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Popular Calculus Problems

derivative of xy^2-x^2y+xy	\frac{d}{dx}(xy^{2}-x^{2}y+xy)
integral of (x^3)/((x^2-256)^{3/2)}	\int\:\frac{x^{3}}{(x^{2}-256)^{\frac{3}{2}}}dx
slope of (0,-10),(6,10)	slope\:(0,-10),(6,10)
taylor 1/x ,\at 1	taylor\:\frac{1}{x},\at\:1
integral of e^{ipiz}	\int\:e^{iπz}dz
derivative of f(t)=sqrt(t)-1/(sqrt(t))	derivative\:f(t)=\sqrt{t}-\frac{1}{\sqrt{t}}
integral of (sec(x)tan(x))/(sec(x)-2)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)-2}dx
derivative of (2x^3)/3+(x^2)/2+6x+6	derivative\:\frac{2x^{3}}{3}+\frac{x^{2}}{2}+6x+6
limit as x approaches 2 of ln(x)	\lim\:_{x\to\:2}(\ln(x))
limit as x approaches 58 of (sqrt(x+6)-8)/(x-58)	\lim\:_{x\to\:58}(\frac{\sqrt{x+6}-8}{x-58})
derivative of y=2xe^{-kx}	derivative\:y=2xe^{-kx}
integral from 0 to 1 of sqrt(1-x^2)	\int\:_{0}^{1}\sqrt{1-x^{2}}dx
derivative of cot^2(7x)	\frac{d}{dx}(\cot^{2}(7x))
integral of k/(k-x)	\int\:\frac{k}{k-x}dx
integral of e^{(5x)/6}	\int\:e^{\frac{5x}{6}}dx
integral of 20xe^{-5x}	\int\:20xe^{-5x}dx
(ln(1+x))^'	(\ln(1+x))^{\prime\:}
integral of cos(x)+sec(x)tan(x)	\int\:\cos(x)+\sec(x)\tan(x)dx
integral of (2e^x+4)/(2e^x-4)	\int\:\frac{2e^{x}+4}{2e^{x}-4}dx
integral of 1/(ln(n))	\int\:\frac{1}{\ln(n)}
limit as x approaches+1+of 2/x-1/(ln(x))	\lim\:_{x\to\:+1+}(\frac{2}{x}-\frac{1}{\ln(x)})
(\partial)/(\partial x)(x^2-y^2+z^2-2z-4)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}+z^{2}-2z-4)
integral of-17sin^4(x)cos(x)	\int\:-17\sin^{4}(x)\cos(x)dx
derivative of 5x^{1/3}-5x^{-2/3}	derivative\:5x^{\frac{1}{3}}-5x^{-\frac{2}{3}}
derivative of (x^2+1)^x	derivative\:(x^{2}+1)^{x}
inverse oflaplace (16)/(s(s^2+4s+16))	inverselaplace\:\frac{16}{s(s^{2}+4s+16)}
derivative of (1-y)/(x-1)	derivative\:\frac{1-y}{x-1}
(\partial)/(\partial x)(1+y)	\frac{\partial\:}{\partial\:x}(1+y)
integral of yxe^{xy}	\int\:yxe^{xy}dy
taylor e^{-2x},0	taylor\:e^{-2x},0
d/(d{x)}(ln(sqrt({x)^2+{y}^2+{z}^2}))	\frac{d}{d{x}}(\ln(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}))
(\partial)/(\partial x)((xy)^{0.5})	\frac{\partial\:}{\partial\:x}((xy)^{0.5})
laplacetransform 80t^2	laplacetransform\:80t^{2}
limit as x approaches 0 of ((x-1)^2+1)/x	\lim\:_{x\to\:0}(\frac{(x-1)^{2}+1}{x})
