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Popular Calculus Problems

derivative of f(x)=8sin(2x^4)	derivative\:f(x)=8\sin(2x^{4})
tangent of f(x)=xsqrt(x),\at x=16	tangent\:f(x)=x\sqrt{x},\at\:x=16
integral of sec^2(4xta)n^54x	\int\:\sec^{2}(4xta)n^{5}4xdx
integral of (x^3+2x^2)/(sqrt(x))	\int\:\frac{x^{3}+2x^{2}}{\sqrt{x}}dx
derivative of (1+3x^2)	\frac{d}{dx}((1+3x)^{2})
6y^{''}-5y^'+y=0	6y^{\prime\:\prime\:}-5y^{\prime\:}+y=0
limit as x approaches 0 of e^{sin(x)}	\lim\:_{x\to\:0}(e^{\sin(x)})
area sec^2(x),8cos(x)	area\:\sec^{2}(x),8\cos(x)
limit as x approaches 3 of cx^2-4x	\lim\:_{x\to\:3}(cx^{2}-4x)
derivative of ((1-4e^x)/(1-5cos(x)))	\frac{d}{dx}(\frac{(1-4e^{x})}{1-5\cos(x)})
limit as x approaches-8 of 10x+1	\lim\:_{x\to\:-8}(10x+1)
(x^2+1)*(dy)/(dx)+6x(y-1)=0	(x^{2}+1)\cdot\:\frac{dy}{dx}+6x(y-1)=0
10y^{''}-10y^'+25y=0	10y^{\prime\:\prime\:}-10y^{\prime\:}+25y=0
derivative of f(x)=((2+3x)/(3x))(9-4x)	derivative\:f(x)=(\frac{2+3x}{3x})(9-4x)
derivative of 5sin(xcos(x))	\frac{d}{dx}(5\sin(x)\cos(x))
integral of (x+1)(9x-8)	\int\:(x+1)(9x-8)dx
integral of (x^7-4x)/(x^5)	\int\:\frac{x^{7}-4x}{x^{5}}dx
derivative of sin(10x)	derivative\:\sin(10x)
derivative of e^{sqrt(1+sin(2x)})	\frac{d}{dx}(e^{\sqrt{1+\sin(2x)}})
taylor tan(x),-pi/4	taylor\:\tan(x),-\frac{π}{4}
x^3y^'+xy=1	x^{3}y^{\prime\:}+xy=1
sum from n=1 to infinity of (2+n)/(1-2n)	\sum\:_{n=1}^{\infty\:}\frac{2+n}{1-2n}
integral of 2e^{x/3}	\int\:2e^{\frac{x}{3}}dx
laplacetransform sin(5t)e^{(-2t)}	laplacetransform\:\sin(5t)e^{(-2t)}
tangent of y=2e^x+x,(0,2)	tangent\:y=2e^{x}+x,(0,2)
slope of y=sqrt(6x+3)	slope\:y=\sqrt{6x+3}
integral of 1/16	\int\:\frac{1}{16}dx
derivative of f(x)=(48)/(x^4)	derivative\:f(x)=\frac{48}{x^{4}}
sum from m=1 to infinity of 5^{m-1}	\sum\:_{m=1}^{\infty\:}5^{m-1}
sum from k=0 to infinity of (5x)^k	\sum\:_{k=0}^{\infty\:}(5x)^{k}
limit as x approaches infinity of 4^{-x}	\lim\:_{x\to\:\infty\:}(4^{-x})
(\partial)/(\partial x)(1/(2x))	\frac{\partial\:}{\partial\:x}(\frac{1}{2x})
d/(dt)(kte^{3t})	\frac{d}{dt}(kte^{3t})
derivative of (2x/(x-1))	\frac{d}{dx}(\frac{2x}{x-1})
