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Popular Calculus Problems

derivative of f(x)=4e^{5x^2}(5-x)^7	derivative\:f(x)=4e^{5x^{2}}(5-x)^{7}
(\partial)/(\partial x)((x+y)e^{y^2})	\frac{\partial\:}{\partial\:x}((x+y)e^{y^{2}})
integral of (sin(x^2))	\int\:(\sin(x^{2}))dx
(\partial)/(\partial x)(sqrt(9+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{9+x^{2}+y^{2}})
(d^2)/(dx^2)((10)/(3x^3))	\frac{d^{2}}{dx^{2}}(\frac{10}{3x^{3}})
(\partial)/(\partial x)(x^2-xy^2+4y^5)	\frac{\partial\:}{\partial\:x}(x^{2}-xy^{2}+4y^{5})
derivative of f(x)=12sqrt(x)	derivative\:f(x)=12\sqrt{x}
derivative of ((x^2+1/(2x+1))^2)	\frac{d}{dx}((\frac{x^{2}+1}{2x+1})^{2})
(dy)/(dx)=15-(3y)/(290)	\frac{dy}{dx}=15-\frac{3y}{290}
limit as x approaches 0 of sin(4/x)	\lim\:_{x\to\:0}(\sin(\frac{4}{x}))
(dy)/(dx)=xy+x/y	\frac{dy}{dx}=xy+\frac{x}{y}
integral of (x^e+e^x)	\int\:(x^{e}+e^{x})dx
(\partial)/(\partial x)((4x+6y)^4)	\frac{\partial\:}{\partial\:x}((4x+6y)^{4})
derivative of 5sec(x-2x)	\frac{d}{dx}(5\sec(x)-2x)
slope of (-1.2)(3.4)	slope\:(-1.2)(3.4)
derivative of (3x^2^{2x})	\frac{d}{dx}((3x^{2})^{2x})
integral of (5x-4)/(sqrt(8x-5x^2+9))	\int\:\frac{5x-4}{\sqrt{8x-5x^{2}+9}}dx
integral from 1/3 to 5 of 8xln(3x)	\int\:_{\frac{1}{3}}^{5}8x\ln(3x)dx
derivative of ln(sin(x^2))	\frac{d}{dx}(\ln(\sin(x^{2})))
derivative of 1/(f(x^2(x)))	\frac{d}{dx}(\frac{1}{f(x)^{2}(x)})
slope of-10x^3+6x^{40}y+y^4=3	slope\:-10x^{3}+6x^{40}y+y^{4}=3
integral of (x^3)/(1-x^2)	\int\:\frac{x^{3}}{1-x^{2}}dx
limit as x approaches 4-of 2-x-x^2	\lim\:_{x\to\:4-}(2-x-x^{2})
derivative of f(x)=(x^3+9)e^x	derivative\:f(x)=(x^{3}+9)e^{x}
integral from e to e^3 of (15)/y	\int\:_{e}^{e^{3}}\frac{15}{y}dy
integral of x^2cos^2(x)	\int\:x^{2}\cos^{2}(x)dx
y^{''}+8y^'-9y=0,y(1)=2,y^'(1)=0	y^{\prime\:\prime\:}+8y^{\prime\:}-9y=0,y(1)=2,y^{\prime\:}(1)=0
(dy)/(dx)=(e^{2x})/(4y^3)	\frac{dy}{dx}=\frac{e^{2x}}{4y^{3}}
derivative of ln(cos^2(x+5x^3))	\frac{d}{dx}(\ln(\cos^{2}(x)+5x^{3}))
y^{''}=-k^2y	y^{\prime\:\prime\:}=-k^{2}y
derivative of ax^3+bx^2+cx+d	\frac{d}{dx}(ax^{3}+bx^{2}+cx+d)
derivative of f(x)=(2x^3)/3-12x	derivative\:f(x)=\frac{2x^{3}}{3}-12x
derivative of (5x^3+4(3x^7-5))	\frac{d}{dx}((5x^{3}+4)(3x^{7}-5))
area 2x^2-3x,(0,5)	area\:2x^{2}-3x,(0,5)
derivative of (3t-1)^4(2t+1)^{-3}	derivative\:(3t-1)^{4}(2t+1)^{-3}
integral of (x/(1+x^2))	\int\:(\frac{x}{1+x^{2}})dx
limit as x approaches 4+of 1/(x-4)	\lim\:_{x\to\:4+}(\frac{1}{x-4})
(dy)/(dx)=2x-y	\frac{dy}{dx}=2x-y
limit as x approaches 2 of 9(ln(5x)+1)	\lim\:_{x\to\:2}(9(\ln(5x)+1))
integral of 3sin(t)-2cos(t)	\int\:3\sin(t)-2\cos(t)dt
integral of tan(x)sec^4(x)	\int\:\tan(x)\sec^{4}(x)dx
y^{''}+2y^'+3y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+3y=0
area y=x^3-3x^2-27x+14,y=x+14	area\:y=x^{3}-3x^{2}-27x+14,y=x+14
integral of (x^3+6x^2+3x+6)/(x^3+2x^2)	\int\:\frac{x^{3}+6x^{2}+3x+6}{x^{3}+2x^{2}}dx
integral of (x^{-1}-x^{-2}+x^{-3})/(x^2)	\int\:\frac{x^{-1}-x^{-2}+x^{-3}}{x^{2}}dx
integral of ((x^4))/(x-1)	\int\:\frac{(x^{4})}{x-1}dx
integral of cos^4(9x)	\int\:\cos^{4}(9x)dx
(ln(x))^3	(\ln(x))^{3}
integral of tan^3(4x)	\int\:\tan^{3}(4x)dx
area 8-3x,6-x,3	area\:8-3x,6-x,3
