Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60101	Find the Antiderivative	h(t)=4cos(t)	$h (t) = 4 \cos (t)$
60102	Find the Antiderivative	g(z) = square root of z^5	$g (z) = \sqrt{z^{5}}$
60103	Find the Antiderivative	g(t)=t^6+t^5	$g (t) = t^{6} + t^{5}$
60104	Find the Antiderivative	f(x)=x^9	$f (x) = x^{9}$
60105	Divide	3522519.53/10	$\frac{3522519.53}{10}$
60106	Find the Derivative - d/dy	y^2(6-2x)	$y^{2} (6 - 2 x)$
60107	Find the Derivative - d/dz	e^z	$e^{z}$
60108	Find the Derivative - d/dz	x^2y^2+z^2	$x^{2} y^{2} + z^{2}$
60109	Find the Derivative - d/dy	arctan(y/x)	$\arctan (\frac{y}{x})$
60110	Find the Derivative - d/dy	e^(14xy)	$e^{14 x y}$
60111	Find the Derivative - d/dy	6y natural log of x	$6 y \ln (x)$
60112	Find the Derivative - d/dy	square root of 1-y^2	$\sqrt{1 - y^{2}}$
60113	Find the Derivative - d/dy	natural log of x^2+y^2	$\ln (x^{2} + y^{2})$
60114	Find the Derivative - d/dt	sin(2t)^3	$\sin^{3} (2 t)$
60115	Find the Derivative - d/du	2u-pi/2	$2 u - \frac{π}{2}$
60116	Find the Derivative - d/dt	t( natural log of 2t)^2	$t \ln^{2} (2 t)$
60117	Find the Derivative - d/dt	1-t	$1 - t$
60118	Find the Derivative - d/dt	arccsc(-6t^2)	$arccsc (- 6 t^{2})$
60119	Find the Derivative - d/dt	-cos(t)	$- \cos (t)$
60120	Find the Derivative - d/dt	(t^2-3)^2	${(t^{2} - 3)}^{2}$
60121	Find the Area Between the Curves	y=3x^2 ; y=27	$y = 3 x^{2}$ ; $y = 27$
60122	Find the Area Between the Curves	x=-5 , x=1 , y=11x , y=x^2-12	$x = - 5$ , $x = 1$ , $y = 11 x$ , $y = x^{2} - 12$
60123	Find the Area Between the Curves	x=-5 , x=3 , y=5x , y=x^2-6	$x = - 5$ , $x = 3$ , $y = 5 x$ , $y = x^{2} - 6$
60124	Find the Area Between the Curves	y=x^2-39 , y=9-2x	$y = x^{2} - 39$ , $y = 9 - 2 x$
60125	Find the Area Between the Curves	y=-x^2+10x , y=0	$y = - x^{2} + 10 x$ , $y = 0$
60126	Find the Area Between the Curves	y=-x^2+4x , y=x	$y = - x^{2} + 4 x$ , $y = x$
60127	Find the Local Maxima and Minima	f(x,y)=y^3-3y^2-x^2-9y+10x-60	$f (x, y) = y^{3} - 3 y^{2} - x^{2} - 9 y + 10 x - 60$
60128	Find the Local Maxima and Minima	f(x,y)=x^3+y^3-3xy	$f (x, y) = x^{3} + y^{3} - 3 x y$
60129	Find the Maximum/Minimum Value	f(x,y)=4xy-x^3-2y^2	$f (x, y) = 4 x y - x^{3} - 2 y^{2}$
60130	Find the Inverse	square root of 6x	$\sqrt{6 x}$
60131	Solve the System of @WORD	2x^(-1/3)(x-3)^(1/3)+x^(2/3)(x-3)^(-2/3)>=0	$2 x^{- \frac{1}{3}} {(x - 3)}^{\frac{1}{3}} + x^{\frac{2}{3}} {(x - 3)}^{- \frac{2}{3}} \geq 0$
60132	Find the Area Under the Curve	y=7/x ; [1,5]	$y = \frac{7}{x}$ ; $[1, 5]$
