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Popular Calculus Problems

derivative of 4x^2sec(2x)	\frac{d}{dx}(4x^{2}\sec(2x))
y^{''}-2y^'+y=((e^x))/((1+x^2))	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{(e^{x})}{(1+x^{2})}
derivative of sin(4t)	derivative\:\sin(4t)
derivative of 5^{-x}	derivative\:5^{-x}
integral of (38)/((1-x^2)^{3/2)}	\int\:\frac{38}{(1-x^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial x)(((ax+by))/((cx+dy)))	\frac{\partial\:}{\partial\:x}(\frac{(ax+by)}{(cx+dy)})
derivative of ((3x+5)(2x-7))/(8x^2-3)	derivative\:\frac{(3x+5)(2x-7)}{8x^{2}-3}
(\partial)/(\partial x)(xy-3f(x,y)-f(x,y)x^2+f(x,y)y)	\frac{\partial\:}{\partial\:x}(xy-3f(x,y)-f(x,y)x^{2}+f(x,y)y)
integral of sqrt(1+3x^2)(6x)	\int\:\sqrt{1+3x^{2}}(6x)dx
integral of cos(x/3)	\int\:\cos(\frac{x}{3})dx
integral of (2x^3+2x^2+6x+9)/(x^3+3x)	\int\:\frac{2x^{3}+2x^{2}+6x+9}{x^{3}+3x}dx
integral of (x^2-8)^5(2x)	\int\:(x^{2}-8)^{5}(2x)dx
(\partial)/(\partial y)(x^2y+(xe^x)/(y^3))	\frac{\partial\:}{\partial\:y}(x^{2}y+\frac{xe^{x}}{y^{3}})
area 2x^2-2x-6,-2,2	area\:2x^{2}-2x-6,-2,2
integral from 0 to 5 of 46216.8x	\int\:_{0}^{5}46216.8xdx
integral of (sin(sqrt(x)))/(2sqrt(x))	\int\:\frac{\sin(\sqrt{x})}{2\sqrt{x}}dx
derivative of f(x)=5sqrt(x)sin(x)	derivative\:f(x)=5\sqrt{x}\sin(x)
integral from 0 to pi of cos(2x)	\int\:_{0}^{π}\cos(2x)dx
integral of x/(x^2-3)	\int\:\frac{x}{x^{2}-3}dx
inverse oflaplace 1/(x(x^2+2x+x))	inverselaplace\:\frac{1}{x(x^{2}+2x+x)}
derivative of 1/(sqrt(6x+5))	\frac{d}{dx}(\frac{1}{\sqrt{6x+5}})
(\partial)/(\partial y)(7ln(2x^5-3y))	\frac{\partial\:}{\partial\:y}(7\ln(2x^{5}-3y))
area 1/(10x^2),x, x/(10)	area\:\frac{1}{10x^{2}},x,\frac{x}{10}
(dy)/(dx)=ky	\frac{dy}{dx}=ky
(\partial)/(\partial x)(e^x*cos(x))	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:\cos(x))
derivative of 9(x^6-2)^5	derivative\:9(x^{6}-2)^{5}
derivative of (x^2-1/(x+1))	\frac{d}{dx}(\frac{x^{2}-1}{x+1})
derivative of f(x)=3x^2+6x	derivative\:f(x)=3x^{2}+6x
limit as x approaches-2 of 3-5x^2	\lim\:_{x\to\:-2}(3-5x^{2})
(\partial)/(\partial x)(1/(2pi)arctan(x/y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2π}\arctan(\frac{x}{y}))
y^'=(xy)/(x^2-1)	y^{\prime\:}=\frac{xy}{x^{2}-1}
slope of (-7,-9),(1,3)	slope\:(-7,-9),(1,3)
