Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45701	Find the Antiderivative	-csc(x)cot(x)	$- \csc (x) \cot (x)$
45702	Find the Antiderivative	square root of 1+cos(x)^2	$\sqrt{1 + \cos^{2} (x)}$
45703	Find the Antiderivative	2xdx	$2 x d x$
45704	Find the Antiderivative	-6x^2	$- 6 x^{2}$
45705	Find the Antiderivative	1-2sin(x)	$1 - 2 \sin (x)$
45706	Find the Antiderivative	-1/4sin(2x)	$- \frac{1}{4} \sin (2 x)$
45707	Find the Antiderivative	1/ydy	$\frac{1}{y} d y$
45708	Find the Antiderivative	21x^2	$21 x^{2}$
45709	Find the Antiderivative	1/8x	$\frac{1}{8} x$
45710	Find the Antiderivative	cos(y)^2	$\cos^{2} (y)$
45711	Find the Roots (Zeros)	x^4-625	$x^{4} - 625$
45712	Find the Roots (Zeros)	6x^2+72x+210	$6 x^{2} + 72 x + 210$
45713	Find the Roots (Zeros)	x^2-4x+6	$x^{2} - 4 x + 6$
45714	Find the Roots (Zeros)	4x^3-2x square root of 3-6x	$4 x^{3} - 2 x \sqrt{3} - 6 x$
45715	Find the Roots (Zeros)	2cos(x)+2cos(2x)	$2 \cos (x) + 2 \cos (2 x)$
45716	Find the Roots (Zeros)	x^3-11x^2+43x-65	$x^{3} - 11 x^{2} + 43 x - 65$
45717	Find the Roots (Zeros)	(x^3-2x^2-23x+60)÷(x-4)	$(x^{3} - 2 x^{2} - 23 x + 60) \div (x - 4)$
45718	Find the Antiderivative	1/(1+4x^2)	$\frac{1}{1 + 4 x^{2}}$
45719	Find the Antiderivative	1/3sin(3x)	$\frac{1}{3} \sin (3 x)$
45720	Find the Antiderivative	2x^-4	$2 x^{- 4}$
45721	Find the Asymptotes	f(x)=(x^3-8)/(x-2)	$f (x) = \frac{x^{3} - 8}{x - 2}$
45722	Find the Asymptotes	f(x)=(5x^2-2x+3)/(3x^2-7)	$f (x) = \frac{5 x^{2} - 2 x + 3}{3 x^{2} - 7}$
45723	Find the Asymptotes	f(x)=(2x^2+3x-2)/(x^2-x-2)	$f (x) = \frac{2 x^{2} + 3 x - 2}{x^{2} - x - 2}$
45724	Find the Asymptotes	f(x)=3-5/x	$f (x) = 3 - \frac{5}{x}$
45725	Find the Asymptotes	g(t)=(t-8)/(t^2+64)	$g (t) = \frac{t - 8}{t^{2} + 64}$
45726	Find the Asymptotes	g(t)=(t-4)/(t^2+16)	$g (t) = \frac{t - 4}{t^{2} + 16}$
45727	Find the Asymptotes	f(x)=(2 square root of x)/(x-4 square root of x+4)	$f (x) = \frac{2 \sqrt{x}}{x - 4 \sqrt{x} + 4}$
45728	Find the Asymptotes	f(x)=(2x^2+6x-5)/(7x^2+3)	$f (x) = \frac{2 x^{2} + 6 x - 5}{7 x^{2} + 3}$
45729	Find the Asymptotes	f(x)=(5x)/(x^2-7x)	$f (x) = \frac{5 x}{x^{2} - 7 x}$
45730	Find the Asymptotes	f(x)=(x+5)/(x^2+14x+45)	$f (x) = \frac{x + 5}{x^{2} + 14 x + 45}$
45731	Find the Asymptotes	f(x)=(x^2-5x-50)/(x^2-15x+50)	$f (x) = \frac{x^{2} - 5 x - 50}{x^{2} - 15 x + 50}$
45732	Find the Asymptotes	r(x)=(6x-6)/(x+2)	$r (x) = \frac{6 x - 6}{x + 2}$
45733	Find the Maximum/Minimum Value	x^2+2x+16	$x^{2} + 2 x + 16$
45734	Find the Maximum/Minimum Value	x+49/x	$x + \frac{49}{x}$
45735	Find the Maximum/Minimum Value	x^2-12x+7	$x^{2} - 12 x + 7$
45736	Find the Maximum/Minimum Value	-5x^2+8x-6	$- 5 x^{2} + 8 x - 6$
45737	Find the Derivative Using Chain Rule - d/dq	q=cos(t/( square root of t+8))	$q = \cos (\frac{t}{\sqrt{t + 8}})$
