Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
49701	Find the Derivative Using Chain Rule - d/dh	V=1/3pir^2h	$V = \frac{1}{3} π r^{2} h$
49702	Find the Derivative Using Chain Rule - d/dp	p=(10+sec(q))/(10-sec(q))	$p = \frac{10 + \sec (q)}{10 - \sec (q)}$
49703	Find the Derivative Using Chain Rule - d/dr	r=6(sec(theta)-tan(theta))^(3/2)	$r = 6 {(\sec (θ) - \tan (θ))}^{\frac{3}{2}}$
49704	Find the Derivative Using Chain Rule - d/ds	s=sin((3pit)/2)-cos((3pit)/2)	$s = \sin (\frac{3 π t}{2}) - \cos (\frac{3 π t}{2})$
49705	Find the Derivative Using Chain Rule - d/ds	s=t^7 natural log of \|t\|	$s = t^{7} \ln (\| t \|)$
49706	Find the Derivative Using Chain Rule - d/dt	integral from -2 to 2x of (3t^2+2t) with respect to t	$\int_{- 2}^{2 x} (3 t^{2} + 2 t) d t$
49707	Find the Derivative Using Chain Rule - d/dt	integral from 4 to x^2 of (3t^2+2t) with respect to t	$\int_{4}^{x^{2}} (3 t^{2} + 2 t) d t$
49708	Find the Derivative Using Chain Rule - d/dt	s=sin((3pit)/2)-cos((3pit)/2)	$s = \sin (\frac{3 π t}{2}) - \cos (\frac{3 π t}{2})$
49709	Find the Derivative Using Chain Rule - d/dt	w=(t^5+1)^93	$w = {(t^{5} + 1)}^{93}$
49710	Find the Derivative Using Chain Rule - d/dt	y=3t(2t^2-5)^4	$y = 3 t {(2 t^{2} - 5)}^{4}$
49711	Find the Derivative Using Chain Rule - d/dt	y=arccot( square root of 2t)	$y = arccot (\sqrt{2 t})$
49712	Find the Derivative Using Chain Rule - d/dt	y=dcos(t)+t^2sin(t)	$y = d \cos (t) + t^{2} \sin (t)$
49713	Find the Derivative Using Chain Rule - d/du	d/(du)(9u^0.1-6u^3.4)	$\frac{d}{d u} (9 u^{0.1} - 6 u^{3.4})$
49714	Find the Derivative Using Chain Rule - d/dv	v=1/3pir^2h	$v = \frac{1}{3} π r^{2} h$
49715	Find the Derivative Using Chain Rule - d/dw	(1+ square root of w^3+3)^4	${(1 + \sqrt{w^{3} + 3})}^{4}$
49716	Find the Derivative Using Chain Rule - d/dz	z=a/(y^12)+Be^y	$z = \frac{a}{y^{12}} + B e^{y}$
49717	Find the Tangent Line at (1,1)	y=5x-4 square root of x , (1,1)	$y = 5 x - 4 \sqrt{x}$ , $(1, 1)$
49718	Find the Tangent Line at x=a	y=3+4x^2-2x^3 , x=a	$y = 3 + 4 x^{2} - 2 x^{3}$ , $x = a$
49719	Find the Tangent Line at (4,57)	y=x^3-2x+1 (4,57)	$y = x^{3} - 2 x + 1$ $(4, 57)$
49720	Find the Tangent Line at (1,1/e)	y=x^4e^(-x) , (1,1/e)	$y = x^{4} e^{- x}$ , $(1, \frac{1}{e})$
49721	Find the Tangent Line at (3,22)	y=x^3-2x+1 , (3,22)	$y = x^{3} - 2 x + 1$ , $(3, 22)$
49722	Find the Tangent Line at (4,1/6)	y=( square root of x)/(x+8) , (4,1/6)	$y = \frac{\sqrt{x}}{x + 8}$ , $(4, \frac{1}{6})$
