac{3}{2}}x
integral of 3/(5-2x)	\int\:\frac{3}{5-2x}dx
derivative of f(x)=3sec(8x)	derivative\:f(x)=3\sec(8x)
integral of cos^6(x/2)	\int\:\cos^{6}(\frac{x}{2})dx
derivative of f(x)=3e^x+4/(\sqrt[3]{x)}	derivative\:f(x)=3e^{x}+\frac{4}{\sqrt[3]{x}}
integral of 9e^{-t}	\int\:9e^{-t}dt
limit as x approaches infinity of-1*x	\lim\:_{x\to\:\infty\:}(-1\cdot\:x)
derivative of f(x)=sec^2(x)-tan^2(x)	derivative\:f(x)=\sec^{2}(x)-\tan^{2}(x)
integral of e^{2x}*x	\int\:e^{2x}\cdot\:xdx
y^'=0.05ln((4000)/y)y	y^{\prime\:}=0.05\ln(\frac{4000}{y})y
taylor ln(1+2x)	taylor\:\ln(1+2x)
derivative of 6x^2-6x-12	\frac{d}{dx}(6x^{2}-6x-12)
derivative of (ln(x))^3	derivative\:(\ln(x))^{3}
integral of (2t)/(sqrt(1-4t^4))	\int\:\frac{2t}{\sqrt{1-4t^{4}}}dt
(dx)/(dt)=-sqrt(x)	\frac{dx}{dt}=-\sqrt{x}
derivative of 1.5	\frac{d}{dx}(1.5)
derivative of-2x^2+3x-6	\frac{d}{dx}(-2x^{2}+3x-6)
f(x)=7e^xcos(x)	f(x)=7e^{x}\cos(x)
derivative of 2xe^{-x}-x^2e^{-x}	\frac{d}{dx}(2xe^{-x}-x^{2}e^{-x})
(dy)/(dx)=((4x)/((1+x^2)^{1/3)})	\frac{dy}{dx}=(\frac{4x}{(1+x^{2})^{\frac{1}{3}}})
derivative of 3x^2sin(xtan(x))	\frac{d}{dx}(3x^{2}\sin(x)\tan(x))
derivative of ln(x^2+6)	derivative\:\ln(x^{2}+6)
derivative of sqrt(12x)	derivative\:\sqrt{12x}
integral of 1/((x-2)(x^2+1))	\int\:\frac{1}{(x-2)(x^{2}+1)}dx
integral of (4z+1)^2	\int\:(4z+1)^{2}dz
derivative of xnx	\frac{d}{dx}(xnx)
derivative of x^5-10/9 x^3+5/21 x	\frac{d}{dx}(x^{5}-\frac{10}{9}x^{3}+\frac{5}{21}x)
(\partial)/(\partial x)(4^x)	\frac{\partial\:}{\partial\:x}(4^{x})
limit as x approaches-2 of sqrt(4-x^2)	\lim\:_{x\to\:-2}(\sqrt{4-x^{2}})
derivative of (sin(x)-1)/(sin(x)+4)	derivative\:\frac{\sin(x)-1}{\sin(x)+4}
integral of 1/(f(x))	\int\:\frac{1}{f(x)}dx
integral of 1-cos(2t)	\int\:1-\cos(2t)dt
tangent of y=x^3-2x-2,\at x=1	tangent\:y=x^{3}-2x-2,\at\:x=1
derivative of-sin(x)	derivative\:-\sin(x)
derivative of x^pe^{ax}	\frac{d}{dx}(x^{p}e^{ax})
integral of y/(1-y^2)	\int\:\frac{y}{1-y^{2}}dy
(\partial)/(\partial x)(-1+ln(x))	\frac{\partial\:}{\partial\:x}(-1+\ln(x))
integral of 1/(\sqrt[4]{8-3x)}	\int\:\frac{1}{\sqrt[4]{8-3x}}dx
derivative of (4x+x^2-2)/((2+x)^2)	derivative\:\frac{4x+x^{2}-2}{(2+x)^{2}}
derivative of (3x^2-5/(2x^2+1))	\frac{d}{dx}(\frac{3x^{2}-5}{2x^{2}+1})
limit as x approaches-8+of ((x+7))/(x+8)	\lim\:_{x\to\:-8+}(\frac{(x+7)}{x+8})
derivative of e^{-a\|x\|}	\frac{d}{dx}(e^{-a\left\|x\right\|})
integral of (2x)/((x^2+1)^{90)}	\int\:\frac{2x}{(x^{2}+1)^{90}}dx
derivative of f(8)=2(x-5)	derivative\:f(8)=2(x-5)
limit as h approaches c of h^3+4h^2-3	\lim\:_{h\to\:c}(h^{3}+4h^{2}-3)
derivative of (x^3/3+3x^2-7x)	\frac{d}{dx}(\frac{x^{3}}{3}+3x^{2}-7x)