integral from 1 to e^2 of (ln^4(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{4}(x^{2})}{x}dx
taylor ln(1-5y)	taylor\:\ln(1-5y)
inverse oflaplace 1/(s^2+9s+9)	inverselaplace\:\frac{1}{s^{2}+9s+9}
derivative of f(t)=2t^2+3t-6	derivative\:f(t)=2t^{2}+3t-6
(\partial)/(\partial x)(((ax+by))/(cx+dy))	\frac{\partial\:}{\partial\:x}(\frac{(ax+by)}{cx+dy})
xy^{''}+y^'=1	xy^{\prime\:\prime\:}+y^{\prime\:}=1
(\partial)/(\partial x)(6xsin(x+2y-z))	\frac{\partial\:}{\partial\:x}(6x\sin(x+2y-z))
(\partial)/(\partial y)(2x^2+2y-8)	\frac{\partial\:}{\partial\:y}(2x^{2}+2y-8)
integral of (csc^2(x)+4)	\int\:(\csc^{2}(x)+4)dx
derivative of x^2*e^{2x}	\frac{d}{dx}(x^{2}\cdot\:e^{2x})
integral of (2^{2x})/(1+2^{2x)}	\int\:\frac{2^{2x}}{1+2^{2x}}dx
xy^2y^'=y^3-5x^3,y(1)=2	xy^{2}y^{\prime\:}=y^{3}-5x^{3},y(1)=2
tangent of f(x)=-x^2+4	tangent\:f(x)=-x^{2}+4
derivative of sin(x)+4/5 cot(x)	derivative\:\sin(x)+\frac{4}{5}\cot(x)
tangent of f(x)=3x^2-4x+1,\at x=2	tangent\:f(x)=3x^{2}-4x+1,\at\:x=2
integral of (2u^2-2u^{-1})	\int\:(2u^{2}-2u^{-1})du
3y^{''}+2y^'+y=0	3y^{\prime\:\prime\:}+2y^{\prime\:}+y=0
(\partial)/(\partial y)(y/((x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{y}{(x^{2}+y^{2})})
derivative of f(x)=4x^6-7x^5	derivative\:f(x)=4x^{6}-7x^{5}
derivative of 5xsin(pix)	derivative\:5x\sin(πx)
limit as t approaches-2 of (t^3+8)/(t+2)	\lim\:_{t\to\:-2}(\frac{t^{3}+8}{t+2})
limit as x approaches 3-of 3-x	\lim\:_{x\to\:3-}(3-x)
y^{''}+2y^'=1,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}=1,y(0)=1,y^{\prime\:}(0)=0
integral from 0 to 2 of 4	\int\:_{0}^{2}4dx
integral of (e^x+e^{-x})^2	\int\:(e^{x}+e^{-x})^{2}dx
integral from 0 to pi/3 of 6sec^3(x)	\int\:_{0}^{\frac{π}{3}}6\sec^{3}(x)dx
limit as x approaches-0.001 of (e^x-1)/x	\lim\:_{x\to\:-0.001}(\frac{e^{x}-1}{x})
integral from-2 to 3 of x^3	\int\:_{-2}^{3}x^{3}dx
integral of 1/(sqrt((x^2-1)^3))	\int\:\frac{1}{\sqrt{(x^{2}-1)^{3}}}dx
limit as x approaches 3 of 4x^2	\lim\:_{x\to\:3}(4x^{2})
(\partial)/(\partial x)(acos(x)sin(y))	\frac{\partial\:}{\partial\:x}(a\cos(x)\sin(y))
limit as x approaches 1 of e^{1/(1-x)}	\lim\:_{x\to\:1}(e^{\frac{1}{1-x}})
derivative of 2x^{3/4}	\frac{d}{dx}(2x^{\frac{3}{4}})
(\partial)/(\partial y)(xy+z^2)	\frac{\partial\:}{\partial\:y}(xy+z^{2})
