Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21901	Simplify/Condense	20e^((t/30)(- natural log of 2))	$20 e^{(\frac{t}{30}) (- \ln (2))}$
21902	Simplify/Condense	natural log of u^2+1+ natural log of sin(u)-1/2* natural log of uv	$\ln (u^{2} + 1) + \ln (\sin (u)) - \frac{1}{2} \cdot \ln (u v)$
21903	Find the Critical Points	f(x)=ax^2+bx+c	$f (x) = a x^{2} + b x + c$
21904	Simplify/Condense	1/9* natural log of (x+2)^9+1/2*( natural log of x- natural log of (x^2+3x+2)^2)	$\frac{1}{9} \cdot \ln ({(x + 2)}^{9}) + \frac{1}{2} \cdot (\ln (x) - \ln ({(x^{2} + 3 x + 2)}^{2}))$
21905	Simplify/Condense	natural log of (4x+3)^2- natural log of 3x+1	$\ln ({(4 x + 3)}^{2}) - \ln (3 x + 1)$
21906	Find the Critical Points	y=3x^5-5x^3+1	$y = 3 x^{5} - 5 x^{3} + 1$
21907	Simplify/Condense	1/2* natural log of (x)^2	$\frac{1}{2} \cdot \ln ({(x)}^{2})$
21908	Simplify/Condense	1/2* natural log of 25	$\frac{1}{2} \cdot \ln (25)$
21909	Simplify/Condense	1/2* natural log of xy+3/2* natural log of x/y	$\frac{1}{2} \cdot \ln (x y) + \frac{3}{2} \cdot \ln (\frac{x}{y})$
21910	Simplify/Condense	1/8* natural log of 2	$\frac{1}{8} \cdot \ln (2)$
21911	Simplify/Condense	1/3* log of x	$\frac{1}{3} \cdot \log (x)$
21912	Simplify/Condense	1/2* natural log of x+4 natural log of y-2 natural log of z	$\frac{1}{2} \cdot \ln (x) + 4 \ln (y) - 2 \ln (z)$
21913	Simplify/Condense	(31 natural log of 4(57)+1)-(57/3)	$(31 \ln (4 (57) + 1)) - (\frac{57}{3})$
21914	Find the Derivative - d/d@VAR	s(t)=2arccos(t-1)	$s (t) = 2 \arccos (t - 1)$
21915	Find the Derivative - d/d@VAR	s(t)=6t^2+30t	$s (t) = 6 t^{2} + 30 t$
21916	Find the Derivative - d/d@VAR	s(x)=3x+7	$s (x) = 3 x + 7$
21917	Find the Derivative - d/d@VAR	P(x)=30x-0.03x^2-550	$P (x) = 30 x - 0.03 x^{2} - 550$
21918	Find the Derivative - d/d@VAR	r(x)=3-x^2	$r (x) = 3 - x^{2}$
21919	Find the Derivative - d/d@VAR	r(x)=xp(x)	$r (x) = x p (x)$
21920	Find the Local Maxima and Minima	(x^2-4)^2	${(x^{2} - 4)}^{2}$
21921	Find the Derivative - d/d@VAR	v(t)=3t square root of 9-t^2	$v (t) = 3 t \sqrt{9 - t^{2}}$
21922	Find the Derivative - d/d@VAR	y(x)=3xy-x^2-4	$y (x) = 3 x y - x^{2} - 4$
21923	Find the Horizontal Tangent Line	2y^3+y^2-y^5=x^4-2x^3+x^2	$2 y^{3} + y^{2} - y^{5} = x^{4} - 2 x^{3} + x^{2}$
21924	Find the Derivative - d/d@VAR	h(x)=( natural log of x)/(f(x))	$h (x) = \frac{\ln (x)}{f (x)}$
21925	Find the Derivative - d/d@VAR	s(x)=2x+1	$s (x) = 2 x + 1$
21926	Find the Derivative - d/d@VAR	V(t)=45(1-e^(-1.6t))+31	$V (t) = 45 (1 - e^{- 1.6 t}) + 31$
21927	Find the Local Maxima and Minima	(x^2-2x)e^x	$(x^{2} - 2 x) e^{x}$
21928	Find the Local Maxima and Minima	x^3-3x^2-9x	$x^{3} - 3 x^{2} - 9 x$
21929	Find the Local Maxima and Minima	x^3+12x^2-60x+1	$x^{3} + 12 x^{2} - 60 x + 1$
21930	Find the Local Maxima and Minima	-x^3+12x-7	$- x^{3} + 12 x - 7$
21931	Find the Local Maxima and Minima	x^3-12x^2	$x^{3} - 12 x^{2}$