(\partial)/(\partial x)(2x^2y-3)	\frac{\partial\:}{\partial\:x}(2x^{2}y-3)
derivative of y=sqrt(x^3+1)	derivative\:y=\sqrt{x^{3}+1}
derivative of arcsin(x/4)	derivative\:\arcsin(\frac{x}{4})
derivative of cos(2x+sin(2pi))	\frac{d}{dx}(\cos(2x)+\sin(2π))
integral from 1 to t of (25)/(x^3)	\int\:_{1}^{t}\frac{25}{x^{3}}dx
derivative of cos(x+a)	\frac{d}{dx}(\cos(x+a))
inverse oflaplace 7/(s^5)	inverselaplace\:\frac{7}{s^{5}}
integral of (x^2)/((a^2-x^2)^{3/2)}	\int\:\frac{x^{2}}{(a^{2}-x^{2})^{\frac{3}{2}}}dx
limit as x approaches 0 of xInx	\lim\:_{x\to\:0}(xInx)
integral of 3x^2*e^{x^3}	\int\:3x^{2}\cdot\:e^{x^{3}}dx
e^yy^'=e^y+5x,y(3)=7	e^{y}y^{\prime\:}=e^{y}+5x,y(3)=7
integral of 1/(81e^{-3x)+e^{3x}}	\int\:\frac{1}{81e^{-3x}+e^{3x}}dx
derivative of (cos(x)(sin(x)))	\frac{d}{dx}((\cos(x))(\sin(x)))
limit as x approaches 4 of ((5-x))/(x-4)	\lim\:_{x\to\:4}(\frac{(5-x)}{x-4})
integral from-ln(4) to 0 of 4sqrt(3)e^t	\int\:_{-\ln(4)}^{0}4\sqrt{3}e^{t}dt
integral from 0 to x of x^2e^{-x/4}	\int\:_{0}^{x}x^{2}e^{-\frac{x}{4}}dx
limit as x approaches infinity of x-e^x	\lim\:_{x\to\:\infty\:}(x-e^{x})
slope of (3,-4),(5,2)	slope\:(3,-4),(5,2)
integral of (x^2)/(sqrt(1-x^2))	\int\:\frac{x^{2}}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(2g(x)(x^{-2})(D/L))	\frac{\partial\:}{\partial\:x}(2g(x)\cdot\:(x^{-2})\cdot\:(\frac{D}{L}))
tangent of f(x)= 7/(sqrt(x)),\at x=4	tangent\:f(x)=\frac{7}{\sqrt{x}},\at\:x=4
tangent of f(x)=2x^3+4x^2-5x-3,\at x=-1	tangent\:f(x)=2x^{3}+4x^{2}-5x-3,\at\:x=-1
derivative of arctan(e^{3x})	\frac{d}{dx}(\arctan(e^{3x}))
limit as x approaches 5 of 2/(x-5)	\lim\:_{x\to\:5}(\frac{2}{x-5})
derivative of tan(sin(x))	\frac{d}{dx}(\tan(\sin(x)))
integral of 1/(x^2sqrt(3x^2+4))	\int\:\frac{1}{x^{2}\sqrt{3x^{2}+4}}dx
(\partial)/(\partial y)(x/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{2}+y^{2}+z^{2}})
integral from 1 to 5e of 1/(3x)	\int\:_{1}^{5e}\frac{1}{3x}dx
integral of (2-3x)^5	\int\:(2-3x)^{5}dx
sum from n=5 to infinity of sin^2(n)	\sum\:_{n=5}^{\infty\:}\sin^{2}(n)
integral of 4sin(3t)+1.2e^{-6t}	\int\:4\sin(3t)+1.2e^{-6t}dt
tangent of y= 2/x ,(-4,-1/2)	tangent\:y=\frac{2}{x},(-4,-\frac{1}{2})
integral of (3x)/(16-9x^2)	\int\:\frac{3x}{16-9x^{2}}dx
