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Popular Calculus Problems

derivative of (tsin(t))/(1+t)	derivative\:\frac{t\sin(t)}{1+t}
area x/(1+x^2),((x^2))/(1+x^3)	area\:\frac{x}{1+x^{2}},\frac{(x^{2})}{1+x^{3}}
y^'=(xy+2y)/(x+3)	y^{\prime\:}=\frac{xy+2y}{x+3}
x(x^3+1)y^'+(2x^3-1)y=(x^3-2)/x	x(x^{3}+1)y^{\prime\:}+(2x^{3}-1)y=\frac{x^{3}-2}{x}
integral of sqrt(x^2-49)	\int\:\sqrt{x^{2}-49}dx
y^{''}+2y^'+2=0	y^{\prime\:\prime\:}+2y^{\prime\:}+2=0
(\partial)/(\partial x)(sin(xy^2)e^{2x-3y})	\frac{\partial\:}{\partial\:x}(\sin(xy^{2})e^{2x-3y})
integral of 5sin(6pi)x	\int\:5\sin(6π)xdx
integral of 6e^{-0.2x}	\int\:6e^{-0.2x}dx
taylor sin(3x),0	taylor\:\sin(3x),0
12(t+1)((dy)/(dt))-8y=32t,y(0)=2	12(t+1)(\frac{dy}{dt})-8y=32t,y(0)=2
derivative of y= 1/(t^3+2t^2-1)	derivative\:y=\frac{1}{t^{3}+2t^{2}-1}
area x=-5,x=1,y=3x,y=x^2-4	area\:x=-5,x=1,y=3x,y=x^{2}-4
derivative of (4x-7/(2x+1))	\frac{d}{dx}(\frac{4x-7}{2x+1})
integral of (6x^2-5x+3)/x	\int\:\frac{6x^{2}-5x+3}{x}dx
(\partial)/(\partial x)(3xye^{y-x})	\frac{\partial\:}{\partial\:x}(3xye^{y-x})
slope of (3,3),(2,-5)	slope\:(3,3),(2,-5)
(x^2-5)yy^'=2x	(x^{2}-5)yy^{\prime\:}=2x
integral of x/3*sin(x^2)	\int\:\frac{x}{3}\cdot\:\sin(x^{2})dx
integral of (x)	\int\:(x)dx
tangent of 12x^2-8x-4	tangent\:12x^{2}-8x-4
integral of 1/(sqrt(e^x-1))	\int\:\frac{1}{\sqrt{e^{x}-1}}dx
y^{''}-4y^'-12y=sin(2x)	y^{\prime\:\prime\:}-4y^{\prime\:}-12y=\sin(2x)
tangent of f(x)= 2/(x-2),\at x=-4	tangent\:f(x)=\frac{2}{x-2},\at\:x=-4
limit as x approaches 0 of (cos(x)-x)/x	\lim\:_{x\to\:0}(\frac{\cos(x)-x}{x})
area y=x^3,y=x^{1/2}	area\:y=x^{3},y=x^{\frac{1}{2}}
(\partial)/(\partial x)(x^3+4x^2+x^4+3x^5)	\frac{\partial\:}{\partial\:x}(x^{3}+4x^{2}+x^{4}+3x^{5})
integral from 0 to 6pi of x^2sin(2x)	\int\:_{0}^{6π}x^{2}\sin(2x)dx
derivative of ln(x^2-4x+1)	derivative\:\ln(x^{2}-4x+1)
(\partial)/(\partial y)(x*y^2)	\frac{\partial\:}{\partial\:y}(x\cdot\:y^{2})
implicit (dy)/(dx),y^3-2xy+7=3x+1	implicit\:\frac{dy}{dx},y^{3}-2xy+7=3x+1
limit as x approaches 0 of ((\sqrt[3]{x+8}-2))/x	\lim\:_{x\to\:0}(\frac{(\sqrt[3]{x+8}-2)}{x})
integral of 5x*cos(8x)	\int\:5x\cdot\:\cos(8x)dx
derivative of-sin^2(x)	\frac{d}{dx}(-\sin^{2}(x))