21932	Find the Local Maxima and Minima	x^3-9x^2+15x+3	$x^{3} - 9 x^{2} + 15 x + 3$
21933	Find the Local Maxima and Minima	x^4-12x^3	$x^{4} - 12 x^{3}$
21934	Find the Local Maxima and Minima	x^4-12x^3+48x^2-64x	$x^{4} - 12 x^{3} + 48 x^{2} - 64 x$
21935	Find the Local Maxima and Minima	x^4-18x^2+81	$x^{4} - 18 x^{2} + 81$
21936	Find the Local Maxima and Minima	x^4-2x^3	$x^{4} - 2 x^{3}$
21937	Find the Local Maxima and Minima	x^2e^x	$x^{2} e^{x}$
21938	Find the Local Maxima and Minima	x^2-2x	$x^{2} - 2 x$
21939	Find the Local Maxima and Minima	x^2-8x	$x^{2} - 8 x$
21940	Find the Local Maxima and Minima	square root of x^2+4x+8	$\sqrt{x^{2} + 4 x + 8}$
21941	Find the Local Maxima and Minima	sin(x)^2	$\sin^{2} (x)$
21942	Find the Local Maxima and Minima	square root of 9-x^2	$\sqrt{9 - x^{2}}$
21943	Find the Local Maxima and Minima	cube root of x-3	$\sqrt[3]{x - 3}$
21944	Find the Local Maxima and Minima	x^(4/5)(x-6)^2	$x^{\frac{4}{5}} {(x - 6)}^{2}$
21945	Find the Local Maxima and Minima	x^(1/3)(x+4)	$x^{\frac{1}{3}} (x + 4)$
21946	Find the Local Maxima and Minima	x^(2/3)	$x^{\frac{2}{3}}$
21947	Find the Local Maxima and Minima	(12x^3-239x^2-2462x+584777)/78601	$\frac{12 x^{3} - 239 x^{2} - 2462 x + 584777}{78601}$
21948	Find the Local Maxima and Minima	1/2x^2-x	$\frac{1}{2} x^{2} - x$
21949	Find the Local Maxima and Minima	4x^3+3x^2-6x+1	$4 x^{3} + 3 x^{2} - 6 x + 1$
21950	Find the Local Maxima and Minima	9x^2-36	$9 x^{2} - 36$
21951	Find the Local Maxima and Minima	f(t)=2cos(t)+sin(2t)	$f (t) = 2 \cos (t) + \sin (2 t)$
21952	Find the Local Maxima and Minima	C(x)=375+0.75x^(3/4)	$C (x) = 375 + 0.75 x^{\frac{3}{4}}$
21953	Find the Local Maxima and Minima	a(t)=28.31t^3+381.86t^2-1162.07t+16905.87	$a (t) = 28.31 t^{3} + 381.86 t^{2} - 1162.07 t + 16905.87$
21954	Find the Local Maxima and Minima	f(x)=x^2-16	$f (x) = x^{2} - 16$
21955	Find the Local Maxima and Minima	4x^3-16	$4 x^{3} - 16$
21956	Find the Local Maxima and Minima	6+12x^2-8x^3	$6 + 12 x^{2} - 8 x^{3}$
21957	Find the Local Maxima and Minima	4x-64x^-3	$4 x - 64 x^{- 3}$
21958	Find the Local Maxima and Minima	x^4-6x^2-1	$x^{4} - 6 x^{2} - 1$
21959	Find the Local Maxima and Minima	x^5-11x^4+14x^3-8	$x^{5} - 11 x^{4} + 14 x^{3} - 8$
21960	Find the Local Maxima and Minima	x^5-5x	$x^{5} - 5 x$
21961	Find the Local Maxima and Minima	2x^2+255x+5000	$2 x^{2} + 255 x + 5000$
21962	Find the Local Maxima and Minima	2x^3-3x^2-36x	$2 x^{3} - 3 x^{2} - 36 x$
21963	Find the Local Maxima and Minima	-12x^5+135x^4-400x^3	$- 12 x^{5} + 135 x^{4} - 400 x^{3}$
21964	Find the Local Maxima and Minima	10+4x^2	$10 + 4 x^{2}$
21965	Find the Local Maxima and Minima	12x^2-176x+484	$12 x^{2} - 176 x + 484$
21966	Find the Local Maxima and Minima	190+8x^3+x^4	$190 + 8 x^{3} + x^{4}$
21967	Find the Local Maxima and Minima	2x^3+3x^2-120x	$2 x^{3} + 3 x^{2} - 120 x$