60133	Find the Area Under the Curve	y=4/x ; [1,6]	$y = \frac{4}{x}$ ; $[1, 6]$
60134	Find the Asymptotes	f(x)=(2x^3+5x)/(2-x^3)	$f (x) = \frac{2 x^{3} + 5 x}{2 - x^{3}}$
60135	Find the Asymptotes	j(x)=(4x^3-2x-10)/(3x^2+5x-2)	$j (x) = \frac{4 x^{3} - 2 x - 10}{3 x^{2} + 5 x - 2}$
60136	Solve for y	y=x^(2/3)	$y = x^{\frac{2}{3}}$
60137	Solve for y	(dy)/(dt)=63t^8	$\frac{d y}{d t} = 63 t^{8}$
60138	Solve for y	5/(3y)+5/2=5	$\frac{5}{3 y} + \frac{5}{2} = 5$
60139	Solve for y	(dy)/(dt)=45t^4	$\frac{d y}{d t} = 45 t^{4}$
60140	Solve for t	e^(2t)=900	$e^{2 t} = 900$
60141	Solve for t	e^(3t)=2000	$e^{3 t} = 2000$
60142	Solve for t	x=sin(t)	$x = \sin (t)$
60143	Solve for y	(dy)/(dx)=3y	$\frac{d y}{d x} = 3 y$
60144	Solve for L	5L=69120*(L^4)/(13824^2)	$5 L = 69120 \cdot \frac{L^{4}}{13824^{2}}$
60145	Solve for n	sum from i=1 to n of (4i+5)/(n^2)	$\sum_{i = 1}^{n} \frac{4 i + 5}{n^{2}}$
60146	Solve for c	2000=750e^(-0.04(6))+200(6)+c	$2000 = 750 e^{- 0.04 (6)} + 200 (6) + c$
60147	Solve for P	A=P+Prt	$A = P + P r t$
60148	Solve for t	2=e^(0.06t)	$2 = e^{0.06 t}$
60149	Solve for t	144t-16t^2=0	$144 t - 16 t^{2} = 0$
60150	Solve for t	10=40e^(-5t)	$10 = 40 e^{- 5 t}$
60151	Find the Domain	h(x)=1/( fourth root of x^2-5x)	$h (x) = \frac{1}{\sqrt[4]{x^{2} - 5 x}}$
60152	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (e^(3t)-1)/(sin(t))	$lim_{t \to 0} \frac{e^{3 t} - 1}{\sin (t)}$
60153	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(2x))/(x^5)	$lim_{x \to 0} \frac{e^{2 x}}{x^{5}}$
60154	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^(4/3)+4x^(1/3)	$f (x) = x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}$
60155	Find Where Increasing/Decreasing Using Derivatives	f(x)=5x^4-30x^2	$f (x) = 5 x^{4} - 30 x^{2}$
60156	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+9x^2+12x+6	$f (x) = 2 x^{3} + 9 x^{2} + 12 x + 6$
60157	Find the Roots (Zeros)	x^2-2x	$x^{2} - 2 x$
60158	Find the Roots (Zeros)	x^2-2x-2	$x^{2} - 2 x - 2$
60159	Find the Roots (Zeros)	x^2-6x+3	$x^{2} - 6 x + 3$
60160	Find the Quadrant of the Angle	-340 degrees	$- 340 °$
60161	Find the x and y Intercepts	x^3-3x^2	$x^{3} - 3 x^{2}$
60162	Find the Local Maxima and Minima	x^3-16x^2+64x	$x^{3} - 16 x^{2} + 64 x$
60163	Find the Local Maxima and Minima	x square root of 2-x^2	$x \sqrt{2 - x^{2}}$
60164	Find the Local Maxima and Minima	e^(5x)+e^(-x)	$e^{5 x} + e^{- x}$
60165	Find the Inflection Points	y=3x^2 natural log of x/4	$y = 3 x^{2} \ln (\frac{x}{4})$
60166	Find the Second Derivative	f(x)=(x^2+7)^6	$f (x) = {(x^{2} + 7)}^{6}$