49723	Find the Tangent Line at (0,p/12)	cos(6y)=x ; (0,pi/12)	$\cos (6 y) = x$ ; $(0, \frac{π}{12})$
49724	Find the Tangent Line at (1,3)	y=5x-2 square root of x , (1,3)	$y = 5 x - 2 \sqrt{x}$ , $(1, 3)$
49725	Find the Tangent Line at (0,8)	y=8e^x+x , (0,8)	$y = 8 e^{x} + x$ , $(0, 8)$
49726	Find the Tangent Line at (0,0.5)	x^2+y^2=(5x^2+2y^2-x)^2 , (0,0.5)	$x^{2} + y^{2} = {(5 x^{2} + 2 y^{2} - x)}^{2}$ , $(0, 0.5)$
49727	Find the Tangent Line at (4,p/4)	y=arctan(1/4x) ; (4,pi/4)	$y = \arctan (\frac{1}{4} x)$ ; $(4, \frac{π}{4})$
49728	Find the Tangent Line at x=3	y=125/(x^2+25) , x=3	$y = \frac{125}{x^{2} + 25}$ , $x = 3$
49729	Find the Tangent Line at (3,0)	y=(x^3-9x)^8 , (3,0)	$y = {(x^{3} - 9 x)}^{8}$ , $(3, 0)$
49730	Find the Tangent Line at x=p/3	8sin(x)cos(x) ; x=pi/3	$8 \sin (x) \cos (x)$ ; $x = \frac{π}{3}$
49731	Find the Tangent Line at (1,e)	y=x^2e^x-2xe^x+2e^x , (1,e)	$y = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}$ , $(1, e)$
49732	Find the Tangent Line at a=5	y=x^3-25x+5 ; a=5	$y = x^{3} - 25 x + 5$ ; $a = 5$
49733	Find the Tangent Line at (16,32)	y=8 square root of x , (16,32)	$y = 8 \sqrt{x}$ , $(16, 32)$
49734	Find the Tangent Line at x=25	y=-9x^(1/2)+x^(3/2) ; x=25	$y = - 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}$ ; $x = 25$
49735	Find the Tangent Line at x=3	y=64/(x^2+16) , x=3	$y = \frac{64}{x^{2} + 16}$ , $x = 3$
49736	Find the Linearization at x=1	f(x)=cos(pi/6x) , x=1	$f (x) = \cos (\frac{π}{6} x)$ , $x = 1$
49737	Find the Linearization at a=5p/2	f(x)=cos(x) , a=(5pi)/2	$f (x) = \cos (x)$ , $a = \frac{5 π}{2}$
49738	Find the Linearization at a=0	cube root of 1+x , a=0	$\sqrt[3]{1 + x}$ , $a = 0$
49739	Find the Linearization at a=1	x^4+2x^2 , a=1	$x^{4} + 2 x^{2}$ , $a = 1$
49740	Solve Using the Quadratic Formula	h=-16t^2+64t+80	$h = - 16 t^{2} + 64 t + 80$
49741	Solve Using the Quadratic Formula	3x^2-16x-8=0	$3 x^{2} - 16 x - 8 = 0$
49742	Solve Using the Quadratic Formula	12x^2-276x+1080=0	$12 x^{2} - 276 x + 1080 = 0$
49743	Solve Using the Quadratic Formula	3x(x+5)=-8	$3 x (x + 5) = - 8$
49744	Solve Using the Quadratic Formula	2x^2-6x-2=0	$2 x^{2} - 6 x - 2 = 0$
49745	Convert to Rectangular	x=sin(theta/2) , y=cos(theta/2)	$x = \sin (\frac{θ}{2})$ , $y = \cos (\frac{θ}{2})$
49746	Eliminate the Parameter	x=sin(theta) , y=cos(theta)	$x = \sin (θ)$ , $y = \cos (θ)$
