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Popular Calculus Problems

9x-4ysqrt((x^2+1))((dy)/(dx))=0	9x-4y\sqrt{(x^{2}+1)}(\frac{dy}{dx})=0
integral of x/((x+4)^{1/3)}	\int\:\frac{x}{(x+4)^{\frac{1}{3}}}dx
f(x)=e^x+1	f(x)=e^{x}+1
derivative of (8t)/(t^2+9)	derivative\:\frac{8t}{t^{2}+9}
tangent of ((x-1))/((x+1))	tangent\:\frac{(x-1)}{(x+1)}
derivative of e^{0.5x^2}	\frac{d}{dx}(e^{0.5x^{2}})
(\partial)/(\partial y)(x^{-3}y^2+xy^2+3xy)	\frac{\partial\:}{\partial\:y}(x^{-3}y^{2}+xy^{2}+3xy)
sum from n=2 to infinity of 5(-3/4)^n	\sum\:_{n=2}^{\infty\:}5(-\frac{3}{4})^{n}
derivative of f(x)=e^{-3/(t^2)}	derivative\:f(x)=e^{-\frac{3}{t^{2}}}
derivative of cos(x*tan(x))	\frac{d}{dx}(\cos(x)\cdot\:\tan(x))
derivative of f(x)=10^x	derivative\:f(x)=10^{x}
integral of (x^3-5x^2-sqrt(x))/(x^2)	\int\:\frac{x^{3}-5x^{2}-\sqrt{x}}{x^{2}}dx
(\partial)/(\partial y)(xe^ycos(z)-z)	\frac{\partial\:}{\partial\:y}(xe^{y}\cos(z)-z)
integral of x/(sqrt(144x^2-1))	\int\:\frac{x}{\sqrt{144x^{2}-1}}dx
integral of x/(x^2-4x+7)	\int\:\frac{x}{x^{2}-4x+7}dx
limit as x approaches 1 of absval	\lim\:_{x\to\:1}(absval)
(dy)/(dx)=((x^2-y^2))/(-xy)	\frac{dy}{dx}=\frac{(x^{2}-y^{2})}{-xy}
inverse oflaplace 4/(s^2+4)	inverselaplace\:\frac{4}{s^{2}+4}
sum from n=0 to infinity of 3^nx^n	\sum\:_{n=0}^{\infty\:}3^{n}x^{n}
integral from-2 to 3 of (8x^3+3x-1)	\int\:_{-2}^{3}(8x^{3}+3x-1)dx
integral of e^x-1/2 y^2	\int\:e^{x}-\frac{1}{2}y^{2}dx
-2x^{3/2}	-2x^{\frac{3}{2}}
(dy)/(dx)=(1-x-y)/(x+y)	\frac{dy}{dx}=\frac{1-x-y}{x+y}
derivative of y=9x^3	derivative\:y=9x^{3}
(\partial)/(\partial x)(2y+x^2cos(t))	\frac{\partial\:}{\partial\:x}(2y+x^{2}\cos(t))
y^'=(x-4)/(y-6)	y^{\prime\:}=\frac{x-4}{y-6}
slope ofintercept (4,5),(1,2)	slopeintercept\:(4,5),(1,2)
limit as x approaches 0 of (\|2x\|)/x	\lim\:_{x\to\:0}(\frac{\left\|2x\right\|}{x})
(\partial)/(\partial x)(1/(t^2+1))	\frac{\partial\:}{\partial\:x}(\frac{1}{t^{2}+1})
tangent of y= 2/(x^2),(2, 2/49)	tangent\:y=\frac{2}{x^{2}},(2,\frac{2}{49})
area x=y^2-6y,x=3y-y^2	area\:x=y^{2}-6y,x=3y-y^{2}
integral of x^2cos(nxpi)	\int\:x^{2}\cos(nxπ)dx
integral of 1/(ysqrt(5y^2-3))	\int\:\frac{1}{y\sqrt{5y^{2}-3}}dy
integral of (x-0.1)^2(x-0.75)^2	\int\:(x-0.1)^{2}(x-0.75)^{2}dx
integral of (ln(x))/4	\int\:\frac{\ln(x)}{4}dx
integral of x(x+1)^{1/2}	\int\:x(x+1)^{\frac{1}{2}}dx
(\partial)/(\partial x)(y^{0.75}x^{0.25})	\frac{\partial\:}{\partial\:x}(y^{0.75}x^{0.25})
tangent of f(x)=9e^5x+e^{-x^2},\at x=1	tangent\:f(x)=9e^{5}x+e^{-x^{2}},\at\:x=1
(dy)/(dx)=6x^2y^2	\frac{dy}{dx}=6x^{2}y^{2}
limit as x approaches 2-of 4-x^2	\lim\:_{x\to\:2-}(4-x^{2})
derivative of f(r)= 5/(r^3)	derivative\:f(r)=\frac{5}{r^{3}}
derivative of 2xy+y	\frac{d}{dx}(2xy+y)
(\partial)/(\partial t)(ssqrt(t))	\frac{\partial\:}{\partial\:t}(s\sqrt{t})
derivative of f(x)=(x^2)/(sqrt(4-x^2))	derivative\:f(x)=\frac{x^{2}}{\sqrt{4-x^{2}}}
integral of cos^5(xsi)n^4x	\int\:\cos^{5}(xsi)n^{4}x
derivative of w	derivative\:w
integral of 3x^{5/2}	\int\:3x^{\frac{5}{2}}dx
integral of (12x+3x^4)(10x^2+x^5-2)^6	\int\:(12x+3x^{4})(10x^{2}+x^{5}-2)^{6}dx
limit as x approaches 0 of 3x^2+x	\lim\:_{x\to\:0}(3x^{2}+x)
derivative of (8-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{8-\sec(x)}{\tan(x)})
