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Popular Calculus Problems

laplacetransform e^{17t}t^7	laplacetransform\:e^{17t}t^{7}
tangent of f(x)=50sqrt(x)-5x	tangent\:f(x)=50\sqrt{x}-5x
y^{''}-6y^'+2y=xe^x	y^{\prime\:\prime\:}-6y^{\prime\:}+2y=xe^{x}
(\partial)/(\partial y)(cos(y)e^x+2/x)	\frac{\partial\:}{\partial\:y}(\cos(y)e^{x}+\frac{2}{x})
derivative of x^2(x^3-1)	derivative\:x^{2}(x^{3}-1)
limit as x approaches 0 of (b-c)/(x^a)	\lim\:_{x\to\:0}(\frac{b-c}{x^{a}})
derivative of sqrt(4+\sqrt{6x)}	derivative\:\sqrt{4+\sqrt{6x}}
derivative of y=4\sqrt[5]{x}	derivative\:y=4\sqrt[5]{x}
derivative of sqrt(9)	derivative\:\sqrt{9}
limit as x approaches 9 of 9x+\|x-9\|	\lim\:_{x\to\:9}(9x+\left\|x-9\right\|)
derivative of 1/(sqrt(e^x))	\frac{d}{dx}(\frac{1}{\sqrt{e^{x}}})
laplacetransform t^3\delta(t-1)	laplacetransform\:t^{3}\delta(t-1)
derivative of \sqrt[3]{r^2}	derivative\:\sqrt[3]{r^{2}}
limit as x approaches 8 of 2x-1	\lim\:_{x\to\:8}(2x-1)
derivative of cos(14x)	\frac{d}{dx}(\cos(14x))
integral of cos((npit)/2)	\int\:\cos(\frac{nπt}{2})dt
derivative of (ln(x^2)/(e^{2x)})	\frac{d}{dx}(\frac{\ln(x^{2})}{e^{2x}})
integral of (3x^2-4x)e^{2x}	\int\:(3x^{2}-4x)e^{2x}dx
sum from n=0 to infinity of 1/(n^2+3n+2)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+3n+2}
limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)}	\lim\:_{x\to\:0}(\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}})
derivative of sqrt(1-\sqrt{x)}	\frac{d}{dx}(\sqrt{1-\sqrt{x}})
slope of (0,-4),(1,2)	slope\:(0,-4),(1,2)
xy^'+3y=3e^x	xy^{\prime\:}+3y=3e^{x}
(1-5y+x)(dy)/(dx)+y=5x-1	(1-5y+x)\frac{dy}{dx}+y=5x-1
y'(t)=10-e^y,y(0)=1	y\prime\:(t)=10-e^{y},y(0)=1
derivative of y=x^3-(x^2)/(16)	derivative\:y=x^{3}-\frac{x^{2}}{16}
integral of 5x+y	\int\:5x+ydy
derivative of-sqrt(2x)	\frac{d}{dx}(-\sqrt{2x})
integral of sqrt(1+3sin^2(x))	\int\:\sqrt{1+3\sin^{2}(x)}dx
integral of (esqrt(x))/(sqrt(x))	\int\:\frac{e\sqrt{x}}{\sqrt{x}}dx
integral of (sec(x))^6	\int\:(\sec(x))^{6}dx
limit as x approaches 0+of (-5+x)/(4+x)	\lim\:_{x\to\:0+}(\frac{-5+x}{4+x})
integral from 0 to 2 of (4ti-t^3j+4t^7k)	\int\:_{0}^{2}(4ti-t^{3}j+4t^{7}k)dt
derivative of y=x^4+2x^2-x	derivative\:y=x^{4}+2x^{2}-x
limit as x approaches 2 of 2x^3	\lim\:_{x\to\:2}(2x^{3})
derivative of-x^{-3}	\frac{d}{dx}(-x^{-3})
integral of-(x+1)/x	\int\:-\frac{x+1}{x}dx
4y^{''}-4y^'-3y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=0
implicit (dy)/(dx),y^2=2x	implicit\:\frac{dy}{dx},y^{2}=2x
derivative of 10x^3	\frac{d}{dx}(10x^{3})
integral of sqrt(a^2-r^2)r	\int\:\sqrt{a^{2}-r^{2}}rdr
(\partial)/(\partial x)(10x+4y)	\frac{\partial\:}{\partial\:x}(10x+4y)
derivative of-4/(x^2)	derivative\:-\frac{4}{x^{2}}
integral of 1/(3-7x)	\int\:\frac{1}{3-7x}dx
derivative of f(x)=arcsin(x^6)	derivative\:f(x)=\arcsin(x^{6})
(\partial)/(\partial x)(-x/((x^2+y^2+1)))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x^{2}+y^{2}+1)})
derivative of sqrt(2+ln(x))	\frac{d}{dx}(\sqrt{2+\ln(x)})
integral of (sqrt(361-x^2))/x	\int\:\frac{\sqrt{361-x^{2}}}{x}dx
derivative of acos(2x)	\frac{d}{dx}(a\cos(2x))
integral of 8cos(θ)	\int\:8\cos(θ)dθ