integral of 7xsec^2(x)	\int\:7x\sec^{2}(x)dx
integral of 2e^{-x^2}-1	\int\:2e^{-x^{2}}-1dx
(\partial)/(\partial z)(x^{y/z})	\frac{\partial\:}{\partial\:z}(x^{\frac{y}{z}})
derivative of (4x^2+3/(2x-1))	\frac{d}{dx}(\frac{4x^{2}+3}{2x-1})
derivative of f(x)=x^3+y^3=16	derivative\:f(x)=x^{3}+y^{3}=16
area x=5-5y^2,x=5y^2-5	area\:x=5-5\cdot\:y^{2},x=5\cdot\:y^{2}-5
derivative of (x^4+48/(24x))	\frac{d}{dx}(\frac{x^{4}+48}{24x})
inverse oflaplace (e^{-pis})/s	inverselaplace\:\frac{e^{-πs}}{s}
area x^2-3x,3x+7,-1,7	area\:x^{2}-3x,3x+7,-1,7
d/(dt)(2^t)	\frac{d}{dt}(2^{t})
integral of 1/y e^{-x/y}	\int\:\frac{1}{y}e^{-\frac{x}{y}}dx
slope of sin(x^2)	slope\:\sin(x^{2})
(\partial)/(\partial x)(y^3sin(x+y))	\frac{\partial\:}{\partial\:x}(y^{3}\sin(x+y))
derivative of x/(x^{-1+9})	\frac{d}{dx}(\frac{x}{x^{-1}+9})
integral of ((3x^2)/(sqrt(64-x^2)))	\int\:(\frac{3x^{2}}{\sqrt{64-x^{2}}})dx
limit as x approaches 0+of (x^{-2})/x	\lim\:_{x\to\:0+}(\frac{x^{-2}}{x})
integral of xsqrt(36-x^2)	\int\:x\sqrt{36-x^{2}}dx
integral of (e^t)/((1+e^{(2t)))^{(3/2)}}	\int\:\frac{e^{t}}{(1+e^{(2t)})^{(\frac{3}{2})}}dt
(dy)/(dx)=sqrt(3y)*e^{x+3}	\frac{dy}{dx}=\sqrt{3y}\cdot\:e^{x+3}
area y=(x^2+7)/(5x-x^2),1,4	area\:y=\frac{x^{2}+7}{5x-x^{2}},1,4
(\partial)/(\partial x)(rsin(x))	\frac{\partial\:}{\partial\:x}(r\sin(x))
y^'=1	y^{\prime\:}=1
integral of 5cos(v)-7/(sqrt(1-v^2))	\int\:5\cos(v)-\frac{7}{\sqrt{1-v^{2}}}dv
(\partial)/(\partial y)(sqrt(4-x^2-5y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-5y^{2}})
(\partial)/(\partial x)(5e^x)	\frac{\partial\:}{\partial\:x}(5e^{x})
inverse oflaplace (s-3)/(s^2-4s+3)	inverselaplace\:\frac{s-3}{s^{2}-4s+3}
limit as x approaches 0 of (ln(x^2+1))/x	\lim\:_{x\to\:0}(\frac{\ln(x^{2}+1)}{x})
area x^2,x-4,-4,4	area\:x^{2},x-4,-4,4
derivative of f(x)= 1/10 x-1/6	derivative\:f(x)=\frac{1}{10}x-\frac{1}{6}
derivative of f(x)=e^{x/2}	derivative\:f(x)=e^{\frac{x}{2}}
integral of 5t^4cos(t^5+1)	\int\:5t^{4}\cos(t^{5}+1)dt
integral of (csc^2(θ)-1)	\int\:(\csc^{2}(θ)-1)dθ
derivative of (xsqrt(2x+1)/(sqrt(4-5x)))	\frac{d}{dx}(\frac{x\sqrt{2x+1}}{\sqrt{4-5x}})
integral of (4-3x^2)/((3x^2+4)^2)	\int\:\frac{4-3x^{2}}{(3x^{2}+4)^{2}}dx

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