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Popular Calculus Problems

derivative of x/(a^2sqrt(a^2+x^2))	\frac{d}{dx}(\frac{x}{a^{2}\sqrt{a^{2}+x^{2}}})
derivative of 25ln(x^2-x^2)	\frac{d}{dx}(25\ln(x^{2})-x^{2})
(d^2)/(dx^2)((x^2+4)^5)	\frac{d^{2}}{dx^{2}}((x^{2}+4)^{5})
integral from 1 to 4 of x	\int\:_{1}^{4}xdx
integral of e^{-5x}x	\int\:e^{-5x}xdx
implicit (dy)/(dx),x^{2/3}+y^{2/3}=3	implicit\:\frac{dy}{dx},x^{\frac{2}{3}}+y^{\frac{2}{3}}=3
integral of ((x^2-2x))/((x-1)^2)	\int\:\frac{(x^{2}-2x)}{(x-1)^{2}}dx
integral of x^6ln(x)	\int\:x^{6}\ln(x)dx
integral of e^{3-x}	\int\:e^{3-x}dx
(\partial)/(\partial z)(xe^{y/z})	\frac{\partial\:}{\partial\:z}(xe^{\frac{y}{z}})
derivative of e^{cos(x}*sin(x^2-x))	\frac{d}{dx}(e^{\cos(x)}\cdot\:\sin(x^{2}-x))
area 2x^2,2x+6,-1.3,2.3	area\:2x^{2},2x+6,-1.3,2.3
inverse oflaplace s/(s^2+10s+25)	inverselaplace\:\frac{s}{s^{2}+10s+25}
limit as x approaches 0 of 5/x-5/(x^2+x)	\lim\:_{x\to\:0}(\frac{5}{x}-\frac{5}{x^{2}+x})
limit as t approaches 1 of sqrt(t+3)	\lim\:_{t\to\:1}(\sqrt{t+3})
tangent of f(x)=2x^2-5x+3	tangent\:f(x)=2x^{2}-5x+3
limit as x approaches 0+of ln(1+sqrt(x))	\lim\:_{x\to\:0+}(\ln(1+\sqrt{x}))
tangent of y=5tan(x),(pi/4 ,5)	tangent\:y=5\tan(x),(\frac{π}{4},5)
tangent of f(x)= 2/x ,(-4,-1/2)	tangent\:f(x)=\frac{2}{x},(-4,-\frac{1}{2})
derivative of x^2(x+3^4)	\frac{d}{dx}(x^{2}(x+3)^{4})
sum from n=1 to infinity of (5^n)/(6^nn)	\sum\:_{n=1}^{\infty\:}\frac{5^{n}}{6^{n}n}
xy^'+y=3xy	xy^{\prime\:}+y=3xy
integral of (x^2+7x-3)sin(2x)	\int\:(x^{2}+7x-3)\sin(2x)dx
integral of 3/(x(x^2+1))	\int\:\frac{3}{x(x^{2}+1)}dx
derivative of \|(-3^x\|)	\frac{d}{dx}(\left\|(-3)^{x}\right\|)
y^'x^2+yx^2=xy^5	y^{\prime\:}x^{2}+yx^{2}=xy^{5}
derivative of f(x)= 1/2	derivative\:f(x)=\frac{1}{2}
derivative of (2x^2-1)/(x+1)	derivative\:\frac{2x^{2}-1}{x+1}
derivative of t^3	derivative\:t^{3}
derivative of f(x)=20x+(420)/x	derivative\:f(x)=20x+\frac{420}{x}
derivative of f(x)=2x^2+1	derivative\:f(x)=2x^{2}+1
integral of 1/((x-3)sqrt(x^2)-6x)	\int\:\frac{1}{(x-3)\sqrt{x^{2}}-6x}dx
integral of x^7ln(5x)	\int\:x^{7}\ln(5x)dx
integral of (x^4)/(x^3-1)	\int\:\frac{x^{4}}{x^{3}-1}dx
integral from-pi to pi of sin(nx)	\int\:_{-π}^{π}\sin(nx)dx
laplacetransform e^t(t+5)^3	laplacetransform\:e^{t}(t+5)^{3}
(\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2})	\frac{\partial\:^{2}}{\partial\:{h}(w)\partial\:w}(\frac{w}{{h}(w)(w)^{2}})
inverse oflaplace (5e^{-s})/(4s^2+36)	inverselaplace\:\frac{5e^{-s}}{4s^{2}+36}
derivative of-2cos(x/2)	derivative\:-2\cos(\frac{x}{2})
limit as x approaches infinity of arctan(4x)	\lim\:_{x\to\:\infty\:}(\arctan(4x))
tangent of f(x)=ln(3x+4),(2,ln(10))	tangent\:f(x)=\ln(3x+4),(2,\ln(10))
laplacetransform-5cos(3t)	laplacetransform\:-5\cos(3t)
derivative of f(t)=2t^3+t	derivative\:f(t)=2t^{3}+t
(\partial)/(\partial x)((xy)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{xy}{x+y})
derivative of f(x)=ln(6-x^2)	derivative\:f(x)=\ln(6-x^{2})
(\partial)/(\partial x)(xcos(y)-ysin(x))	\frac{\partial\:}{\partial\:x}(x\cos(y)-y\sin(x))
tangent of y=(2x)/(x^2+1),(-1,-1)	tangent\:y=\frac{2x}{x^{2}+1},(-1,-1)
limit as x approaches 1 of ((5-5x))/(1-sqrt(x))	\lim\:_{x\to\:1}(\frac{(5-5x)}{1-\sqrt{x}})
x(dy)/(dx)-y=0,y(a)=b	x\frac{dy}{dx}-y=0,y(a)=b
y^'+2xy=x	y^{\prime\:}+2xy=x
