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Popular Calculus Problems

derivative of sqrt(9x-(sin^2(2x)))	derivative\:\sqrt{9x-(\sin^{2}(2x))}
f(x)=arccsc(x)	f(x)=\arccsc(x)
tangent of f(x)=ln(tan(2x)),\at x= pi/8	tangent\:f(x)=\ln(\tan(2x)),\at\:x=\frac{π}{8}
sum from n=1 to infinity of ((-3)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(-3)^{n}}{n}
y^'-3/x y=(y^4)/(x^2)	y^{\prime\:}-\frac{3}{x}y=\frac{y^{4}}{x^{2}}
derivative of (x^2+1)/(sqrt(x))	derivative\:\frac{x^{2}+1}{\sqrt{x}}
integral of sin(x)cos(n)x	\int\:\sin(x)\cos(n)xdx
y^'= t/(1+t^2)*e^y	y^{\prime\:}=\frac{t}{1+t^{2}}\cdot\:e^{y}
d/(d{r)}(1/({r)^2})	\frac{d}{d{r}}(\frac{1}{{r}^{2}})
d/(dn)((n+1)^n)	\frac{d}{dn}((n+1)^{n})
derivative of f(x)=(sin(5x))/(3x)	derivative\:f(x)=\frac{\sin(5x)}{3x}
integral of 1/(sqrt(1-49x^2))	\int\:\frac{1}{\sqrt{1-49x^{2}}}dx
integral of (x^2-25)/(x-5)	\int\:\frac{x^{2}-25}{x-5}dx
derivative of 7e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(7e^{x}+\frac{2}{\sqrt[3]{x}})
integral from 0 to pi of sec^2(x)	\int\:_{0}^{π}\sec^{2}(x)dx
derivative of y=8arcsin(x/4)-(xsqrt(16-x^2))/2	derivative\:y=8\arcsin(\frac{x}{4})-\frac{x\sqrt{16-x^{2}}}{2}
(\partial)/(\partial x)(e^ycos(x))	\frac{\partial\:}{\partial\:x}(e^{y}\cos(x))
derivative of 1/(1+x+x^2)	\frac{d}{dx}(\frac{1}{1+x+x^{2}})
laplacetransform e^{-2t}sin(t)	laplacetransform\:e^{-2t}\sin(t)
limit as x approaches a of 3/0	\lim\:_{x\to\:a}(\frac{3}{0})
derivative of (-x^2-4)/((x^2-4)^2)	derivative\:\frac{-x^{2}-4}{(x^{2}-4)^{2}}
sum from n=0 to infinity of 1/((1+n^2))	\sum\:_{n=0}^{\infty\:}\frac{1}{(1+n^{2})}
sum from n=0 to infinity of 1/(7^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{7^{n}}
(dy}{dx}=\frac{(x+sec^2(x)))/y	\frac{dy}{dx}=\frac{(x+\sec^{2}(x))}{y}
integral of x/(x^4+16)	\int\:\frac{x}{x^{4}+16}dx
area y=3x^2-12,y=0	area\:y=3x^{2}-12,y=0
derivative of (3+sin(x)/(3x+cos(x)))	\frac{d}{dx}(\frac{3+\sin(x)}{3x+\cos(x)})
area y=e^x,y=e^{-3x},x=-2,x=1	area\:y=e^{x},y=e^{-3x},x=-2,x=1
derivative of e^{3(x-1})	\frac{d}{dx}(e^{3(x-1)})
integral of 3/(2+3x)	\int\:\frac{3}{2+3x}dx
limit as x approaches-3 of (4x)/(x-3)	\lim\:_{x\to\:-3}(\frac{4x}{x-3})
integral of sin(9x)cos(2x)	\int\:\sin(9x)\cos(2x)dx
derivative of f(x)=(x^2)/((3+x))	derivative\:f(x)=\frac{x^{2}}{(3+x)}
taylor e^{1/6 x^6},0	taylor\:e^{\frac{1}{6}x^{6}},0
integral from 1 to 3 of (3-x)^2	\int\:_{1}^{3}(3-x)^{2}dx
integral of 4x^3+2xy^2ln(x^2+y^2)	\int\:4x^{3}+2xy^{2}\ln(x^{2}+y^{2})dx
(x^2-xy)dx+xdy=0	(x^{2}-xy)dx+xdy=0
integral of (x+1)/(x-2)	\int\:\frac{x+1}{x-2}dx
sum from n=0 to infinity of 7/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{7}{5^{n}}
integral of-7sec(2x)tan(2x)	\int\:-7\sec(2x)\tan(2x)dx
integral of (3x)/(x^2+1)	\int\:\frac{3x}{x^{2}+1}dx
derivative of e^{3x-2}	\frac{d}{dx}(e^{3x-2})
integral of cot^3(5x)	\int\:\cot^{3}(5x)dx
integral of (2x^3+7x^2+2x+9)/(2x+3)	\int\:\frac{2x^{3}+7x^{2}+2x+9}{2x+3}dx
y^'-2y=-4y^3	y^{\prime\:}-2y=-4y^{3}
integral of x^3e^2	\int\:x^{3}e^{2}dx
integral of (1+t)^2	\int\:(1+t)^{2}dt
derivative of y=(2x+4)/(1-x)	derivative\:y=\frac{2x+4}{1-x}
(dN)/(dt)+N=Nte^{t+4}	\frac{dN}{dt}+N=Nte^{t+4}
integral from 0 to 1 of x^2e^{x^3}	\int\:_{0}^{1}x^{2}e^{x^{3}}dx