49747	Eliminate the Parameter	x=e^t , y=te^(-t)	$x = e^{t}$ , $y = t e^{- t}$
49748	Eliminate the Parameter	x=3cos(t) , y=3sin(t)	$x = 3 \cos (t)$ , $y = 3 \sin (t)$
49749	Eliminate the Parameter	x=1-t^2 , y=t-5	$x = 1 - t^{2}$ , $y = t - 5$
49750	Eliminate the Parameter	x=1-t^2 , y=t-3	$x = 1 - t^{2}$ , $y = t - 3$
49751	Eliminate the Parameter	x=tan(theta) , y=sec(theta) , (1, square root of 2)	$x = \tan (θ)$ , $y = \sec (θ)$ , $(1, \sqrt{2})$
49752	Eliminate the Parameter	x=t^2+2 , y=t^2-4	$x = t^{2} + 2$ , $y = t^{2} - 4$
49753	Rationalize the Denominator	( square root of 11)/( square root of 3)	$\frac{\sqrt{11}}{\sqrt{3}}$
49754	Rationalize the Denominator	( square root of 11+ square root of 3)/( square root of 11- square root of 3)	$\frac{\sqrt{11} + \sqrt{3}}{\sqrt{11} - \sqrt{3}}$
49755	Find the Derivative Using Quotient Rule - d/dx	(5x)/(3y)	$\frac{5 x}{3 y}$
49756	Find the Derivative Using Quotient Rule - d/dx	(20x^3+14x^2-3)/(5x^2-4x)	$\frac{(20 x^{3} + 14 x^{2} - 3)}{(5 x^{2} - 4 x)}$
49757	Find the Derivative Using Quotient Rule - d/dx	-(y^(1/3))/(x^(1/3))	$- \frac{y^{\frac{1}{3}}}{x^{\frac{1}{3}}}$
49758	Find the Derivative Using Quotient Rule - d/dx	y=((x-6)^9)/((x-5)^6)	$y = \frac{{(x - 6)}^{9}}{{(x - 5)}^{6}}$
49759	Find the Derivative Using Quotient Rule - d/dx	y=(x^9)/(x^4)	$y = \frac{x^{9}}{x^{4}}$
49760	Find the Derivative Using Quotient Rule - d/dx	-(2x^2)/(3y^2)	$- \frac{2 x^{2}}{3 y^{2}}$
49761	Find the Derivative Using Quotient Rule - d/dx	(tan(x)-1)/(sec(x))	$\frac{(\tan (x) - 1)}{\sec (x)}$
49762	Find Where Increasing/Decreasing	f(x)=sin(x)-3	$f (x) = \sin (x) - 3$
49763	Find Where Increasing/Decreasing	f(x)=16x^2-9	$f (x) = 16 x^{2} - 9$
49764	Find Where Increasing/Decreasing	f(x)=8-3x	$f (x) = 8 - 3 x$
49765	Find Where Increasing/Decreasing	f(x)=1/3e^(-x)	$f (x) = \frac{1}{3} e^{- x}$
49766	Find the Derivative Using Quotient Rule - d/dy	(5x)/(3y)	$\frac{5 x}{3 y}$
49767	Find the Derivative Using Quotient Rule - d/dv	v=(2t)/((t+1)^2)	$v = \frac{2 t}{{(t + 1)}^{2}}$
49768	Find the Derivative Using Quotient Rule - d/dt	y=(t^2+4)/(t^4-3t^2+5)	$y = \frac{t^{2} + 4}{t^{4} - 3 t^{2} + 5}$
49769	Find the Derivative Using Quotient Rule - d/dt	d/(dt)((t^2+1)/(t^2-1))	$\frac{d}{d t} (\frac{t^{2} + 1}{t^{2} - 1})$
49770	Find the Derivative Using Quotient Rule - d/dw	(6w^6-w)/w	$\frac{6 w^{6} - w}{w}$
49771	Find the Derivative Using Quotient Rule - d/dw	(5w^4-w)/w	$\frac{5 w^{4} - w}{w}$