45738	Find the Derivative Using Chain Rule - d/dq	q=cos(t/( square root of t+3))	$q = \cos (\frac{t}{\sqrt{t + 3}})$
45739	Find the Derivative Using Chain Rule - d/dq	q=tan(t/( square root of t+4))	$q = \tan (\frac{t}{\sqrt{t + 4}})$
45740	Find the Derivative Using Chain Rule - d/dt	q=tan(t/( square root of t+2))	$q = \tan (\frac{t}{\sqrt{t + 2}})$
45741	Find the Derivative Using Chain Rule - d/dy	ysin(2x)=xcos(2y)	$y \sin (2 x) = x \cos (2 y)$
45742	Find the Derivative Using Chain Rule - d/dy	3sin(2x-x^2)^5-4x^2y^7+5y^2=1	$3 \sin^{5} (2 x - x^{2}) - 4 x^{2} y^{7} + 5 y^{2} = 1$
45743	Find the Derivative Using Chain Rule - d/d@VAR	g(y)=((y-1)^5)/((y^2+2y)^9)	$g (y) = \frac{{(y - 1)}^{5}}{{(y^{2} + 2 y)}^{9}}$
45744	Find the Derivative Using Chain Rule - d/dk	y=8xe^(-kx)	$y = 8 x e^{- k x}$
45745	Find the Derivative Using Chain Rule - d/dx	y=sin(tan(7x))	$y = \sin (\tan (7 x))$
45746	Find the Derivative Using Chain Rule - d/dx	y=tan(6x^3)	$y = \tan (6 x^{3})$
45747	Find the Derivative Using Chain Rule - d/dx	y=8xe^(-kx)	$y = 8 x e^{- k x}$
45748	Find the Derivative Using Chain Rule - d/dx	y=(5x+9)^10	$y = {(5 x + 9)}^{10}$
45749	Find the Derivative Using Chain Rule - d/dx	((-cos(x))/(1+sin(x)))^2	${(\frac{- \cos (x)}{1 + \sin (x)})}^{2}$
45750	Find Where Increasing/Decreasing Using Derivatives	9x^4+4x^3	$9 x^{4} + 4 x^{3}$
45751	Find Where Increasing/Decreasing Using Derivatives	x square root of 50-x^2	$x \sqrt{50 - x^{2}}$
45752	Find Where Increasing/Decreasing Using Derivatives	x^4-8x^3	$x^{4} - 8 x^{3}$
45753	Find Where Increasing/Decreasing Using Derivatives	x-3 cube root of x	$x - 3 \sqrt[3]{x}$
45754	Find Where Increasing/Decreasing Using Derivatives	(x+9)/(x^2-81)	$\frac{x + 9}{x^{2} - 81}$
45755	Find Where Increasing/Decreasing Using Derivatives	(x-6)^(2/3)	${(x - 6)}^{\frac{2}{3}}$
45756	Find Where Increasing/Decreasing Using Derivatives	2x^3-3x^2-12x+5	$2 x^{3} - 3 x^{2} - 12 x + 5$
45757	Find Where Increasing/Decreasing Using Derivatives	18x(x-1)^3	$18 x {(x - 1)}^{3}$
45758	Find Where Increasing/Decreasing Using Derivatives	3x^3-36x-1	$3 x^{3} - 36 x - 1$
45759	Find the Derivative Using Chain Rule - d/d@VAR	f(z)=z^3sin(2z)^2	$f (z) = z^{3} \sin^{2} (2 z)$
45760	Identify the Polar Equation	r=4sin(theta)+4cos(theta)	$r = 4 \sin (θ) + 4 \cos (θ)$
45761	Identify the Polar Equation	r=6sin(theta)	$r = 6 \sin (θ)$
45762	Find the Difference Quotient	f(x)=1-3x^3	$f (x) = 1 - 3 x^{3}$
45763	Find the Difference Quotient	f(x)=-4x^2-3x-4	$f (x) = - 4 x^{2} - 3 x - 4$
45764	Convert to Logarithmic Form	fourth root of 81=3	$\sqrt[4]{81} = 3$
45765	Find the Asymptotes	(x+4)/(x^3-9x^2+20x)	$\frac{x + 4}{x^{3} - 9 x^{2} + 20 x}$
45766	Find the Asymptotes	(x+4)/(x^3-12x^2+32x)	$\frac{x + 4}{x^{3} - 12 x^{2} + 32 x}$
45767	Find the Asymptotes	(4x)/(x^2-9)	$\frac{4 x}{x^{2} - 9}$
