Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
57501	Find the Second Derivative	y=5cos(x)+4(x+6)^-2-3x	$y = 5 \cos (x) + 4 {(x + 6)}^{- 2} - 3 x$
57502	Find the Second Derivative	xy=sin(y)	$x y = \sin (y)$
57503	Find the Second Derivative	y=5e^(-x)-3e^(-5x)	$y = 5 e^{- x} - 3 e^{- 5 x}$
57504	Find the Second Derivative	y=6sec(theta)	$y = 6 \sec (θ)$
57505	Find the Second Derivative	y=(17x^3)/6-2	$y = \frac{17 x^{3}}{6} - 2$
57506	Find the Second Derivative	s=t^3-6t^2+12t	$s = t^{3} - 6 t^{2} + 12 t$
57507	Find the Second Derivative	y=2x^3+5x^2	$y = 2 x^{3} + 5 x^{2}$
57508	Find the Second Derivative	f(theta)=7cos(theta)	$f (θ) = 7 \cos (θ)$
57509	Find the Second Derivative	20x^2+y^2=7	$20 x^{2} + y^{2} = 7$
57510	Find the Second Derivative	y^11-11/2x^2=2	$y^{11} - \frac{11}{2} x^{2} = 2$
57511	Find the Second Derivative	y=7x-8	$y = 7 x - 8$
57512	Find the Second Derivative	y=5x^2-14x-6x^-3	$y = 5 x^{2} - 14 x - 6 x^{- 3}$
57513	Find the Second Derivative	y=9/(x^2)-4/x	$y = \frac{9}{x^{2}} - \frac{4}{x}$
57514	Find the Second Derivative	y=14x-12x^2	$y = 14 x - 12 x^{2}$
57515	Find the Second Derivative	s=-t^3+12t^2-36t	$s = - t^{3} + 12 t^{2} - 36 t$
57516	Find the Second Derivative	v=2t^2+4t+15	$v = 2 t^{2} + 4 t + 15$
57517	Find the Second Derivative	y=9x^-5-7/x	$y = 9 x^{- 5} - \frac{7}{x}$
57518	Find the Second Derivative	y = square root of 7x+9	$y = \sqrt{7 x + 9}$
57519	Find the Second Derivative	y = natural log of xcos(x)	$y = \ln (x) \cos (x)$
57520	Find the Second Derivative	e^(3y)+x=y	$e^{3 y} + x = y$
57521	Find the Symmetry	x^2+25y^2=25	$x^{2} + 25 y^{2} = 25$
57522	Find the Symmetry	\|x\|+\|y\|=7.3	$\| x \| + \| y \| = 7.3$
57523	Find the Symmetry	x^2+y-121=0	$x^{2} + y - 121 = 0$
57524	Find the Symmetry	x^2+y-9=0	$x^{2} + y - 9 = 0$
57525	Find the Symmetry	y=x^3-27	$y = x^{3} - 27$
57526	Find the Symmetry	y=-4x+1	$y = - 4 x + 1$
57527	Find the Behavior (Leading Coefficient Test)	f(x)=(x+1)^3(x^2-1)^2(1-x^4)(2x+3)	$f (x) = {(x + 1)}^{3} {(x^{2} - 1)}^{2} (1 - x^{4}) (2 x + 3)$
57528	Eliminate the Parameter	x=cos(theta) , y=5sec(theta)	$x = \cos (θ)$ , $y = 5 \sec (θ)$
57529	Eliminate the Parameter	x=7cos(t) , y=3cos(7t)	$x = 7 \cos (t)$ , $y = 3 \cos (7 t)$
57530	Eliminate the Parameter	x=cos(t) , y=2sin(2t)	$x = \cos (t)$ , $y = 2 \sin (2 t)$
57531	Eliminate the Parameter	x=cos(thetay)=cos(theta)^2+8cos(theta)	$x = \cos (θ)$ $y = \cos^{2} (θ) + 8 \cos (θ)$
57532	Eliminate the Parameter	x=4t-3 , y=3t+1	$x = 4 t - 3$ , $y = 3 t + 1$
57533	Eliminate the Parameter	x=5cos(theta) , y=6sin(theta)	$x = 5 \cos (θ)$ , $y = 6 \sin (θ)$
57534	Eliminate the Parameter	x=sin(1/2t) , y=cos(1/2t)	$x = \sin (\frac{1}{2} t)$ , $y = \cos (\frac{1}{2} t)$
57535	Eliminate the Parameter	x=e^t , y=e^(-4t)	$x = e^{t}$ , $y = e^{- 4 t}$
57536	Eliminate the Parameter	x=e^t , y=e^(-3t)	$x = e^{t}$ , $y = e^{- 3 t}$