21968	Find the Local Maxima and Minima	3x^2-12x+9	$3 x^{2} - 12 x + 9$
21969	Find the Local Maxima and Minima	3x^3-3x^2+1	$3 x^{3} - 3 x^{2} + 1$
21970	Find the Local Maxima and Minima	3x^2-15	$3 x^{2} - 15$
21971	Find the Local Maxima and Minima	3x^2-28x+63	$3 x^{2} - 28 x + 63$
21972	Find the Local Maxima and Minima	2x-4	$2 x - 4$
21973	Find the Local Maxima and Minima	3x^4-4x^3-12x^2+2	$3 x^{4} - 4 x^{3} - 12 x^{2} + 2$
21974	Find the Local Maxima and Minima	4x^3-27/2x^2+8x	$4 x^{3} - \frac{27}{2} x^{2} + 8 x$
21975	Find the Local Maxima and Minima	3x^4-96x+7	$3 x^{4} - 96 x + 7$
21976	Find the Local Maxima and Minima	4x^3+6x^2-24x+8	$4 x^{3} + 6 x^{2} - 24 x + 8$
21977	Find the Local Maxima and Minima	f(x)=0.2x^2-2.4x+5.9	$f (x) = 0.2 x^{2} - 2.4 x + 5.9$
21978	Find the Local Maxima and Minima	f(x)=-0.3x^2+2.1x+8	$f (x) = - 0.3 x^{2} + 2.1 x + 8$
21979	Find the Local Maxima and Minima	f(x)=(x-1)e^x	$f (x) = (x - 1) e^{x}$
21980	Find the Local Maxima and Minima	f(x)=(x-5)(x^2-10x-50)	$f (x) = (x - 5) (x^{2} - 10 x - 50)$
21981	Evaluate the Integral	integral from 3 to square root of 13 of x with respect to x	$\int_{3}^{\sqrt{13}} x d x$
21982	Find the Local Maxima and Minima	f(x)=(2x^2-8)^2	$f (x) = {(2 x^{2} - 8)}^{2}$
21983	Find the Local Maxima and Minima	f(x)=(2x)/(7x^2+10)	$f (x) = \frac{2 x}{7 x^{2} + 10}$
21984	Find the Local Maxima and Minima	f(x)=(2x)^x	$f (x) = {(2 x)}^{x}$
21985	Find the Tangent Line at (4π,0)	y=sin(sin(x)) , (4pi,0)	$f (x) = (\sin (x) + 1) (2 \cos (x) + \sqrt{3})$
21986	Find the Local Maxima and Minima	f(t)=t square root of 25-t^2	$f (t) = t \sqrt{25 - t^{2}}$
21987	Find the Local Maxima and Minima	f(t)=2+e^t	$f (t) = 2 + e^{t}$
21988	Find the 2nd Derivative	e^(ax)sin(Bx)	$e^{a x} \sin (B x)$
21989	Find the 3rd Derivative	y=x^-7+x^7	$y = x^{- 7} + x^{7}$
21990	Find the Local Maxima and Minima	f(x)=\|x\|	$f (x) = \| x \|$
21991	Find the Local Maxima and Minima	f(x)=\|x-3\|	$f (x) = \| x - 3 \|$
21992	Find the Local Maxima and Minima	f(x)=1/(x^2)	$f (x) = \frac{1}{x^{2}}$
21993	Find the Local Maxima and Minima	f(x)=(4x)/(x^2+16)	$f (x) = \frac{4 x}{x^{2} + 16}$
21994	Find the Local Maxima and Minima	f(x)=5^2-2x^5+10	$f (x) = 5^{2} - 2 x^{5} + 10$
21995	Find the Local Maxima and Minima	f(x)=4/3x^3-12x^2+10x+45	$f (x) = \frac{4}{3} x^{3} - 12 x^{2} + 10 x + 45$
21996	Find the Local Maxima and Minima	f(x)=(4e^x)/(x^4)	$f (x) = \frac{4 e^{x}}{x^{4}}$
21997	Find the Local Maxima and Minima	f(x)=(3x^7)/(e^x)	$f (x) = \frac{3 x^{7}}{e^{x}}$
21998	Find the Local Maxima and Minima	f(x)=10/3x^351/2x^2+5x+16	$f (x) = \frac{10}{3} x^{3} \cdot \frac{51}{2} \cdot x^{2} + 5 x + 16$
21999	Find the Local Maxima and Minima	f(x)=1/4x^4-3x^3-81/2x^2+729x	$f (x) = \frac{1}{4} x^{4} - 3 x^{3} - \frac{81}{2} x^{2} + 729 x$
22000	Find the Local Maxima and Minima	f(x)=1/4x^4-x	$f (x) = \frac{1}{4} x^{4} - x$