(d^2)/(dx^2)(3/(4x^6))	\frac{d^{2}}{dx^{2}}(\frac{3}{4x^{6}})
integral of sin(ax)cos(bx)	\int\:\sin(ax)\cos(bx)dx
limit as x approaches c of mx+b	\lim\:_{x\to\:c}(mx+b)
tangent of 2x^2-13+1	tangent\:2x^{2}-13+1
integral from 0 to infinity of e^{-5t}	\int\:_{0}^{\infty\:}e^{-5t}dt
derivative of f(x)=sqrt(x)(1-x^2)	derivative\:f(x)=\sqrt{x}(1-x^{2})
derivative of y=((x^2+3)/(x^2-3))^8	derivative\:y=(\frac{x^{2}+3}{x^{2}-3})^{8}
derivative of f(x)= 7/(1-x)	derivative\:f(x)=\frac{7}{1-x}
derivative of x^2sqrt(x^3+1)	derivative\:x^{2}\sqrt{x^{3}+1}
limit as x approaches 8 of x	\lim\:_{x\to\:8}(x)
integral of y^3(4y^2-25)	\int\:y^{3}(4y^{2}-25)dy
sum from n=4 to infinity of 1/(sqrt(n))	\sum\:_{n=4}^{\infty\:}\frac{1}{\sqrt{n}}
integral of 8x^3(2x^4+4)^4	\int\:8x^{3}(2x^{4}+4)^{4}dx
derivative of 1+(2/5)x(2/3)-sqrt(25)	derivative\:1+(\frac{2}{5})^{\circ\:}x(\frac{2}{3})^{\circ\:}-\sqrt{25}
derivative of g(x)=[ln(5x-2)]^4	derivative\:g(x)=[\ln(5x-2)]^{4}
derivative of 1/(12x^3)	derivative\:\frac{1}{12x^{3}}
integral from 0 to infinity of 4/(x^2+4)	\int\:_{0}^{\infty\:}\frac{4}{x^{2}+4}dx
derivative of sqrt(tan(e^x))	\frac{d}{dx}(\sqrt{\tan(e^{x})})
sum from n=1 to infinity of (-1)^nnx^n	\sum\:_{n=1}^{\infty\:}(-1)^{n}nx^{n}
derivative of f(x)=(8x^2+6x+4)/(sqrt(x))	derivative\:f(x)=\frac{8x^{2}+6x+4}{\sqrt{x}}
(dy)/(dt)=tsqrt(1-y^2)	\frac{dy}{dt}=t\sqrt{1-y^{2}}
integral of f(1/2 \sqrt[3]{x})	\int\:f(\frac{1}{2}\sqrt[3]{x})dx
(\partial)/(\partial x)(4x^3-4yz)	\frac{\partial\:}{\partial\:x}(4x^{3}-4yz)
(\partial)/(\partial x)(e^y-ye^x)	\frac{\partial\:}{\partial\:x}(e^{y}-ye^{x})
derivative of (a-1)+1	derivative\:(a-1)+1
y^'+(2y)/(t+2)=(t+2)^5,y(0)=5	y^{\prime\:}+\frac{2y}{t+2}=(t+2)^{5},y(0)=5
inverse oflaplace 1/(s^3+4s)	inverselaplace\:\frac{1}{s^{3}+4s}
integral of 7x^5e^x	\int\:7x^{5}e^{x}dx
derivative of \sqrt[7]{x^2}+2sqrt(x^5)	\frac{d}{dx}(\sqrt[7]{x^{2}}+2\sqrt{x^{5}})
tangent of f(x)=x-1/(x^2),\at x=1	tangent\:f(x)=x-\frac{1}{x^{2}},\at\:x=1
integral of 27sqrt(x)	\int\:27\sqrt{x}dx
integral of (2x+1)^{17}	\int\:(2x+1)^{17}dx
derivative of sqrt(tan(x+y))	\frac{d}{dx}(\sqrt{\tan(x)+y})
