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Popular Calculus Problems

(\partial)/(\partial x)(x^3y^2e^{xz})	\frac{\partial\:}{\partial\:x}(x^{3}y^{2}e^{xz})
derivative of (1+e^{-2x}/(2+cos(2x)))	\frac{d}{dx}(\frac{1+e^{-2x}}{2+\cos(2x)})
integral of (cos(x/2))^2	\int\:(\cos(\frac{x}{2}))^{2}dx
tangent of f(x)=3x^3-x^2+1,(2,21)	tangent\:f(x)=3x^{3}-x^{2}+1,(2,21)
integral from-2 to 1 of 1/(x^2)	\int\:_{-2}^{1}\frac{1}{x^{2}}dx
integral of (2x)^2	\int\:(2x)^{2}dx
slope of (-2,-6),(2,2)	slope\:(-2,-6),(2,2)
tangent of f(x)=9+4x^2-2x^3,\at x=1	tangent\:f(x)=9+4x^{2}-2x^{3},\at\:x=1
derivative of y=ln(ln(x^3))	derivative\:y=\ln(\ln(x^{3}))
derivative of y=(sin(x))/(1+sin(x))	derivative\:y=\frac{\sin(x)}{1+\sin(x)}
integral of x/(x^2+3)	\int\:\frac{x}{x^{2}+3}dx
integral of (x^3)/(sqrt(x^2-49))	\int\:\frac{x^{3}}{\sqrt{x^{2}-49}}dx
derivative of 1-e^{-x^2}	\frac{d}{dx}(1-e^{-x^{2}})
limit as x approaches 2 of x^4+5^x-2	\lim\:_{x\to\:2}(x^{4}+5^{x}-2)
limit as x approaches-1 of 2x^3+3x^2-6	\lim\:_{x\to\:-1}(2x^{3}+3x^{2}-6)
integral from-1 to 3 of \|x^2-2x\|	\int\:_{-1}^{3}\left\|x^{2}-2x\right\|dx
taylor 1/(x^{1/2)}	taylor\:\frac{1}{x^{\frac{1}{2}}}
tangent of f(x)=2x^2+x-1,\at x=1	tangent\:f(x)=2x^{2}+x-1,\at\:x=1
slope of (5.6)(6.9)	slope\:(5.6)(6.9)
integral of 2r	\int\:2rdr
derivative of 7ln(x)	derivative\:7\ln(x)
y^{''}+3y^'+4y=0	y^{\prime\:\prime\:}+3y^{\prime\:}+4y=0
integral of x/(x^3+x^2+x-3)	\int\:\frac{x}{x^{3}+x^{2}+x-3}dx
(\partial)/(\partial x)(7x+sqrt(y^4+1))	\frac{\partial\:}{\partial\:x}(7x+\sqrt{y^{4}+1})
taylor xe^{-x+1}	taylor\:xe^{-x+1}
integral of [cot(x)+1/x ]	\int\:[\cot(x)+\frac{1}{x}]dx
integral from 0 to 1 of sqrt(t^4+t^2)	\int\:_{0}^{1}\sqrt{t^{4}+t^{2}}dt
integral of (x^2+16)/x	\int\:\frac{x^{2}+16}{x}dx
y^'=(yln(x))/(xln(y))	y^{\prime\:}=\frac{y\cdot\:\ln(x)}{x\cdot\:\ln(y)}
sum from n=1 to infinity of (x^n)/(9^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{9^{n}}
(dy)/(dt)+2y=3*sin(6t)	\frac{dy}{dt}+2y=3\cdot\:\sin(6t)
limit as x approaches-2-of (-1)/(x^2-4)	\lim\:_{x\to\:-2-}(\frac{-1}{x^{2}-4})
limit as x approaches 7 of 5/(x-7)	\lim\:_{x\to\:7}(\frac{5}{x-7})
derivative of (yx^2)	\frac{d}{dx}((y)x^{2})
(\partial)/(\partial x)(xzt^2sqrt(y+1))	\frac{\partial\:}{\partial\:x}(xzt^{2}\sqrt{y+1})
derivative of f(x)=e^{3e^x}	derivative\:f(x)=e^{3e^{x}}
slope of (5.4)8x^2-9y^3=-376	slope\:(5.4)8x^{2}-9y^{3}=-376
x((dy)/(dx))=-y+2x^2y	x(\frac{dy}{dx})=-y+2x^{2}y
integral of y*e^y	\int\:y\cdot\:e^{y}dy
integral of xsin(bx)	\int\:x\sin(bx)dx
integral of-x^2+3	\int\:-x^{2}+3dx
derivative of xsqrt(x-3)	\frac{d}{dx}(x\sqrt{x-3})
integral of 3sin(2t)	\int\:3\sin(2t)dt
tangent of f(x)=4x^2-4x+1,\at x=1	tangent\:f(x)=4x^{2}-4x+1,\at\:x=1
tangent of f(x)=((x+2)/(x-2))^2,\at x=6	tangent\:f(x)=(\frac{x+2}{x-2})^{2},\at\:x=6
f^'(x)= 1/((1-x^2)^2)	f^{\prime\:}(x)=\frac{1}{(1-x^{2})^{2}}
derivative of 2x^{1/4}(x^3-11)	\frac{d}{dx}(2x^{\frac{1}{4}}(x^{3}-11))
tangent of f(x)=5x^2+4	tangent\:f(x)=5x^{2}+4
derivative of (-2/(2x+5))	\frac{d}{dx}(\frac{-2}{2x+5})
(\partial)/(\partial y)((x+y)(x^2+2y^2))	\frac{\partial\:}{\partial\:y}((x+y)(x^{2}+2y^{2}))