(\partial)/(\partial y)(2ln(y))	\frac{\partial\:}{\partial\:y}(2\ln(y))
integral of 1/(9x-5)	\int\:\frac{1}{9x-5}dx
tangent of sin(7x)-cos(4x)	tangent\:\sin(7x)-\cos(4x)
derivative of h(x)= 1/(x^5)	derivative\:h(x)=\frac{1}{x^{5}}
(\partial)/(\partial x)(pixsqrt(x^2+h^2))	\frac{\partial\:}{\partial\:x}(πx\sqrt{x^{2}+h^{2}})
integral of ((e^x-e^{-x}))/2	\int\:\frac{(e^{x}-e^{-x})}{2}dx
simplify x^2-25ln(x^2)	simplify\:x^{2}-25\ln(x^{2})
laplacetransform 2e^{-t}	laplacetransform\:2e^{-t}
derivative of f(x)=-9x^{-1/9}	derivative\:f(x)=-9x^{-\frac{1}{9}}
limit as x approaches-infinity of 1-e^x	\lim\:_{x\to\:-\infty\:}(1-e^{x})
derivative of (x^3-8)^{2/3}	derivative\:(x^{3}-8)^{\frac{2}{3}}
d/(da)(sin(a)+sin(2a)+sin(3a))	\frac{d}{da}(\sin(a)+\sin(2a)+\sin(3a))
inverse oflaplace-(5s)/((s^2+1)^2)	inverselaplace\:-\frac{5s}{(s^{2}+1)^{2}}
integral of (x+1)(x+3)	\int\:(x+1)(x+3)dx
inverse oflaplace (-0.1s)/(s^2-9.8)	inverselaplace\:\frac{-0.1s}{s^{2}-9.8}
derivative of y= 4/3 (x+1)^{3/2}	derivative\:y=\frac{4}{3}(x+1)^{\frac{3}{2}}
integral from 0 to-0.5 of 150x	\int\:_{0}^{-0.5}150xdx
derivative of (x^2+5)^2(x-5)	derivative\:(x^{2}+5)^{2}(x-5)
integral of 6x^2+16x-10	\int\:6x^{2}+16x-10dx
(\partial)/(\partial y)(sin(pi(5x-2y)))	\frac{\partial\:}{\partial\:y}(\sin(π(5x-2y)))
integral of cosh^2(x)	\int\:\cosh^{2}(x)dx
integral of ye^{-3y}	\int\:ye^{-3y}dy
derivative of (x^2+3x^4)	\frac{d}{dx}((x^{2}+3x)^{4})
derivative of X^{1/5}	derivative\:X^{\frac{1}{5}}
integral of 2/(e^x+e^{-x)}	\int\:\frac{2}{e^{x}+e^{-x}}dx
integral of 6cos(sqrt(8x))	\int\:6\cos(\sqrt{8x})dx
derivative of 1/z	derivative\:\frac{1}{z}
integral of (3x^2-2x+5)	\int\:(3x^{2}-2x+5)dx
f(x)=-3/x	f(x)=-\frac{3}{x}
y^{''}-5y^'+6y=cos(x)e^{-x}	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=\cos(x)e^{-x}
integral of (sin(2x))/(32+cos^2(x))	\int\:\frac{\sin(2x)}{32+\cos^{2}(x)}dx
(dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200	\frac{dP}{dt}=0.16P(1-\frac{P}{1000})-30,P(0)=200
derivative of 6cos(t)-2sin(t)	derivative\:6\cos(t)-2\sin(t)
slope of f(t)=t^3-27t+5	slope\:f(t)=t^{3}-27t+5
integral from 0 to 1 of 5/(sqrt(4-x^2))	\int\:_{0}^{1}\frac{5}{\sqrt{4-x^{2}}}dx
