Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
15301	Find the Derivative Using Quotient Rule - d/dt	(tsin(t))/(1+t)	$\frac{t \sin (t)}{1 + t}$
15302	Find the Derivative Using Quotient Rule - d/d@VAR	f(x)=(cos(t))/(t^5)	$f (x) = \frac{\cos (t)}{t^{5}}$
15303	Find the Derivative Using Quotient Rule - d/dr	r/( square root of r^2+1)	$\frac{r}{\sqrt{r^{2} + 1}}$
15304	Find the Derivative Using Quotient Rule - d/dt	(1-14t)/((7t)^(1/2))	$\frac{1 - 14 t}{{(7 t)}^{\frac{1}{2}}}$
15305	Find the Derivative Using Quotient Rule - d/d@VAR	f(x)=(e^x)/(x^2)	$f (x) = \frac{e^{x}}{x^{2}}$
15306	Find the Derivative Using Quotient Rule - d/d@VAR	f(x) = square root of x-1/( square root of x)	$f (x) = \sqrt{x} - \frac{1}{\sqrt{x}}$
15307	Find the Derivative Using Product Rule - d/dy	p(y)=(y^-1+y^-2)(8y^-3-10y^-4)	$p (y) = (y^{- 1} + y^{- 2}) (8 y^{- 3} - 10 y^{- 4})$
15308	Find the Derivative Using Product Rule - d/dx	y=7x^2(3x+9)^4	$y = 7 x^{2} {(3 x + 9)}^{4}$
15309	Find the Derivative Using Product Rule - d/dy	e^y*y^e	$e^{y} \cdot y^{e}$
15310	Find the Derivative Using Product Rule - d/dx	y=(5x-3)^4(6x+7)^2	$y = {(5 x - 3)}^{4} {(6 x + 7)}^{2}$
15311	Find the Derivative Using Product Rule - d/dx	y=a/2*(e^(x/a)-e^((-x)/a))	$y = \frac{a}{2} \cdot (e^{\frac{x}{a}} - e^{\frac{- x}{a}})$
15312	Find the Derivative Using Product Rule - d/dx	y=-x^3(3x^4-2)	$y = - x^{3} (3 x^{4} - 2)$
15313	Find the Derivative Using Product Rule - d/dx	y=3x^3(4x^4-7x^3)	$y = 3 x^{3} (4 x^{4} - 7 x^{3})$
15314	Find the Derivative Using Product Rule - d/dx	y=5x^3sin(2x)	$y = 5 x^{3} \sin (2 x)$
15315	Find the Derivative Using Product Rule - d/dx	y=(5x^2-1)(4x+3)	$y = (5 x^{2} - 1) (4 x + 3)$
15316	Graph	theta=(7pi)/4	$θ = \frac{7 π}{4}$
15317	Find the Derivative Using Product Rule - d/dx	sin(x)	$\sin (x)$
15318	Find the Derivative Using Product Rule - d/dx	tan(x)*cos(x)	$\tan (x) \cdot \cos (x)$
15319	Find the Derivative Using Product Rule - d/dx	x(x-4)^3	$x {(x - 4)}^{3}$
15320	Find the Derivative Using Product Rule - d/dx	x square root of x	$x \sqrt{x}$
15321	Find the Derivative Using Product Rule - d/dx	h(x)=7x^2(3x+8)^4	$h (x) = 7 x^{2} {(3 x + 8)}^{4}$
15322	Find the Derivative Using Product Rule - d/dx	h(x)=7x^2(5x+4)^4	$h (x) = 7 x^{2} {(5 x + 4)}^{4}$
15323	Find the Derivative Using Product Rule - d/dx	f(x)=x^5cos(x)	$f (x) = x^{5} \cos (x)$
15324	Find the Derivative Using Product Rule - d/dx	f(x)=2x^(3/4)+4x^(-1/4)	$f (x) = 2 x^{\frac{3}{4}} + 4 x^{- \frac{1}{4}}$
15325	Find the Derivative Using Product Rule - d/dx	f(x) = natural log of \|x\|	$f (x) = \ln (\| x \|)$
15326	Find the Derivative Using Quotient Rule - d/dx	(x+8)/(x-2)	$\frac{x + 8}{x - 2}$
15327	Find the Derivative Using Quotient Rule - d/dx	(sin(3sin(x)))/(sin(x))	$\frac{\sin (3 \sin (x))}{\sin (x)}$
15328	Find the Derivative Using Quotient Rule - d/dx	(sec(x))/(1+tan(x))	$\frac{\sec (x)}{1 + \tan (x)}$