(dy)/(dt)+e^ty=-24e^t	\frac{dy}{dt}+e^{t}y=-24e^{t}
integral of 3^{x+2}	\int\:3^{x+2}dx
(sin(x)+cos(x))^'	(\sin(x)+\cos(x))^{\prime\:}
integral of ((x+sin(x)))/((1+cos(x)))	\int\:\frac{(x+\sin(x))}{(1+\cos(x))}dx
integral of (x+3)/(x^2(x+1)^2)	\int\:\frac{x+3}{x^{2}(x+1)^{2}}dx
(\partial)/(\partial x)(-a/x)	\frac{\partial\:}{\partial\:x}(-\frac{a}{x})
normal of y=x^2-8x,(3,-15)	normal\:y=x^{2}-8x,(3,-15)
integral of 1/(x^3+8x)	\int\:\frac{1}{x^{3}+8x}dx
f(x)=4cos(2x)	f(x)=4\cos(2x)
sum from n=0 to infinity of 4/n	\sum\:_{n=0}^{\infty\:}\frac{4}{n}
tangent of y=tan^2(x),(pi/4 ,1)	tangent\:y=\tan^{2}(x),(\frac{π}{4},1)
derivative of 2^{3x+1}ln(5x-11)	\frac{d}{dx}(2^{3x+1}\ln(5x-11))
integral of 9sin(ln(x))	\int\:9\sin(\ln(x))dx
integral of 2xe^{2y}	\int\:2xe^{2y}dy
integral of (x+18)sqrt(36x+x^2)	\int\:(x+18)\sqrt{36x+x^{2}}dx
derivative of f(x)=(x-2)^2	derivative\:f(x)=(x-2)^{2}
(2x+3)y^'=y+(2x+3)^{1/2}	(2x+3)y^{\prime\:}=y+(2x+3)^{\frac{1}{2}}
(\partial)/(\partial x)(e^{-2y}sin(2x))	\frac{\partial\:}{\partial\:x}(e^{-2y}\sin(2x))
integral of (9(x-9))/((x+5)(x-2))	\int\:\frac{9(x-9)}{(x+5)(x-2)}dx
derivative of ((4x^2/(2-x))^3)	\frac{d}{dx}((\frac{4x^{2}}{2-x})^{3})
integral from 0 to 2 of (2-x)^2	\int\:_{0}^{2}(2-x)^{2}dx
derivative of cos(x)	derivative\:\cos(x)
area 3x^2,18x-6x^2	area\:3x^{2},18x-6x^{2}
integral from 1 to 3 of 2x^2-2x+3	\int\:_{1}^{3}2x^{2}-2x+3dx
integral from 0 to 1 of (sin(2pit))^2	\int\:_{0}^{1}(\sin(2πt))^{2}dt
derivative of (460t)/((t^2+5)^3)	derivative\:\frac{460t}{(t^{2}+5)^{3}}
integral of 3sqrt(x+9)	\int\:3\sqrt{x+9}dx
derivative of ln(sin(x+cos(x)))	\frac{d}{dx}(\ln(\sin(x)+\cos(x)))
integral of-x^2+6x	\int\:-x^{2}+6xdx
integral of sin^3(2θ)cot(2θ)	\int\:\sin^{3}(2θ)\cot(2θ)dθ
limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7}	\lim\:_{x\to\:\infty\:}(\frac{\sqrt[3]{x}+5x+3}{-2x+x^{\frac{2}{3}}+7})
tangent of f(x)=2x^3-x^2+2,(1,3)	tangent\:f(x)=2x^{3}-x^{2}+2,(1,3)
limit as x approaches-1+of f(x)	\lim\:_{x\to\:-1+}(f(x))
integral of 5xcos(6x)	\int\:5x\cos(6x)dx
limit as x approaches 0 of (1+1/x)^{3x}	\lim\:_{x\to\:0}((1+\frac{1}{x})^{3x})
x(dy)/(dx)-4y=6x^4e^x	x\frac{dy}{dx}-4y=6x^{4}e^{x}
integral from 0 to 5 of (22+t)	\int\:_{0}^{5}(22+t)dt
derivative of-4/((4x-3)^{3/2)}	derivative\:-\frac{4}{(4x-3)^{\frac{3}{2}}}
(\partial}{\partial t}(\frac{(2r+s))/t)	\frac{\partial\:}{\partial\:t}(\frac{(2r+s)}{t})
limit as x approaches 0 of 2(tan(x))^x	\lim\:_{x\to\:0}(2(\tan(x))^{x})
integral of x^2e^{22x}	\int\:x^{2}e^{22x}dx
derivative of y=(x^3+1)/(x^2-1)	derivative\:y=\frac{x^{3}+1}{x^{2}-1}
derivative of f(x)=(x^2)/(x^2+2)	derivative\:f(x)=\frac{x^{2}}{x^{2}+2}
integral of 54	\int\:54
derivative of (sqrt(x))^{5x}	derivative\:(\sqrt{x})^{5x}
((x^2+1)dy)/(dx)+3x(y-1)=0	\frac{(x^{2}+1)dy}{dx}+3x(y-1)=0
tangent of y=(6x)/(x^2+1),(1,3)	tangent\:y=\frac{6x}{x^{2}+1},(1,3)
integral of 1/(2*sqrt(x))	\int\:\frac{1}{2\cdot\:\sqrt{x}}dx
taylor 1/(x+3)	taylor\:\frac{1}{x+3}
integral from 0 to 2 of sqrt(9x+37)	\int\:_{0}^{2}\sqrt{9x+37}dx

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