(\partial)/(\partial z)(xe^{yz})	\frac{\partial\:}{\partial\:z}(xe^{yz})
derivative of x^2+4x+2	derivative\:x^{2}+4x+2
limit as x approaches pi of pi	\lim\:_{x\to\:π}(π)
tangent of f(x)= 1/(2+x),\at x=2	tangent\:f(x)=\frac{1}{2+x},\at\:x=2
integral of ((12)/(sqrt(x))+12sqrt(x))	\int\:(\frac{12}{\sqrt{x}}+12\sqrt{x})dx
integral of 1/(sqrt(a^2+x^2))	\int\:\frac{1}{\sqrt{a^{2}+x^{2}}}dx
integral of (8x+3sin(x))^2	\int\:(8x+3\sin(x))^{2}dx
integral of (1/(sqrt(4-25x^2)))	\int\:(\frac{1}{\sqrt{4-25x^{2}}})dx
derivative of (14x+4x^2)/((7+4x)^2)	derivative\:\frac{14x+4x^{2}}{(7+4x)^{2}}
y^'=(6x^3+y^3)/(xy^2)	y^{\prime\:}=\frac{6x^{3}+y^{3}}{xy^{2}}
integral of ((x^2+4))/(3x^3+4x^2-4x)	\int\:\frac{(x^{2}+4)}{3x^{3}+4x^{2}-4x}dx
(dy)/(dx)=((2x(y-1)))/((x^2+3))	\frac{dy}{dx}=\frac{(2x(y-1))}{(x^{2}+3)}
tangent of y=2x^3-x^2+2(1.3)	tangent\:y=2x^{3}-x^{2}+2(1.3)
slope of (10.4)(4.15)	slope\:(10.4)(4.15)
integral of (e^x)/(1+sqrt(e^x))	\int\:\frac{e^{x}}{1+\sqrt{e^{x}}}dx
integral of x^2+x+2/(x-1)	\int\:x^{2}+x+\frac{2}{x-1}dx
derivative of y=(x^2)/(x-4)	derivative\:y=\frac{x^{2}}{x-4}
derivative of f(x)=1+x^2	derivative\:f(x)=1+x^{2}
(dy)/(dx)=x-5	\frac{dy}{dx}=x-5
integral of 3sqrt(3x+1)	\int\:3\sqrt{3x+1}dx
integral of x(x+2)^4	\int\:x(x+2)^{4}dx
tangent of f(x)=4x^3-12x^2,\at x=-2	tangent\:f(x)=4x^{3}-12x^{2},\at\:x=-2
integral of sin(9t)	\int\:\sin(9t)dt
integral from 0 to 1 of x(4/9 x(5-x^2))	\int\:_{0}^{1}x(\frac{4}{9}x(5-x^{2}))dx
limit as x approaches 3 of 5+x	\lim\:_{x\to\:3}(5+x)
(\partial)/(\partial x)(3x^2-2y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}-2y^{2})
(\partial)/(\partial x)(ln(6x^2+7y^2+3))	\frac{\partial\:}{\partial\:x}(\ln(6x^{2}+7y^{2}+3))
(\partial)/(\partial x)(x^4y^6+4x^7y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{6}+4x^{7}y)
y^{'''}-3y^{''}+3y^'-y=x-3e^x	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=x-3e^{x}
maclaurin t^2e^{2t}	maclaurin\:t^{2}e^{2t}
integral from-7 to 7 of xsqrt(49-x^2)	\int\:_{-7}^{7}x\sqrt{49-x^{2}}dx
dy-dx+y=e^{4x}	dy-dx+y=e^{4x}
integral from-2 to 3 of (49)/(x^4)	\int\:_{-2}^{3}\frac{49}{x^{4}}dx
integral of 2tan^3(x)sec(x)	\int\:2\tan^{3}(x)\sec(x)dx
derivative of f(x)=(6x)/(x+1)	derivative\:f(x)=\frac{6x}{x+1}
derivative of 1/(2x^{1/2})	\frac{d}{dx}(\frac{1}{2x^{\frac{1}{2}}})
integral of (x^5)/(x^6+5)	\int\:\frac{x^{5}}{x^{6}+5}dx
laplacetransform (e^{4t}-e^{-3t})^2	laplacetransform\:(e^{4t}-e^{-3t})^{2}
derivative of (x^2-4^5(3x+5)^4)	\frac{d}{dx}((x^{2}-4)^{5}(3x+5)^{4})
integral of (5x-3)/((x+1)(x-3))	\int\:\frac{5x-3}{(x+1)(x-3)}dx
tangent of 9x^2	tangent\:9x^{2}
(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0	(y^{2}-2xy+6x)dx-(x^{2}-2xy+2)dy=0
integral from 1 to e^2 of (ln^2(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{2}(x^{2})}{x}dx
integral of e^{9x}cos(4x)	\int\:e^{9x}\cos(4x)dx
integral of 1/(csc(2x))csc(2x)cot(2x)	\int\:\frac{1}{\csc(2x)}\csc(2x)\cot(2x)dx
(dy)/(dx)+3x^2y=sin(x)e^{-x^3},y(0)=1	\frac{dy}{dx}+3x^{2}y=\sin(x)e^{-x^{3}},y(0)=1
integral of-9x^5e^{x^6}	\int\:-9x^{5}e^{x^{6}}dx
limit as x approaches 5-of (3x)/(2x+10)	\lim\:_{x\to\:5-}(\frac{3x}{2x+10})
integral of (20x+3)	\int\:(20x+3)dx
derivative of (arctan(3x)^2)	\frac{d}{dx}((\arctan(3x))^{2})

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