taylor 5x^3+2x^2+6x+10	taylor\:5x^{3}+2x^{2}+6x+10
integral of 1/((x-2)(x+1))	\int\:\frac{1}{(x-2)(x+1)}dx
limit as x approaches 1 of sqrt(x+1)	\lim\:_{x\to\:1}(\sqrt{x+1})
integral of 2/(x^2+11x+18)	\int\:\frac{2}{x^{2}+11x+18}dx
integral of 5cos(3x)-4sin(5x)	\int\:5\cos(3x)-4\sin(5x)dx
derivative of log_{5}(x)	derivative\:\log_{5}(x)
area 1/3 x^{1/2}-x^{3/2},x=0,x= 1/3	area\:\frac{1}{3}x^{\frac{1}{2}}-x^{\frac{3}{2}},x=0,x=\frac{1}{3}
(d^2)/(dx^2)(xsqrt(9-x))	\frac{d^{2}}{dx^{2}}(x\sqrt{9-x})
limit as x approaches 4-of 7/(x-4)	\lim\:_{x\to\:4-}(\frac{7}{x-4})
(\partial)/(\partial x)(6/(x^4))	\frac{\partial\:}{\partial\:x}(\frac{6}{x^{4}})
y^{''}+y=3sin(4x)	y^{\prime\:\prime\:}+y=3\sin(4x)
derivative of f(x)=((x+1)(2x-3))/(2x+3)	derivative\:f(x)=\frac{(x+1)(2x-3)}{2x+3}
y^{''}+2y^'-3y=-16xe^x	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=-16xe^{x}
area y=3-x,y=2x^2,[0,3]	area\:y=3-x,y=2x^{2},[0,3]
derivative of 4x+2y	\frac{d}{dx}(4x+2y)
(\partial)/(\partial x)(-6x^3+y^2+5xy)	\frac{\partial\:}{\partial\:x}(-6x^{3}+y^{2}+5xy)
simplify (-2x)/((x^2+1)^2)	simplify\:\frac{-2x}{(x^{2}+1)^{2}}
derivative of 1/x+e^x	derivative\:\frac{1}{x}+e^{x}
limit as x approaches-6 of (x+9)/(x+6)	\lim\:_{x\to\:-6}(\frac{x+9}{x+6})
tangent of f(x)=110x-16x^2,\at x=0	tangent\:f(x)=110x-16x^{2},\at\:x=0
inverse oflaplace (s*(s+3))/(s+2)	inverselaplace\:\frac{s\cdot\:(s+3)}{s+2}
laplacetransform 4t^3sin(t)	laplacetransform\:4t^{3}\sin(t)
xy^'+y+y^2=0,y(1)=2	xy^{\prime\:}+y+y^{2}=0,y(1)=2
(\partial)/(\partial x)(1/2 xy^2)	\frac{\partial\:}{\partial\:x}(\frac{1}{2}xy^{2})
limit as x approaches 0 of (10^x-e^x)/x	\lim\:_{x\to\:0}(\frac{10^{x}-e^{x}}{x})
limit as x approaches-infinity of x/3	\lim\:_{x\to\:-\infty\:}(\frac{x}{3})
lcm f(x)=,sqrt(x)	lcm\:f(x)=,\sqrt{x}
derivative of 15-x^2	\frac{d}{dx}(15-x^{2})
integral of (-7x-7)/(2x^2+5x-3)	\int\:\frac{-7x-7}{2x^{2}+5x-3}dx
limit as t approaches 0 of ((5e^t-5))/t	\lim\:_{t\to\:0}(\frac{(5e^{t}-5)}{t})
derivative of log_{10}(1+cos(x))	\frac{d}{dx}(\log_{10}(1+\cos(x)))
derivative of ln(7/(x^2-x+2))	\frac{d}{dx}(\ln(\frac{7}{x^{2}-x+2}))
y^{''}-8y^'+13y=0,y(0)=0,y^'(0)=5	y^{\prime\:\prime\:}-8y^{\prime\:}+13y=0,y(0)=0,y^{\prime\:}(0)=5
integral from-infinity to 0 of xe^{9x}	\int\:_{-\infty\:}^{0}xe^{9x}dx
(\partial)/(\partial y)(y^3-y)	\frac{\partial\:}{\partial\:y}(y^{3}-y)
derivative of f(x)=x^2-8	derivative\:f(x)=x^{2}-8
inverse oflaplace (s+1)/(s^2(s+2)^3)	inverselaplace\:\frac{s+1}{s^{2}(s+2)^{3}}
integral of 5t	\int\:5tdt
laplacetransform 7sin(3/2 t)	laplacetransform\:7\sin(\frac{3}{2}t)
y^{''}-y^'+5y=0	y^{\prime\:\prime\:}-y^{\prime\:}+5y=0

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