49772	Find the Derivative Using Quotient Rule - d/dv	y=(v^3-2v square root of v)/v	$y = \frac{v^{3} - 2 v \sqrt{v}}{v}$
49773	Find the Derivative Using Quotient Rule - d/dw	(w^3-w)/w	$\frac{w^{3} - w}{w}$
49774	Find the Derivative Using Quotient Rule - d/dt	(cos(t))/(t^7)	$\frac{\cos (t)}{t^{7}}$
49775	Find the Derivative Using Quotient Rule - d/dw	(3w^5-w)/w	$\frac{3 w^{5} - w}{w}$
49776	Find the Derivative Using Quotient Rule - d/d@VAR	h(w)=(5w^6-w)/w	$h (w) = \frac{5 w^{6} - w}{w}$
49777	Find the Derivative Using Quotient Rule - d/dc	(cx+a)/(ax+b)	$\frac{c x + a}{a x + b}$
49778	Find the Derivative Using Quotient Rule - d/d@VAR	p(t)=(500t)/(2t^2+9)	$p (t) = \frac{500 t}{2 t^{2} + 9}$
49779	Find Where Increasing/Decreasing	f(x)=-2x^2-2x-4	$f (x) = - 2 x^{2} - 2 x - 4$
49780	Find Where Increasing/Decreasing	f(x)=3-8x	$f (x) = 3 - 8 x$
49781	Find Three Ordered Pair Solutions	x=9	$x = 9$
49782	Find the Inverse	y=2/3x-5	$y = \frac{2}{3} x - 5$
49783	Find the Inverse	y=x^3-5	$y = x^{3} - 5$
49784	Find the Inverse	y=(x-3)^3	$y = {(x - 3)}^{3}$
49785	Find the Directrix	x=1/16y^2	$x = \frac{1}{16} y^{2}$
49786	Find the Directrix	6x+y^2-8y+4=0	$6 x + y^{2} - 8 y + 4 = 0$
49787	Find the Directrix	y^2=6x	$y^{2} = 6 x$
49788	Find the Directrix	y=1/12x^2	$y = \frac{1}{12} x^{2}$
49789	Find the Points of Intersection	x^2-y^2=7 , x-y=1	$x^{2} - y^{2} = 7$ , $x - y = 1$
49790	Find the Center and Radius	x^2+y^2+6x-10y+18=0	$x^{2} + y^{2} + 6 x - 10 y + 18 = 0$
49791	Find the Center and Radius	x^2+y^2+2x-8y+26=0	$x^{2} + y^{2} + 2 x - 8 y + 26 = 0$
49792	Find the Center and Radius	x^2+y^2+12x+6y+44=0	$x^{2} + y^{2} + 12 x + 6 y + 44 = 0$
49793	Find the Center and Radius	x^2+y^2-4x-2y-20=0	$x^{2} + y^{2} - 4 x - 2 y - 20 = 0$
49794	Find the Center and Radius	x^2+y^2-6x-4y-23=0	$x^{2} + y^{2} - 6 x - 4 y - 23 = 0$
49795	Find the Center and Radius	x^2+y^2-6x-10y+34=0	$x^{2} + y^{2} - 6 x - 10 y + 34 = 0$
49796	Find the Center and Radius	x^2+y^2+4x-10y+33=0	$x^{2} + y^{2} + 4 x - 10 y + 33 = 0$
49797	Find the Center and Radius	(x-17)^2+(y-19)^2=49	${(x - 17)}^{2} + {(y - 19)}^{2} = 49$
49798	Find the Center and Radius	3x^2+3y^2-6x+2y-14=0	$3 x^{2} + 3 y^{2} - 6 x + 2 y - 14 = 0$
49799	Find the Local Maxima and Minima	x^3-5x^2-8x-4	$x^{3} - 5 x^{2} - 8 x - 4$
49800	Find the Local Maxima and Minima	square root of x^4-7x^2+16	$\sqrt{x^{4} - 7 x^{2} + 16}$