6=(dx)/(dt)+(3x)/(20)	6=\frac{dx}{dt}+\frac{3x}{20}
f(y)=2y^2	f(y)=2y^{2}
integral of (15)/(2sqrt(x-4))	\int\:\frac{15}{2\sqrt{x-4}}dx
integral of (5x^2+2x+2)/(x^3-1)	\int\:\frac{5x^{2}+2x+2}{x^{3}-1}dx
limit as x approaches infinity of-xe^{-x}	\lim\:_{x\to\:\infty\:}(-xe^{-x})
y^{''}+2y^'+y=x^2,y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}+2y^{\prime\:}+y=x^{2},y(0)=1,y^{\prime\:}(0)=2
y^{''}-y=0,y(0)=3,y^'(0)=-1	y^{\prime\:\prime\:}-y=0,y(0)=3,y^{\prime\:}(0)=-1
(\partial)/(\partial θ)(r(θ)θ)	\frac{\partial\:}{\partial\:θ}(r(θ)θ)
area x^2,-1,1,-2x^4	area\:x^{2},-1,1,-2x^{4}
derivative of xln(x)	derivative\:x\ln(x)
integral of 1/((x-3)(2x+1)(x^2+x+4))	\int\:\frac{1}{(x-3)(2x+1)(x^{2}+x+4)}dx
derivative of (sqrt(x)+5x)(x^{3/2}-x)	derivative\:(\sqrt{x}+5x)(x^{\frac{3}{2}}-x)
derivative of-2x^4+7xe^x	derivative\:-2x^{4}+7xe^{x}
integral of (b-\|x\|)^2	\int\:(b-\left\|x\right\|)^{2}dx
tangent of f(x)=-8x^2-7,\at x=1	tangent\:f(x)=-8x^{2}-7,\at\:x=1
integral of ln(5x+8)	\int\:\ln(5x+8)dx
expand (x^2*cos(x))/((2x+1)^3)	expand\:\frac{x^{2}\cdot\:\cos(x)}{(2x+1)^{3}}
integral of (5x+2)/(sqrt(3x)\sqrt{1-3x)}	\int\:\frac{5x+2}{\sqrt{3x}\sqrt{1-3x}}dx
limit as x approaches 0 of sin(pix)	\lim\:_{x\to\:0}(\sin(πx))
integral of ((inx)^2)/x	\int\:\frac{(inx)^{2}}{x}dx
sum from n=1 to infinity of 2/(2n-1)	\sum\:_{n=1}^{\infty\:}\frac{2}{2n-1}
derivative of (1-3x^2/(1-2x))	\frac{d}{dx}(\frac{1-3x^{2}}{1-2x})
derivative of sqrt(9x+5)	\frac{d}{dx}(\sqrt{9x+5})
limit as x approaches 5-of 1/((x-5)^2)	\lim\:_{x\to\:5-}(\frac{1}{(x-5)^{2}})
inverse oflaplace 10	inverselaplace\:10
f(x)=(x+1)^{1/2}	f(x)=(x+1)^{\frac{1}{2}}
(dy)/(dx)(x+2)^2=(x^2+1)	\frac{dy}{dx}(x+2)^{2}=(x^{2}+1)
derivative of f(x)=5\sqrt[5]{x}	derivative\:f(x)=5\sqrt[5]{x}
d/(dy)(x)-0.06x=200,y(0)=0	\frac{d}{dy}(x)-0.06x=200,y(0)=0
(d^4)/(dx^4)(cos(2x))	\frac{d^{4}}{dx^{4}}(\cos(2x))
integral of (x^2+5x+2)/((x+1)(x^2+1))	\int\:\frac{x^{2}+5x+2}{(x+1)(x^{2}+1)}dx
limit as x approaches-9 of (x^2-6)/(9-x)	\lim\:_{x\to\:-9}(\frac{x^{2}-6}{9-x})
derivative of ln(1-7x)	derivative\:\ln(1-7x)

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