(dy)/(dx)=-0.5y+x	\frac{dy}{dx}=-0.5y+x
limit as x approaches 2pi of 1/(sin(x))	\lim\:_{x\to\:2π}(\frac{1}{\sin(x)})
maclaurin sin(2x)	maclaurin\:\sin(2x)
integral of xsin(4x^2)	\int\:x\sin(4x^{2})dx
limit as x approaches 0 of x^2cos(7/x)	\lim\:_{x\to\:0}(x^{2}\cos(\frac{7}{x}))
derivative of 8^{-3x^2}	\frac{d}{dx}(8^{-3x^{2}})
integral of 3/(\sqrt[4]{2x+5)}	\int\:\frac{3}{\sqrt[4]{2x+5}}dx
limit as x approaches 5+of-ln(5-x)	\lim\:_{x\to\:5+}(-\ln(5-x))
(\partial)/(\partial x)(x^3+3xy^2)	\frac{\partial\:}{\partial\:x}(x^{3}+3xy^{2})
slope of (7,3),(2,-3)	slope\:(7,3),(2,-3)
area 4x-x^2,x	area\:4x-x^{2},x
derivative of f(x)=ln(ln(x^2))	derivative\:f(x)=\ln(\ln(x^{2}))
limit as x approaches 1 of \|2x\|	\lim\:_{x\to\:1}(\left\|2x\right\|)
implicit (dy)/(dx),x+y^2=1	implicit\:\frac{dy}{dx},x+y^{2}=1
limit as x approaches 0-of 3	\lim\:_{x\to\:0-}(3)
d/(dθ)(8cos(θ)-6sin(θ))	\frac{d}{dθ}(8\cos(θ)-6\sin(θ))
derivative of f(x)=((-2))/x	derivative\:f(x)=\frac{(-2)}{x}
derivative of 4x^4+3x^2	\frac{d}{dx}(4x^{4}+3x^{2})
derivative of f(x)=5+x^2	derivative\:f(x)=5+x^{2}
integral from 0 to 1/2 of t^2	\int\:_{0}^{\frac{1}{2}}t^{2}dt
(\partial)/(\partial x)(8+e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(8+e^{-xy}\cos(y))
tangent of f(x)= 1/(2+3x),(2, 1/8)	tangent\:f(x)=\frac{1}{2+3x},(2,\frac{1}{8})
derivative of g(x)=(x^2+1)^3(x^2+2)^6	derivative\:g(x)=(x^{2}+1)^{3}(x^{2}+2)^{6}
inverse oflaplace (s+3)/(s^2+2s+1)	inverselaplace\:\frac{s+3}{s^{2}+2s+1}
derivative of f(x)=4x^4-1/(4x^4)	derivative\:f(x)=4x^{4}-\frac{1}{4x^{4}}
integral of (x+4)(2x+1)	\int\:(x+4)(2x+1)dx
(d^2)/(dx^2)(2x^2)	\frac{d^{2}}{dx^{2}}(2x^{2})
derivative of cos(θx)	\frac{d}{dx}(\cos(θ)x)
integral of sqrt(5x)	\int\:\sqrt{5x}dx
(\partial)/(\partial y)(sin^2(xy))	\frac{\partial\:}{\partial\:y}(\sin^{2}(xy))
y^'+(4y)/x =-3/x ,y(1)=-2	y^{\prime\:}+\frac{4y}{x}=-\frac{3}{x},y(1)=-2
limit as x approaches 2 of x^2+3x	\lim\:_{x\to\:2}(x^{2}+3x)
integral of 9x^{-2}	\int\:9x^{-2}dx
derivative of (x-2/(x+2))	\frac{d}{dx}(\frac{x-2}{x+2})
derivative of y=xe^{ax}	derivative\:y=xe^{ax}
limit as x approaches-2 of x^2-5	\lim\:_{x\to\:-2}(x^{2}-5)
f^'(x)=6x	f^{\prime\:}(x)=6x
derivative of f(x)= 2/(3x)	derivative\:f(x)=\frac{2}{3x}
(dy)/(dx)=cos(x-y)	\frac{dy}{dx}=\cos(x-y)
sum from n=0 to infinity of (n+6)/6	\sum\:_{n=0}^{\infty\:}\frac{n+6}{6}
(\partial)/(\partial x)(e^{x^2y^3})	\frac{\partial\:}{\partial\:x}(e^{x^{2}y^{3}})
derivative of 12e^2x	\frac{d}{dx}(12e^{2}x)
(\partial)/(\partial x)(y^2zcos(x))	\frac{\partial\:}{\partial\:x}(y^{2}z\cos(x))
(\partial}{\partial x}(\frac{x^3y^3)/3)	\frac{\partial\:}{\partial\:x}(\frac{x^{3}y^{3}}{3})
(\partial}{\partial x}(\frac{g(x))/x-(h(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{g(x)}{x}-\frac{h(x)}{x})
integral of sec^7(x)tan(x)	\int\:\sec^{7}(x)\tan(x)dx
integral of e^{tan(v)}sec^2(v)	\int\:e^{\tan(v)}\sec^{2}(v)dv
integral of (xe^{x^2})/(sqrt(e^{x^2)+2)}	\int\:\frac{xe^{x^{2}}}{\sqrt{e^{x^{2}}+2}}dx
sum from n=1 to infinity of ne^{9n}	\sum\:_{n=1}^{\infty\:}ne^{9n}
integral of sec^4(x)*tan^2(x)	\int\:\sec^{4}(x)\cdot\:\tan^{2}(x)dx

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