y^{''}-10y^'+27y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+27y=0
integral of x^2sqrt(7x+6)	\int\:x^{2}\sqrt{7x+6}dx
derivative of x^2+xy+y^2+3/x+3/y+5	\frac{d}{dx}(x^{2}+xy+y^{2}+\frac{3}{x}+\frac{3}{y}+5)
integral of 11sin((pit)/(12))+10	\int\:11\sin(\frac{πt}{12})+10dt
sum from n=0 to infinity of 0.5^n	\sum\:_{n=0}^{\infty\:}0.5^{n}
y^'-2/x y=x^2e^x	y^{\prime\:}-\frac{2}{x}y=x^{2}e^{x}
integral of (x^3-3x^2+5)/((x-3))	\int\:\frac{x^{3}-3x^{2}+5}{(x-3)}dx
limit as x approaches 1 of 1/(x^2-1)	\lim\:_{x\to\:1}(\frac{1}{x^{2}-1})
inverse oflaplace s/((s-1)^2+1)	inverselaplace\:\frac{s}{(s-1)^{2}+1}
integral from 1 to 5 of 2e^{2x}	\int\:_{1}^{5}2e^{2x}dx
derivative of \sqrt[3]{t}+4sqrt(t^3)	derivative\:\sqrt[3]{t}+4\sqrt{t^{3}}
limit as x approaches-0.001 of 4x^2+7	\lim\:_{x\to\:-0.001}(4x^{2}+7)
(\partial)/(\partial x)(4x^3y^3-18y-x)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{3}-18y-x)
(\partial)/(\partial y)(9xsin(y-z))	\frac{\partial\:}{\partial\:y}(9x\sin(y-z))
integral from-4 to-1 of x^4	\int\:_{-4}^{-1}x^{4}dx
integral of 20tan^6(x)	\int\:20\tan^{6}(x)dx
(dy)/(dx)=2y(1-y/4)	\frac{dy}{dx}=2y(1-\frac{y}{4})
derivative of x^3arccos(x)	\frac{d}{dx}(x^{3}\arccos(x))
derivative of 1/4 x^4-x^3	\frac{d}{dx}(\frac{1}{4}x^{4}-x^{3})
integral from 2 to infinity of ye^{-7y}	\int\:_{2}^{\infty\:}ye^{-7y}dy
integral of x*e^{-x/4}	\int\:x\cdot\:e^{-\frac{x}{4}}dx
integral of (6+t+t^2)/(sqrt(t))	\int\:\frac{6+t+t^{2}}{\sqrt{t}}dt
(\partial)/(\partial x)((2x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}+y^{2}})
area x^6,x^3	area\:x^{6},x^{3}
derivative of x^2-8/(x^3)	\frac{d}{dx}(x^{2}-\frac{8}{x^{3}})
derivative of 1.4^x-2.7	\frac{d}{dx}(1.4^{x}-2.7)
derivative of xarctan(x-1/2 ln(1+x^2))	\frac{d}{dx}(x\arctan(x)-\frac{1}{2}\ln(1+x^{2}))
derivative of x/n	\frac{d}{dx}(\frac{x}{n})
(\partial)/(\partial x)(-y/(4x^2+9y^2))	\frac{\partial\:}{\partial\:x}(-\frac{y}{4x^{2}+9y^{2}})
y^'=x^2y-x^2y^2,y(0)=17	y^{\prime\:}=x^{2}y-x^{2}y^{2},y(0)=17
derivative of f(x)=sqrt(x)+5/(sqrt(x))	derivative\:f(x)=\sqrt{x}+\frac{5}{\sqrt{x}}
derivative of (2x-7/(3x-2))	\frac{d}{dx}(\frac{2x-7}{3x-2})
integral of sqrt(5-x)	\int\:\sqrt{5-x}dx
integral of (e^t)/t	\int\:\frac{e^{t}}{t}dt
integral of e^{-λx}	\int\:e^{-λx}dx
f(x)=x^2-6	f(x)=x^{2}-6
limit as x approaches-1+of x/(x^2+1)	\lim\:_{x\to\:-1+}(\frac{x}{x^{2}+1})
limit as x approaches-1 of 6x^2+5x-1	\lim\:_{x\to\:-1}(6x^{2}+5x-1)
derivative of csc^{11}(x)	\frac{d}{dx}(\csc^{11}(x))
derivative of y=7^x	derivative\:y=7^{x}
tangent of f(x)=9x-6sqrt(x),(1,3)	tangent\:f(x)=9x-6\sqrt{x},(1,3)
integral of x/(\sqrt[4]{x+2)}	\int\:\frac{x}{\sqrt[4]{x+2}}dx
integral of (8sqrt(x^2-1))/(x^2)	\int\:\frac{8\sqrt{x^{2}-1}}{x^{2}}dx
tangent of f(x) 7/x ,\at a=3	tangent\:f(x)\frac{7}{x},\at\:a=3
integral of (e^{9x})/(e^{9x)+8}	\int\:\frac{e^{9x}}{e^{9x}+8}dx
area y=e^x,y=xe^x,x=0	area\:y=e^{x},y=xe^{x},x=0
((-ln(1+6x))/x)^'	(\frac{-\ln(1+6x)}{x})^{\prime\:}
integral of (2x-1)e^x	\int\:(2x-1)e^{x}dx
derivative of f(x)=sqrt(x^2-2x+3)	derivative\:f(x)=\sqrt{x^{2}-2x+3}
tangent of f(x)=9x-6sqrt(x),\at x=1	tangent\:f(x)=9x-6\sqrt{x},\at\:x=1

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