area y=cos(x),y=sin(2x),x=0,x= pi/2	area\:y=\cos(x),y=\sin(2x),x=0,x=\frac{π}{2}
integral of tan^4(3x)	\int\:\tan^{4}(3x)dx
(\partial)/(\partial x)(ln(xyz))	\frac{\partial\:}{\partial\:x}(\ln(xyz))
derivative of f(x)= 3/(4x+7)	derivative\:f(x)=\frac{3}{4x+7}
derivative of (2x-5/(x+1))	\frac{d}{dx}(\frac{2x-5}{x+1})
limit as x approaches 0 of 2xcot(4x)	\lim\:_{x\to\:0}(2x\cot(4x))
derivative of y=(6x)/(x+2)	derivative\:y=\frac{6x}{x+2}
laplacetransform e^{-t}	laplacetransform\:e^{-t}
integral of 1/(u^3)	\int\:\frac{1}{u^{3}}du
(\partial)/(\partial x)(x^7+3^y+x^y)	\frac{\partial\:}{\partial\:x}(x^{7}+3^{y}+x^{y})
d/(dy)(-ln(y))	\frac{d}{dy}(-\ln(y))
integral of-(cos(2x))/2	\int\:-\frac{\cos(2x)}{2}dx
derivative of 3/(4x^4)	derivative\:\frac{3}{4x^{4}}
integral of 1/(w^2sqrt(w^2-7))	\int\:\frac{1}{w^{2}\sqrt{w^{2}-7}}dw
y^{''}-6y^'+9y=xe^x	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=xe^{x}
integral of cos^5(θ)sin^4(θ)	\int\:\cos^{5}(θ)\sin^{4}(θ)dθ
slope of (-5,6),(-3,4)	slope\:(-5,6),(-3,4)
integral of (x^2)/((121+x^2)^2)	\int\:\frac{x^{2}}{(121+x^{2})^{2}}dx
derivative of (x^4/2-3x^2+10)	\frac{d}{dx}(\frac{x^{4}}{2}-3x^{2}+10)
integral of (y^3e^{y^2})/((y^2+1)^2)	\int\:\frac{y^{3}e^{y^{2}}}{(y^{2}+1)^{2}}dy
area f(x)=x^2-2x,(0,2)	area\:f(x)=x^{2}-2x,(0,2)
derivative of x-3\sqrt[3]{x}	\frac{d}{dx}(x-3\sqrt[3]{x})
y^{''}-8y^'+15y=4e^t	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=4e^{t}
integral of x/((1+x^2)^2)	\int\:\frac{x}{(1+x^{2})^{2}}dx
derivative of log_{3}(4x^2+2x)	\frac{d}{dx}(\log_{3}(4x^{2}+2x))
(\partial)/(\partial x)(2x+3e^y+xy)	\frac{\partial\:}{\partial\:x}(2x+3e^{y}+xy)
inverse oflaplace (10s)/((s+1)(s+6))	inverselaplace\:\frac{10s}{(s+1)(s+6)}
derivative of (4(y-x\frac{dy/(dx))}{y^2})	\frac{d}{dx}(\frac{4(y-x\frac{dy}{dx})}{y^{2}})
integral of (ln^2(x))/(3x)	\int\:\frac{\ln^{2}(x)}{3x}dx
integral of (6x+5)/(e^x)	\int\:\frac{6x+5}{e^{x}}dx
derivative of y=ln(1-x^2)	derivative\:y=\ln(1-x^{2})
(\partial)/(\partial y)(2y^3-6y+x^2)	\frac{\partial\:}{\partial\:y}(2y^{3}-6y+x^{2})
derivative of ln(5)	derivative\:\ln(5)
limit as x approaches+0+of 1/x-1/(x^2+x)	\lim\:_{x\to\:+0+}(\frac{1}{x}-\frac{1}{x^{2}+x})
(\partial)/(\partial x)(e^{y/x}-y*e^{-x})	\frac{\partial\:}{\partial\:x}(e^{\frac{y}{x}}-y\cdot\:e^{-x})
limit as x approaches 0 of x^4sin(4/x)	\lim\:_{x\to\:0}(x^{4}\sin(\frac{4}{x}))
inverse oflaplace (1+4s)/(s(2s^2+2s+1))	inverselaplace\:\frac{1+4s}{s(2s^{2}+2s+1)}
derivative of (ln(x)/(1+x))	\frac{d}{dx}(\frac{\ln(x)}{1+x})
y^'-12x^{11}y=e^{x^{12}}	y^{\prime\:}-12x^{11}y=e^{x^{12}}
derivative of-18e^{-2x}	\frac{d}{dx}(-18e^{-2x})
limit as x approaches 1 of sqrt((x^5-1)/(x-1))	\lim\:_{x\to\:1}(\sqrt{\frac{x^{5}-1}{x-1}})
derivative of sin((pix/4))	\frac{d}{dx}(\sin(\frac{πx}{4}))
taylor 1/x ,1	taylor\:\frac{1}{x},1
derivative of 6sin(4x)	derivative\:6\sin(4x)
integral from 1 to 2 of 6x^2	\int\:_{1}^{2}6x^{2}dx
integral of 3e^{-0.5x}	\int\:3e^{-0.5x}dx
inverse oflaplace 4e^{-3s}	inverselaplace\:4e^{-3s}
integral of 5e^7	\int\:5e^{7}dx
derivative of ln(x^2+3)	derivative\:\ln(x^{2}+3)
derivative of sqrt(3-3x^2)	\frac{d}{dx}(\sqrt{3-3x^{2}})

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