45768	Find the Asymptotes	(3x^3-x^2-48x+16)/(x^2+5x+4)	$\frac{3 x^{3} - x^{2} - 48 x + 16}{x^{2} + 5 x + 4}$
45769	Find the Asymptotes	(7x-2)/(x^2-3x-4)	$\frac{7 x - 2}{x^{2} - 3 x - 4}$
45770	Find the Asymptotes	(x^2-9x+20)/(x^2-6x+8)	$\frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 8}$
45771	Find the Difference Quotient	f(x) = square root of 2x+7	$f (x) = \sqrt{2 x + 7}$
45772	Find the Asymptotes	(x-4)/(x+7)	$\frac{x - 4}{x + 7}$
45773	Find the Asymptotes	log base 5 of 1+x^2	$\log_{5} (1 + x^{2})$
45774	Find Where Increasing/Decreasing	f(x)=7cos(x)^2	$f (x) = 7 \cos^{2} (x)$
45775	Find the Derivative Using Quotient Rule - d/dy	-(21x)/y	$- \frac{21 x}{y}$
45776	Find the Derivative Using Quotient Rule - d/dy	-(5x^2)/(4y^2)	$- \frac{5 x^{2}}{4 y^{2}}$
45777	Find the Derivative Using Quotient Rule - d/dx	-(5x^2)/(4y^2)	$- \frac{5 x^{2}}{4 y^{2}}$
45778	Find the Derivative Using Quotient Rule - d/dx	(2x)/(3y^2)	$\frac{2 x}{3 y^{2}}$
45779	Find the Derivative Using Quotient Rule - d/dx	(6x+7)/( square root of x)	$\frac{6 x + 7}{\sqrt{x}}$
45780	Solve Using the Quadratic Formula	12x^2-216x+665=0	$12 x^{2} - 216 x + 665 = 0$
45781	Find the Tangent Line at (0,3)	y=x^4+3e^x , (0,3)	$y = x^{4} + 3 e^{x}$ , $(0, 3)$
45782	Find the Tangent Line at (8,0)	y = natural log of x^2-8x+1 , (8,0)	$y = \ln (x^{2} - 8 x + 1)$ , $(8, 0)$
45783	Find the Tangent Line at (0,0)	y=4xe^x , (0,0)	$y = 4 x e^{x}$ , $(0, 0)$
45784	Find the Linearization at a=3p/2	f(x)=cos(x) , a=(3pi)/2	$f (x) = \cos (x)$ , $a = \frac{3 π}{2}$
45785	Find the Linearization at a=7p/2	f(x)=cos(x) , a=(7pi)/2	$f (x) = \cos (x)$ , $a = \frac{7 π}{2}$
45786	Find the Linearization at a=4	f(x)=x^2 , a=4	$f (x) = x^{2}$ , $a = 4$
45787	Find the Tangent Line at (0,7)	y=14/(1+e^(-x)) , (0,7)	$y = \frac{14}{(1 + e^{- x})}$ , $(0, 7)$
45788	Find the Tangent Line at (2p,0)	y=sin(sin(x)) , (2pi,0)	$y = \sin (\sin (x))$ , $(2 π, 0)$
45789	Find the Critical Points	f(x)=x^3+9x^2-48x	$f (x) = x^{3} + 9 x^{2} - 48 x$
45790	Find the Critical Points	g(x) = square root of 100-x^2	$g (x) = \sqrt{100 - x^{2}}$
45791	Find the Critical Points	f(x)=8x^3-6x+2	$f (x) = 8 x^{3} - 6 x + 2$
45792	Find the Critical Points	f(x)=xe^(-7x)	$f (x) = x e^{- 7 x}$
45793	Find the Critical Points	f(x)=(5x^2)/(x^2-9)	$f (x) = \frac{5 x^{2}}{x^{2} - 9}$
45794	Find the Critical Points	f(x)=(7-2x)/(5+x)	$f (x) = \frac{7 - 2 x}{5 + x}$
45795	Find the Critical Points	f(x)=x^3-2x^2-4x+7	$f (x) = x^{3} - 2 x^{2} - 4 x + 7$
45796	Find the Critical Points	f(x)=-x^3+12x-13	$f (x) = - x^{3} + 12 x - 13$
45797	Find the Critical Points	f(x)=3x^2-27	$f (x) = 3 x^{2} - 27$
45798	Find the Critical Points	f(x)=2x^2+256/x	$f (x) = 2 x^{2} + \frac{256}{x}$
45799	Find the Critical Points	f(x)=4x^3-6x^2-24x+1	$f (x) = 4 x^{3} - 6 x^{2} - 24 x + 1$
45800	Find the Critical Points	f(x)=2x^3+6x-5	$f (x) = 2 x^{3} + 6 x - 5$