57537	Eliminate the Parameter	x=cos(xy)=2sin(x)^2	$x = \cos (x y) = 2 \sin^{2} (x)$
57538	Eliminate the Parameter	x=e^( square root of t) , y=t- natural log of t^2 , t=1	$x = e^{\sqrt{t}}$ , $y = t - \ln (t^{2})$ , $t = 1$
57539	Eliminate the Parameter	x=e^t y=t	$x = e^{t}$ $y = t$
57540	Eliminate the Parameter	x=e^t-5 , y=e^(2t)	$x = e^{t} - 5$ , $y = e^{2 t}$
57541	Eliminate the Parameter	x=e^t-9 , y=e^(2t)	$x = e^{t} - 9$ , $y = e^{2 t}$
57542	Eliminate the Parameter	x = natural log of ty = square root of t	$x = \ln (t) y = \sqrt{t}$
57543	Eliminate the Parameter	x = natural log of t y = square root of t	$x = \ln (t)$ $y = \sqrt{t}$
57544	Eliminate the Parameter	x=3cos(t) , y=4sin(t)	$x = 3 \cos (t)$ , $y = 4 \sin (t)$
57545	Eliminate the Parameter	x=3cos(theta) , y=4sin(theta)	$x = 3 \cos (θ)$ , $y = 4 \sin (θ)$
57546	Eliminate the Parameter	x=1/4t , y=t^2	$x = \frac{1}{4} t$ , $y = t^{2}$
57547	Eliminate the Parameter	x = square root of t , y=6-t	$x = \sqrt{t}$ , $y = 6 - t$
57548	Eliminate the Parameter	x=1-t^2 , y=t-2	$x = 1 - t^{2}$ , $y = t - 2$
57549	Eliminate the Parameter	x=1-t^2 , y=t-4	$x = 1 - t^{2}$ , $y = t - 4$
57550	Eliminate the Parameter	x=1+e^(2t) y=e^t	$x = 1 + e^{2 t}$ $y = e^{t}$
57551	Eliminate the Parameter	x=2cos(t) , y=2sin(t)	$x = 2 \cos (t)$ , $y = 2 \sin (t)$
57552	Eliminate the Parameter	x=t^2 , y=t^7	$x = t^{2}$ , $y = t^{7}$
57553	Eliminate the Parameter	x=t^3 , y=3 natural log of t	$x = t^{3}$ , $y = 3 \ln (t)$
57554	Eliminate the Parameter	x=tcos(t) , y=tsin(t) , t=pi	$x = t \cos (t)$ , $y = t \sin (t)$ , $t = π$
57555	Eliminate the Parameter	x=tcos(t) , y=tsin(t)	$x = t \cos (t)$ , $y = t \sin (t)$
57556	Eliminate the Parameter	x=t-2 , y=t/(t-2)	$x = t - 2$ , $y = \frac{t}{t - 2}$
57557	Rationalize the Denominator	8/(3- square root of 11)	$\frac{8}{3 - \sqrt{11}}$
57558	Rationalize the Denominator	7/(1- square root of 2)	$\frac{7}{1 - \sqrt{2}}$
57559	Rationalize the Denominator	6/(2-3 square root of 2)	$\frac{6}{2 - 3 \sqrt{2}}$
57560	Rationalize the Denominator	cube root of 5/3	$\sqrt[3]{\frac{5}{3}}$
57561	Rationalize the Denominator	3/( cube root of 2)	$\frac{3}{\sqrt[3]{2}}$
57562	Rationalize the Denominator	(1- square root of 1+h)/(7h)	$\frac{1 - \sqrt{1 + h}}{7 h}$
57563	Rationalize the Denominator	(1+ square root of 3)/(1- square root of 3)	$\frac{1 + \sqrt{3}}{1 - \sqrt{3}}$
57564	Rationalize the Denominator	4/(1- square root of 3)	$\frac{4}{1 - \sqrt{3}}$
57565	Rationalize the Denominator	4/(9- square root of 10)	$\frac{4}{9 - \sqrt{10}}$
57566	Rationalize the Denominator	-5/(7-2 square root of 5)	$\frac{- 5}{7 - 2 \sqrt{5}}$
57567	Rationalize the Denominator	(5 square root of 3)/(3 square root of 3-4 square root of 6)	$\frac{5 \sqrt{3}}{3 \sqrt{3} - 4 \sqrt{6}}$
57568	Rationalize the Denominator	(5 square root of 3-3 square root of 2)/(3 square root of 2-2 square root of 3)	$\frac{5 \sqrt{3} - 3 \sqrt{2}}{3 \sqrt{2} - 2 \sqrt{3}}$
