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Popular Calculus Problems

integral of cosh(4x)	\int\:\cosh(4x)dx
(dr)/(dt)=((1+e^t)^2)/(e^{3t)}	\frac{dr}{dt}=\frac{(1+e^{t})^{2}}{e^{3t}}
integral of x^2*e^{-4x}	\int\:x^{2}\cdot\:e^{-4x}dx
integral of sec(4x)tan(4x)	\int\:\sec(4x)\tan(4x)dx
slope of y= 1/(x-3)	slope\:y=\frac{1}{x-3}
(\partial)/(\partial x)(x^2y^3-1)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}-1)
tangent of f(x)=(x^4+2x)^3,\at x=2	tangent\:f(x)=(x^{4}+2x)^{3},\at\:x=2
derivative of 4e^{x+2}+e^{-3}	derivative\:4e^{x+2}+e^{-3}
xy^'+y=y^2,y(1)=-15	xy^{\prime\:}+y=y^{2},y(1)=-15
area y=28-x^2,y=3x,y= 3/5 x	area\:y=28-x^{2},y=3x,y=\frac{3}{5}x
integral of (16/2 x^3+12x^5-2x+1)	\int\:(\frac{16}{2}x^{3}+12x^{5}-2x+1)dx
derivative of f(x)=5e^x(cos(x)-sin(x))	derivative\:f(x)=5e^{x}(\cos(x)-\sin(x))
(\partial)/(\partial x)((x^2+y^2)^{0.5})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{0.5})
y^{''}=1	y^{\prime\:\prime\:}=1
derivative of f(2)=x^3-2x	derivative\:f(2)=x^{3}-2x
limit as x approaches 2-of x+7	\lim\:_{x\to\:2-}(x+7)
(\partial)/(\partial x)(20-(3x^2+y^2))	\frac{\partial\:}{\partial\:x}(20-(3x^{2}+y^{2}))
derivative of (5x/2)	\frac{d}{dx}(\frac{5x}{2})
(\partial)/(\partial y)(-e^xln(y))	\frac{\partial\:}{\partial\:y}(-e^{x}\ln(y))
tangent of y=sin(sin(x)),(pi,0)	tangent\:y=\sin(\sin(x)),(π,0)
derivative of (8x^2/(2x-10))	\frac{d}{dx}(\frac{8x^{2}}{2x-10})
derivative of x/t	\frac{d}{dx}(\frac{x}{t})
limit as 5 approaches 1 of (1/5)/(5-1)	\lim\:_{5\to\:1}(\frac{\frac{1}{5}}{5-1})
area y= 8/x ,y=2x,x=4	area\:y=\frac{8}{x},y=2x,x=4
derivative of (3x^2-5x^9(-2x^4+2x-8)^4)	\frac{d}{dx}((3x^{2}-5x)^{9}(-2x^{4}+2x-8)^{4})
(d^2y)/(dx^2)=k	\frac{d^{2}y}{dx^{2}}=k
derivative of (5x^2/(x+47))	\frac{d}{dx}(\frac{5x^{2}}{x+47})
y^'=x^2-y-2,y(0)=-1	y^{\prime\:}=x^{2}-y-2,y(0)=-1
(\partial)/(\partial y)(2xy+y)	\frac{\partial\:}{\partial\:y}(2xy+y)
laplacetransform e^2	laplacetransform\:e^{2}
derivative of f(x)=-x^2+3x	derivative\:f(x)=-x^{2}+3x
derivative of cx^{-1}	\frac{d}{dx}(cx^{-1})
integral of x^{1/a}	\int\:x^{\frac{1}{a}}dx
tangent of f(x)=3x^3-x^2+5,(2,25)	tangent\:f(x)=3x^{3}-x^{2}+5,(2,25)
y^'+4xy=x^3e^{x^2}	y^{\prime\:}+4xy=x^{3}e^{x^{2}}
dx=4(x^2+1)dt	dx=4(x^{2}+1)dt
inverse oflaplace 1/((s+5))	inverselaplace\:\frac{1}{(s+5)}
inverse oflaplace 1/(5s-2)	inverselaplace\:\frac{1}{5s-2}
integral of (x^2)/(2x)	\int\:\frac{x^{2}}{2x}dx
integral of c^x	\int\:c^{x}dx
limit as x approaches-2 of 4x^2+3x-1	\lim\:_{x\to\:-2}(4x^{2}+3x-1)
integral of (6x^2-3x+5)	\int\:(6x^{2}-3x+5)dx
slope ofintercept (-1,2),(1,-1)	slopeintercept\:(-1,2),(1,-1)
integral of 2x^5y+3x^4y^2	\int\:2x^{5}y+3x^{4}y^{2}dy
(\partial)/(\partial x)(sqrt(xyz))	\frac{\partial\:}{\partial\:x}(\sqrt{xyz})
integral of e^{-2x}(1-2x)	\int\:e^{-2x}(1-2x)dx
derivative of 2^{0.25}	\frac{d}{dx}(2^{0.25})
derivative of sin(7x+cos(2x))	\frac{d}{dx}(\sin(7x)+\cos(2x))
(\partial)/(\partial x)((e^v)/(u(v,x)+v^9))	\frac{\partial\:}{\partial\:x}(\frac{e^{v}}{u(v,x)+v^{9}})
limit as x approaches-1 of-x^2+7x-8	\lim\:_{x\to\:-1}(-x^{2}+7x-8)
