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Popular Calculus Problems

f(x)=x^6ln(x)	f(x)=x^{6}\ln(x)
(\partial)/(\partial y)(x^2ye^{y/z})	\frac{\partial\:}{\partial\:y}(x^{2}ye^{\frac{y}{z}})
(\partial)/(\partial x)(3xsin(7x^2y))	\frac{\partial\:}{\partial\:x}(3x\sin(7x^{2}y))
(\partial)/(\partial x)(xe^y-ye^x)	\frac{\partial\:}{\partial\:x}(xe^{y}-ye^{x})
integral from 0 to 1 of (3^{3x}-1)/(3^x)	\int\:_{0}^{1}\frac{3^{3x}-1}{3^{x}}dx
derivative of y=(2x+1)+2/((2x+1)^3)	derivative\:y=(2x+1)+\frac{2}{(2x+1)^{3}}
integral from-1 to 1 of x(1-x)^2	\int\:_{-1}^{1}x(1-x)^{2}dx
limit as x approaches 0+of 1/(sin^2(x))	\lim\:_{x\to\:0+}(\frac{1}{\sin^{2}(x)})
derivative of (24x(x^2+1)/((1-x^2)^4))	\frac{d}{dx}(\frac{24x(x^{2}+1)}{(1-x^{2})^{4}})
integral of (x^2ln(x))/2	\int\:\frac{x^{2}\ln(x)}{2}dx
sum from n=0 to infinity of (n^2)/(e^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}}{e^{n}}
integral from 0 to pi of (cos(x))^6	\int\:_{0}^{π}(\cos(x))^{6}dx
integral from 2 to 4 of 2cos(pix)	\int\:_{2}^{4}2\cos(πx)dx
integral of (-1)/(1-2x+x^2)	\int\:\frac{-1}{1-2x+x^{2}}dx
limit as x approaches 0 of e^{csc(x)}	\lim\:_{x\to\:0}(e^{\csc(x)})
derivative of f(x)=(4x)/(9e^{5x)}	derivative\:f(x)=\frac{4x}{9e^{5x}}
slope ofintercept (5,-2),(-6,4)	slopeintercept\:(5,-2),(-6,4)
integral of sqrt(4x+3)	\int\:\sqrt{4x+3}dx
2xydy=(y^2+1)dx	2xydy=(y^{2}+1)dx
derivative of (3x/7)	\frac{d}{dx}(\frac{3x}{7})
integral of (175)/(e^{-x)+1}	\int\:\frac{175}{e^{-x}+1}dx
derivative of ln(7x^2)	\frac{d}{dx}(\ln(7)x^{2})
derivative of f(x)=(3x+1)(x^2-2)	derivative\:f(x)=(3x+1)(x^{2}-2)
integral of 4/(sqrt(x^2-4x+13))	\int\:\frac{4}{\sqrt{x^{2}-4x+13}}dx
integral from 0 to 5 of 1/(x-3)	\int\:_{0}^{5}\frac{1}{x-3}dx
limit as x approaches 2 of x^2-7x+12	\lim\:_{x\to\:2}(x^{2}-7x+12)
limit as x approaches 0 of (9sin(1))/1	\lim\:_{x\to\:0}(\frac{9\sin(1)}{1})
(dy)/(dx)+2xy=9x	\frac{dy}{dx}+2xy=9x
limit as x approaches 1 of (3x-1)^{10}	\lim\:_{x\to\:1}((3x-1)^{10})
integral of acos(wt)	\int\:a\cos(wt)dt
derivative of (x-3^3(x+4)(x^2+1))	\frac{d}{dx}((x-3)^{3}(x+4)(x^{2}+1))
tangent of y=x-x^3	tangent\:y=x-x^{3}
integral of (cos(x))^5	\int\:(\cos(x))^{5}dx
(\partial)/(\partial y)((x-y)/(x+z))	\frac{\partial\:}{\partial\:y}(\frac{x-y}{x+z})
(dy)/(dx)=7xsqrt(y)	\frac{dy}{dx}=7x\sqrt{y}
limit as x approaches 0 of 3x+4	\lim\:_{x\to\:0}(3x+4)
integral of (cos^3(x)+4)/(cos^2(x))	\int\:\frac{\cos^{3}(x)+4}{\cos^{2}(x)}dx
integral of 3sin^2(x)cos^2(x)	\int\:3\sin^{2}(x)\cos^{2}(x)dx
(\partial)/(\partial y)((-x-7y)/(y^2+2x^2))	\frac{\partial\:}{\partial\:y}(\frac{-x-7y}{y^{2}+2x^{2}})
integral of 1/(sqrt(x)(1+\sqrt{x))^2}	\int\:\frac{1}{\sqrt{x}(1+\sqrt{x})^{2}}dx
limit as x approaches 4 of (-x+4)/x	\lim\:_{x\to\:4}(\frac{-x+4}{x})
derivative of e^{2x}(x-4(x+6))	\frac{d}{dx}(e^{2x}(x-4)(x+6))
integral of 2sqrt(x^3)	\int\:2\sqrt{x^{3}}dx
(2/t)^'	(\frac{2}{t})^{\prime\:}
maclaurin 1/(5x+7)	maclaurin\:\frac{1}{5x+7}
integral of 1/(x^2-3)	\int\:\frac{1}{x^{2}-3}dx
y^'=x+3y	y^{\prime\:}=x+3y
derivative of (1-2x)^{1/2}	derivative\:(1-2x)^{\frac{1}{2}}
integral of ((1+cos(2x))/2)^2	\int\:(\frac{1+\cos(2x)}{2})^{2}dx
derivative of cos(ln(t))	derivative\:\cos(\ln(t))
x(dy)/(dx)+4y=x^{-3}e^x	x\frac{dy}{dx}+4y=x^{-3}e^{x}
integral of x/2	\int\:\frac{x}{2}dx
(\partial)/(\partial x)(2x^3y+3xy^2)	\frac{\partial\:}{\partial\:x}(2x^{3}y+3xy^{2})
integral of 2y^{3/2}	\int\:2y^{\frac{3}{2}}dy
integral of tan(8x+1)	\int\:\tan(8x+1)dx
integral of (3arctan(x))/(x^2)	\int\:\frac{3\arctan(x)}{x^{2}}dx
(\partial)/(\partial x)((e^x-2x)cos(y))	\frac{\partial\:}{\partial\:x}((e^{x}-2x)\cos(y))
(dy)/(dx)+ay-b=0	\frac{dy}{dx}+ay-b=0
tangent of f(x)=5x^2-4x-2,\at x=1	tangent\:f(x)=5x^{2}-4x-2,\at\:x=1
ty^'+10y= 1/t	ty^{\prime\:}+10y=\frac{1}{t}
integral of 7(cos(x)+sin(2x))/(sin(x))	\int\:7\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
derivative of 1-e^{-2x}	derivative\:1-e^{-2x}
limit as x approaches 8 of e(3/((x-8)))	\lim\:_{x\to\:8}(e(\frac{3}{(x-8)}))
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
(\partial)/(\partial x)(x^2y^3-1)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}-1)
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}))
(\partial)/(\partial y)(-e^xln(y))	\frac{\partial\:}{\partial\:y}(-e^{x}\ln(y))
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
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

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