integral of-xarctan(x)	\int\:-x\arctan(x)dx
integral from 0 to 1 of sqrt(x^2+1)	\int\:_{0}^{1}\sqrt{x^{2}+1}dx
(\partial)/(\partial y)(cos(x+y^2))	\frac{\partial\:}{\partial\:y}(\cos(x+y^{2}))
(\partial)/(\partial x)(2ye^{4x})	\frac{\partial\:}{\partial\:x}(2ye^{4x})
integral of (80-3t-(2t+30))	\int\:(80-3t-(2t+30))dt
derivative of (x-x^2/(2-3x+x^2))	\frac{d}{dx}(\frac{x-x^{2}}{2-3x+x^{2}})
integral from 0 to ln(6) of e^x-e^{-3x}	\int\:_{0}^{\ln(6)}e^{x}-e^{-3x}dx
derivative of y=(4x)/(9-tan(x))	derivative\:y=\frac{4x}{9-\tan(x)}
derivative of arctan(x)	derivative\:\arctan(x)
integral from 0 to 1 of (xsqrt(2-x^2))	\int\:_{0}^{1}(x\sqrt{2-x^{2}})dx
tangent of y= x/((1+x^2),\at (3,0.3))	tangent\:y=\frac{x}{(1+x^{2}),\at\:(3,0.3)}
derivative of sqrt(1+4sin(x))	\frac{d}{dx}(\sqrt{1+4\sin(x)})
integral of-2ysqrt(-y^2+2)	\int\:-2y\sqrt{-y^{2}+2}dy
tangent of f(x)=1-7x^2,(-2,-27)	tangent\:f(x)=1-7x^{2},(-2,-27)
(\partial)/(\partial x)(e^{xy}+x/y)	\frac{\partial\:}{\partial\:x}(e^{xy}+\frac{x}{y})
y^{''}+13y^'+42y=0	y^{\prime\:\prime\:}+13y^{\prime\:}+42y=0
y^{''}+4y=0,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+4y=0,y(0)=0,y^{\prime\:}(0)=0
integral of (x^6)/6	\int\:\frac{x^{6}}{6}dx
integral from 2 to 8 of x	\int\:_{2}^{8}xdx
integral of cos^3(xsi)n^4x	\int\:\cos^{3}(xsi)n^{4}xdx
integral of (x^3)/(324)	\int\:\frac{x^{3}}{324}dx
integral from 0 to infinity of x/(1+x^3)	\int\:_{0}^{\infty\:}\frac{x}{1+x^{3}}dx
limit as x approaches 4 of x^2	\lim\:_{x\to\:4}(x^{2})
9y^{''}+4y=0	9y^{\prime\:\prime\:}+4y=0
y^{''}+4y=x^2+3e^x,y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+4y=x^{2}+3e^{x},y(0)=0,y^{\prime\:}(0)=2
derivative of sqrt(2-4x)	derivative\:\sqrt{2-4x}
integral of 9sin(sqrt(x))	\int\:9\sin(\sqrt{x})dx
integral from 0 to 2 of 2pix(x^2)	\int\:_{0}^{2}2πx(x^{2})dx
derivative of e^{x*cos(x})	\frac{d}{dx}(e^{x\cdot\:\cos(x)})
integral from 0 to 6 of pi(2x)^2	\int\:_{0}^{6}π(2x)^{2}dx
derivative of ln(sqrt((x^2/(x+1))))	\frac{d}{dx}(\ln(\sqrt{\frac{x^{2}}{x+1}}))
integral of ((cos(x)))/(((sin^2(x))^{1/3))}	\int\:\frac{(\cos(x))}{((\sin^{2}(x))^{\frac{1}{3}})}dx
d/(dt)(t^2+4t)	\frac{d}{dt}(t^{2}+4t)
y^'+10y=1	y^{\prime\:}+10y=1
limit as x approaches 0 of 2+(3/x)	\lim\:_{x\to\:0}(2+(\frac{3}{x}))
(\partial)/(\partial y)(xy+1/x+1/y)	\frac{\partial\:}{\partial\:y}(xy+\frac{1}{x}+\frac{1}{y})
integral of tan^3(10x)	\int\:\tan^{3}(10x)dx
integral of (5x-3)/(x^2-2x-3)	\int\:\frac{5x-3}{x^{2}-2x-3}dx
(\partial)/(\partial x)((x+y)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{x-y})
derivative of sin(cos(4x))	\frac{d}{dx}(\sin(\cos(4x)))
derivative of 1/(5x^{4/5)}	derivative\:\frac{1}{5x^{\frac{4}{5}}}
derivative of f(x)=(x^3+1)/(x^3-1)	derivative\:f(x)=\frac{x^{3}+1}{x^{3}-1}
x^3y^{'''}+xy^'-y=0	x^{3}y^{\prime\:\prime\:\prime\:}+xy^{\prime\:}-y=0
integral of e^{-1}	\int\:e^{-1}
derivative of f(x)=(2ln(x))/x	derivative\:f(x)=\frac{2\ln(x)}{x}
(\partial)/(\partial x)(2x(4+y)^{-1})	\frac{\partial\:}{\partial\:x}(2x(4+y)^{-1})
derivative of-2(e^xsin(x+cos(x)e^x))	\frac{d}{dx}(-2(e^{x}\sin(x)+\cos(x)e^{x}))
integral of 1/(5+2x^4)(8x^3)	\int\:\frac{1}{5+2x^{4}}(8x^{3})dx
derivative of 8sin(x-4sqrt(2x))	\frac{d}{dx}(8\sin(x)-4\sqrt{2x})
derivative of 1/(\sqrt[5]{x^2})	\frac{d}{dx}(\frac{1}{\sqrt[5]{x^{2}}})

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