limit as x approaches 0+of xln(x^4)	\lim\:_{x\to\:0+}(x\ln(x^{4}))
integral from-2 to 3 of (26)/(x^4)	\int\:_{-2}^{3}\frac{26}{x^{4}}dx
derivative of 1/(1+x^4)	\frac{d}{dx}(\frac{1}{1+x^{4}})
derivative of 4sec(x-8cos(x))	\frac{d}{dx}(4\sec(x)-8\cos(x))
area y=x^3,y=x,x>= 0	area\:y=x^{3},y=x,x\ge\:0
integral from 0 to 1 of x^9e^{x^5}	\int\:_{0}^{1}x^{9}e^{x^{5}}dx
limit as x approaches 0 of ((ln(cos(2x))))/(x^2)	\lim\:_{x\to\:0}(\frac{(\ln(\cos(2x)))}{x^{2}})
x^2y^{''}+9xy^'-20y= 5/(x^3)	x^{2}y^{\prime\:\prime\:}+9xy^{\prime\:}-20y=\frac{5}{x^{3}}
derivative of f(x)=csc(x)(x+cot(x))	derivative\:f(x)=\csc(x)(x+\cot(x))
derivative of 4x^{5/4}+6x^{3/2}+9x	\frac{d}{dx}(4x^{\frac{5}{4}}+6x^{\frac{3}{2}}+9x)
integral of x^2-y	\int\:x^{2}-ydy
limit as x approaches 0 of (x^2)/(2x)	\lim\:_{x\to\:0}(\frac{x^{2}}{2x})
integral from 0 to 1 of 2pi2/3x*2/3	\int\:_{0}^{1}2π\cdot\:\frac{2}{3}\cdot\:x\cdot\:\frac{2}{3}dx
derivative of ln(8x-5*7^{5x-2})	\frac{d}{dx}(\ln(8x-5)\cdot\:7^{5x-2})
derivative of 5x^2cos(x-4x)	\frac{d}{dx}(5x^{2}\cos(x)-4x)
area y= 4/(1+x^2),y=1	area\:y=\frac{4}{1+x^{2}},y=1
d/(dt)(t^2-2t)	\frac{d}{dt}(t^{2}-2t)
x^'=0.1078(1-x/(105900))x-0.1x	x^{\prime\:}=0.1078\cdot\:(1-\frac{x}{105900})x-0.1\cdot\:x
slope of (2.6)(5.15)	slope\:(2.6)(5.15)
limit as x approaches 0 of arccos(x^2)	\lim\:_{x\to\:0}(\arccos(x^{2}))
integral of-8x+10y-3	\int\:-8x+10y-3dy
integral from 15 to 30 of 6	\int\:_{15}^{30}6dx
derivative of 3/(sqrt(2x+1))	\frac{d}{dx}(\frac{3}{\sqrt{2x+1}})
y^{''}-6y^'+8y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+8y=0
derivative of log_{10}(2x^2+5x+2)	\frac{d}{dx}(\log_{10}(2x^{2}+5x+2))
derivative of (3x-y)/x	derivative\:\frac{3x-y}{x}
(\partial)/(\partial x)(x^{0.2}y^{0.4})	\frac{\partial\:}{\partial\:x}(x^{0.2}y^{0.4})
integral of 1/(sqrt(x^2+4x+20))	\int\:\frac{1}{\sqrt{x^{2}+4x+20}}dx
derivative of f(t)=tsin(pit)	derivative\:f(t)=t\sin(πt)
integral of x^2tan(x^3)	\int\:x^{2}\tan(x^{3})dx
(d^2)/(dx^2)(5cos(2x+10))	\frac{d^{2}}{dx^{2}}(5\cos(2x+10))
limit as q approaches 18 of 0.9q^2-6q+80	\lim\:_{q\to\:18}(0.9q^{2}-6q+80)
derivative of sec(θ)(θ-tan(θ))	derivative\:\sec(θ)(θ-\tan(θ))

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