57569	Rationalize the Denominator	6/( square root of 7)	$\frac{6}{\sqrt{7}}$
57570	Rationalize the Denominator	(4-6i)/(1-4i)	$\frac{4 - 6 i}{1 - 4 i}$
57571	Rationalize the Denominator	( cube root of 2)/( cube root of 3)	$\frac{\sqrt[3]{2}}{\sqrt[3]{3}}$
57572	Rationalize the Denominator	( square root of 6- square root of 5)/( square root of 6+ square root of 5)	$\frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}$
57573	Rationalize the Denominator	( square root of a+ square root of b)/( square root of a- square root of b)	$\frac{\sqrt{a} + \sqrt{b}}{\sqrt{a} - \sqrt{b}}$
57574	Rationalize the Denominator	( square root of h-3)/h	$\frac{\sqrt{h} - 3}{h}$
57575	Graph the Interval	[0,3]	$[0, 3]$
57576	Graph the Interval	[2,5]	$[2, 5]$
57577	Graph the Interval	[0,5]	$[0, 5]$
57578	Graph the Interval	[5,infinity)	$[5, \infty)$
57579	Graph the Interval	[0,2pi)	$[0, 2 π)$
57580	Graph the Interval	[0,2pi]	$[0, 2 π]$
57581	Graph the Interval	[-2,infinity)	$[- 2, \infty)$
57582	Identify the Conic	4x^2-4xy+y^2-8 square root of 5x-16 square root of 5y=0	$4 x^{2} - 4 x y + y^{2} - 8 \sqrt{5} x - 16 \sqrt{5} y = 0$
57583	Identify the Conic	9x^2+4y^2-54x-24y+117=0	$9 x^{2} + 4 y^{2} - 54 x - 24 y + 117 = 0$
57584	Identify the Conic	x^2+8x-10y-34=10	$x^{2} + 8 x - 10 y - 34 = 10$
57585	Expand Using Sum/Difference Formulas	sin(5/6+5/7)	$\sin (\frac{5}{6} + \frac{5}{7})$
57586	Expand Using Sum/Difference Formulas	sin(52 degrees )cos(13 degrees )-cos(52 degrees )sin(13 degrees )	$\sin (52 °) \cos (13 °) - \cos (52 °) \sin (13 °)$
57587	Expand Using Sum/Difference Formulas	sin(4/5+( square root of 2)/2)	$\sin (\frac{4}{5} + \frac{\sqrt{2}}{2})$
57588	Expand Using Sum/Difference Formulas	sin(180 degrees -30 degrees )	$\sin (180 ° - 30 °)$
57589	Expand Using Sum/Difference Formulas	tan((-13pi)/6)	$\tan (\frac{- 13 π}{6})$
57590	Expand Using Sum/Difference Formulas	2sin(37 degrees )cos(101 degrees )	$2 \sin (37 °) \cos (101 °)$
57591	Expand Using Sum/Difference Formulas	sin((5pi)/12)cos(pi/24)	$\sin (\frac{5 π}{12}) \cos (\frac{π}{24})$
57592	Expand Using Sum/Difference Formulas	sin(120 degrees )	$\sin (120 °)$
57593	Expand Using Sum/Difference Formulas	cos((23pi)/30)cos(pi/15)-sin((23pi)/30)sin(pi/15)	$\cos (\frac{23 π}{30}) \cos (\frac{π}{15}) - \sin (\frac{23 π}{30}) \sin (\frac{π}{15})$
57594	Expand Using Sum/Difference Formulas	sin(60 degrees -45 degrees )	$\sin (60 ° - 45 °)$
57595	Expand Using Sum/Difference Formulas	sin(4/5+pi/4)	$\sin (\frac{4}{5} + \frac{π}{4})$
57596	Find the Vertex	x^2+2x-6	$x^{2} + 2 x - 6$
57597	Find the Vertex	2x^2+10x+8	$2 x^{2} + 10 x + 8$
57598	Find the Vertex	(x-5)^2-1	${(x - 5)}^{2} - 1$
57599	Find the Vertex	(x-2)^2+3	${(x - 2)}^{2} + 3$
57600	Find the Vertex	1/3x^2-8/3x+1/3	$\frac{1}{3} x^{2} - \frac{8}{3} x + \frac{1}{3}$