sum from n=1 to infinity of 2e^{-8n}	\sum\:_{n=1}^{\infty\:}2e^{-8n}
derivative of-6/(x^2)	derivative\:-\frac{6}{x^{2}}
derivative of x^5ln(8x)	\frac{d}{dx}(x^{5}\ln(8x))
integral of (5x^2)/((49+x^2)^2)	\int\:\frac{5x^{2}}{(49+x^{2})^{2}}dx
tangent of y=(2x)/(x-1),(-1,1)	tangent\:y=\frac{2x}{x-1},(-1,1)
derivative of x^{ax}	\frac{d}{dx}(x^{ax})
derivative of xsqrt(x^2+4)	\frac{d}{dx}(x\sqrt{x^{2}+4})
integral of (2x+2)	\int\:(2x+2)dx
(\partial)/(\partial x)(x^2+y^2+x+y+xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+x+y+xy)
integral of sqrt(6x-x^2)	\int\:\sqrt{6x-x^{2}}dx
derivative of f(x)=(2x^3+4x+1)	derivative\:f(x)=(2x^{3}+4x+1)
integral of (4+4tan^2(v))	\int\:(4+4\tan^{2}(v))dv
(sin(x/2))^'	(\sin(\frac{x}{2}))^{\prime\:}
(\partial)/(\partial x)(xy^2+ye^{x^2}+5)	\frac{\partial\:}{\partial\:x}(xy^{2}+ye^{x^{2}}+5)
(dy)/(dx)+2xy=2x^3,y(0)=2	\frac{dy}{dx}+2xy=2x^{3},y(0)=2
integral of 1n(x)	\int\:1d\ln(x)dx
(dy)/(dx)+y=xy^2	\frac{dy}{dx}+y=xy^{2}
derivative of y=ln(t^2)-arctan(t/3)	derivative\:y=\ln(t^{2})-\arctan(\frac{t}{3})
derivative of (t+1710)/(50(t+2))	derivative\:\frac{t+1710}{50(t+2)}
inverse oflaplace-2/(s^3(s-3))	inverselaplace\:-\frac{2}{s^{3}(s-3)}
integral from 0 to N of e^{-st}e^{-2t}	\int\:_{0}^{N}e^{-st}e^{-2t}dt
tangent of f(x)=(x^2+3x-5)(1-x),\at x=2	tangent\:f(x)=(x^{2}+3x-5)(1-x),\at\:x=2
derivative of (3x)/(x+1)	derivative\:\frac{3x}{x+1}
integral of 1/(sqrt(2x^2-3))	\int\:\frac{1}{\sqrt{2x^{2}-3}}dx
integral from 0 to 1 of (x^2+2x+3)e^{2x}	\int\:_{0}^{1}(x^{2}+2x+3)e^{2x}dx
derivative of y=ln(x^4(x))	derivative\:y=\ln(x^{4}(x))
derivative of f(x)=3x-x^2	derivative\:f(x)=3x-x^{2}
derivative of 1/(ln(ln(ln(x))))	\frac{d}{dx}(\frac{1}{\ln(\ln(\ln(x)))})
f(x)=(2x^{-2}+3)^{-3}	f(x)=(2x^{-2}+3)^{-3}
derivative of tan(2t)	derivative\:\tan(2t)
derivative of e^x(sin(x))	\frac{d}{dx}(e^{x}(\sin(x)))
laplacetransform 3sin(t)cos(t)	laplacetransform\:3\sin(t)\cos(t)
inverse oflaplace 3/(s^3)	inverselaplace\:\frac{3}{s^{3}}
y^'+10x^4y=50x^9e^{3x^5}	y^{\prime\:}+10x^{4}y=50x^{9}e^{3x^{5}}
integral of 4sin^3(2x)	\int\:4\sin^{3}(2x)dx
integral of 13-x	\int\:13-xdx
limit as x approaches-1 of 4/(x^2+2x+3)	\lim\:_{x\to\:-1}(\frac{4}{x^{2}+2x+3})
integral of (pisin(x)+sqrt(2)cos(x))	\int\:(π\sin(x)+\sqrt{2}\cos(x))dx
integral of sqrt(3-x)*x^2	\int\:\sqrt{3-x}\cdot\:x^{2}dx
integral of (3xsqrt(4x^2-6))/5	\int\:\frac{3x\sqrt{4x^{2}-6}}{5}dx
integral from 1 to infinity of y/(y^4+1)	\int\:_{1}^{\infty\:}\frac{y}{y^{4}+1}dy
taylor e^{9x}	taylor\:e^{9x}
derivative of f(t)=sin^2(t)	derivative\:f(t)=\sin^{2}(t)
derivative of (x^3)/2	derivative\:\frac{x^{3}}{2}
integral of 8	\int\:8dx
integral of 50x^9e^{5x^5}	\int\:50x^{9}e^{5x^{5}}dx
derivative of (x^2/(sin^2(x)))	\frac{d}{dx}(\frac{x^{2}}{\sin^{2}(x)})
limit as x approaches 3-of (\|3-x\|)/(x-3)	\lim\:_{x\to\:3-}(\frac{\left\|3-x\right\|}{x-3})
(\partial)/(\partial x)(2x^2-6y^3+3z^2)	\frac{\partial\:}{\partial\:x}(2x^{2}-6y^{3}+3z^{2})
integral of sin^4(x)cos^5(x)	\int\:\sin^{4}(x)\cos^{5}(x)dx

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