60167	Find the Second Derivative	f(x)=4e^x	$f (x) = 4 e^{x}$
60168	Find dx/dy	x=(y^4)/4+1/(8y^2)	$x = \frac{y^{4}}{4} + \frac{1}{8 y^{2}}$
60169	Find the Foci	(x^2)/36-(y^2)/64=1	$\frac{x^{2}}{36} - \frac{y^{2}}{64} = 1$
60170	Solve the System of @WORD	(x-2)(x-5)<0	$(x - 2) (x - 5) < 0$
60171	Find the Critical Points	x^2 natural log of x	$x^{2} \ln (x)$
60172	Find the Local Maxima and Minima	g(x)=170+8x^3+x^4	$g (x) = 170 + 8 x^{3} + x^{4}$
60173	Find the Local Maxima and Minima	f(x)=3x^4-16x^3+24x^2+10	$f (x) = 3 x^{4} - 16 x^{3} + 24 x^{2} + 10$
60174	Expand the Logarithmic Expression	log base x of 3xy^2	$\log_{x} (3 x y^{2})$
60175	Find the Inflection Points	3x^5-20x^3	$3 x^{5} - 20 x^{3}$
60176	Find the Inflection Points	2x^3-9x^2-24x-10	$2 x^{3} - 9 x^{2} - 24 x - 10$
60177	Find the Inflection Points	(x^2)/(x^2-16)	$\frac{x^{2}}{x^{2} - 16}$
60178	Find the Inflection Points	x^(1/7)(x+8)	$x^{\frac{1}{7}} (x + 8)$
60179	Find the Inflection Points	x^4-54x^2-8x+10	$x^{4} - 54 x^{2} - 8 x + 10$
60180	Find the Fourth Derivative	x^3	$x^{3}$
60181	Find the Fourth Derivative	cos(2x)	$\cos (2 x)$
60182	Find the Fourth Derivative	1/(x+1)	$\frac{1}{x + 1}$
60183	Evaluate the Function	f(x)=4x^2-9+26 ; x=4	$f (x) = 4 x^{2} - 9 + 26$ ; $x = 4$
60184	Find the Tangent Line at the Point	f(x)=15-x^2 , (3,6)	$f (x) = 15 - x^{2}$ , $(3, 6)$
60185	Find the Concavity	x^4-3x^3	$x^{4} - 3 x^{3}$
60186	Find the Concavity	2X^3+3X^2-72X	$2 X^{3} + 3 X^{2} - 72 X$
60187	Simplify	square root of (5x)/7	$\sqrt{\frac{5 x}{7}}$
60188	Find Where Increasing/Decreasing Using Derivatives	x square root of 100-x^2	$x \sqrt{100 - x^{2}}$
60189	Find the Derivative of the Integral	integral from 6 to x^3 of 1/(p^2) with respect to p	$\int_{6}^{x^{3}} \frac{1}{p^{2}} d p$
60190	Find the Concavity	f(x)=2+3x-x^3	$f (x) = 2 + 3 x - x^{3}$
60191	Find the Concavity	f(x)=x^3-12x+2	$f (x) = x^{3} - 12 x + 2$
60192	Find the Antiderivative	r(theta)=sec(theta)tan(theta)-4e^theta	$r (θ) = \sec (θ) \tan (θ) - 4 e^{θ}$
60193	Find the Antiderivative	q(y)=y^5+1/y	$q (y) = y^{5} + \frac{1}{y}$
60194	Find the Antiderivative	f(x)=x(12x+6)	$f (x) = x (12 x + 6)$
60195	Find the Antiderivative	f(x)=x(15x+6)	$f (x) = x (15 x + 6)$
60196	Find the Antiderivative	f(x)=x(7-x)^2	$f (x) = x {(7 - x)}^{2}$
60197	Find the Antiderivative	f(x)=6x^2	$f (x) = 6 x^{2}$
60198	Find the Antiderivative	f(x)=6	$f (x) = 6$
60199	Find the Antiderivative	f(x)=8x^7	$f (x) = 8 x^{7}$
60200	Find the Antiderivative	f(x)=8x+7	$f (x) = 8 x + 7$