tangent of y=ln(x^4-4095),(8,0)	tangent\:y=\ln(x^{4}-4095),(8,0)
integral of-sec(x)tan(x)	\int\:-\sec(x)\tan(x)dx
derivative of ln(x+sqrt(x^2-9))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}-9}))
derivative of (x+1/(x^3+x-2))	\frac{d}{dx}(\frac{x+1}{x^{3}+x-2})
derivative of xln(5x)	\frac{d}{dx}(x\ln(5x))
tangent of 3x^2-4x+6,\at x=2	tangent\:3x^{2}-4x+6,\at\:x=2
y^{''}+4y=0,y(0)=1,y(1)=0	y^{\prime\:\prime\:}+4y=0,y(0)=1,y(1)=0
d/(dt)(ae^tcos(2t)+be^tsin(2t))	\frac{d}{dt}(ae^{t}\cos(2t)+be^{t}\sin(2t))
limit as x approaches 0 of (1+x)^2-1	\lim\:_{x\to\:0}((1+x)^{2}-1)
limit as x approaches 1 of sqrt(6x^2+1)	\lim\:_{x\to\:1}(\sqrt{6x^{2}+1})
limit as x approaches 1 of \sqrt[3]{x}-1	\lim\:_{x\to\:1}(\sqrt[3]{x}-1)
integral of 1/(4+v^2)	\int\:\frac{1}{4+v^{2}}dv
f(x)=(sqrt(1-x^2))/x	f(x)=\frac{\sqrt{1-x^{2}}}{x}
derivative of y=10csc(5x^5-4x+4)	derivative\:y=10\csc(5x^{5}-4x+4)
integral of (3x^2)/((1-x)(x^2+x+1))	\int\:\frac{3x^{2}}{(1-x)(x^{2}+x+1)}dx
limit as x approaches 4 of-x^2+6x-3	\lim\:_{x\to\:4}(-x^{2}+6x-3)
sum from n=0 to infinity of x^{2n+1}	\sum\:_{n=0}^{\infty\:}x^{2n+1}
derivative of 1/(sqrt(1-2x))	\frac{d}{dx}(\frac{1}{\sqrt{1-2x}})
derivative of y=xsin(x)+2	derivative\:y=x\sin(x)+2
x^{''}-x^'-6x=6e^{3t}+2e^{-2t}	x^{\prime\:\prime\:}-x^{\prime\:}-6x=6e^{3t}+2e^{-2t}
limit as x approaches 0 of (sec(x-1))/(xsec(x))	\lim\:_{x\to\:0}(\frac{\sec(x-1)}{x\sec(x)})
integral of e^{kt}	\int\:e^{kt}dt
(\partial)/(\partial x)((5x^3y+4y^5)^3)	\frac{\partial\:}{\partial\:x}((5x^{3}y+4y^{5})^{3})
(dy)/(dx)+4y-e^{-x}=0,y(0)= 4/3	\frac{dy}{dx}+4y-e^{-x}=0,y(0)=\frac{4}{3}
laplacetransform sin^2(6t)	laplacetransform\:\sin^{2}(6t)
derivative of e^{1/x}-(e^{1/x}/x)	\frac{d}{dx}(e^{\frac{1}{x}}-\frac{e^{\frac{1}{x}}}{x})
derivative of sqrt(x^3+x^5)	\frac{d}{dx}(\sqrt{x^{3}+x^{5}})
derivative of-5cot(x+3sec(x))	\frac{d}{dx}(-5\cot(x)+3\sec(x))
integral of x/(sqrt(2-x^2))	\int\:\frac{x}{\sqrt{2-x^{2}}}dx
limit as x approaches infinity of 7x-3	\lim\:_{x\to\:\infty\:}(7x-3)
(\partial)/(\partial x)((x^2)/(x^2+1))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{x^{2}+1})

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