15329	Find the Derivative Using Quotient Rule - d/dx	(8x-16)/(x^2)	$\frac{8 x - 16}{x^{2}}$
15330	Find the Derivative Using Quotient Rule - d/dx	(4x)/(x^2+36)	$\frac{4 x}{x^{2} + 36}$
15331	Find the Derivative Using Quotient Rule - d/dx	7/( cube root of x^2)	$\frac{7}{\sqrt[3]{x^{2}}}$
15332	Find the Derivative Using Quotient Rule - d/dx	(ax+b)/c	$\frac{a x + b}{c}$
15333	Find the Derivative Using Quotient Rule - d/dx	(cos(x))/x	$\frac{\cos (x)}{x}$
15334	Find the Derivative Using Quotient Rule - d/dx	(21 cube root of x)/(x^2-8)	$\frac{21 \sqrt[3]{x}}{x^{2} - 8}$
15335	Find the Derivative Using Quotient Rule - d/dx	(2x)/(x+1)	$\frac{2 x}{x + 1}$
15336	Find the Derivative Using Quotient Rule - d/dx	3/(x^2)	$\frac{3}{x^{2}}$
15337	Find the Derivative Using Quotient Rule - d/dx	(x^6+8y^7)/(x^7+y^8)	$\frac{x^{6} + 8 y^{7}}{x^{7} + y^{8}}$
15338	Find the Derivative Using Quotient Rule - d/dx	1/(x+1)	$\frac{1}{x + 1}$
15339	Find the Derivative Using Quotient Rule - d/dx	14/( cube root of 14x+1)	$\frac{14}{\sqrt[3]{14 x + 1}}$
15340	Find the Derivative Using Quotient Rule - d/dx	F(x)=(x^3+27)/(x+3)	$F (x) = \frac{x^{3} + 27}{x + 3}$
15341	Find the Derivative Using Quotient Rule - d/dx	f(x)=(x^3+3x+2)/(x^2-1)	$f (x) = \frac{x^{3} + 3 x + 2}{x^{2} - 1}$
15342	Find the Derivative Using Quotient Rule - d/dx	f(x)=(3x^2tan(x))/(sec(x))	$f (x) = \frac{3 x^{2} \tan (x)}{\sec (x)}$
15343	Find the Derivative Using Quotient Rule - d/dx	f(x)=x+9/x	$f (x) = x + \frac{9}{x}$
15344	Find the Derivative Using Quotient Rule - d/dx	f(x)=(x+1)/(x-1)	$f (x) = \frac{x + 1}{x - 1}$
15345	Find the Derivative Using Quotient Rule - d/dx	f(x)=(1-4x^2)/(2 square root of x+5)	$f (x) = \frac{1 - 4 x^{2}}{2 \sqrt{x} + 5}$
15346	Find the Derivative Using Quotient Rule - d/dx	y=(x^5)/10* natural log of x-(x^5)/50	$y = \frac{x^{5}}{10} \cdot \ln (x) - \frac{x^{5}}{50}$
15347	Find the Derivative Using Quotient Rule - d/dx	y=-11/( square root of x)	$y = \frac{- 11}{\sqrt{x}}$
15348	Find the Derivative Using Quotient Rule - d/dx	g(x)=(8x^3-1)/(2x-1)	$g (x) = \frac{8 x^{3} - 1}{2 x - 1}$
15349	Find the Derivative Using Quotient Rule - d/dx	y=(3cos(x))/(5x^3)	$y = \frac{3 \cos (x)}{5 x^{3}}$
15350	Find the Derivative Using Quotient Rule - d/dx	y=(5x+8)/( square root of x)	$y = \frac{5 x + 8}{\sqrt{x}}$
15351	Find the Derivative Using Quotient Rule - d/dx	y=(sec(x))/(1+sec(x))	$y = \frac{\sec (x)}{1 + \sec (x)}$
15352	Find the Derivative Using Quotient Rule - d/dx	y=(sin(x))/(x^2)	$y = \frac{\sin (x)}{x^{2}}$
15353	Find the Derivative Using Quotient Rule - d/dy	((9((x7)/6(y7)/2)/((x2)/7y))*1)/2	$\frac{(9 \cdot \frac{\frac{x \cdot 7}{6} \cdot \frac{y \cdot 7}{2}}{\frac{x \cdot 2}{7} \cdot y}) \cdot 1}{2}$
15354	Find the Roots (Zeros)	x=arctan(484.4062/358.7319)	$x = \arctan (\frac{484.4062}{358.7319})$
15355	Simplify	x/(x-1/2)	$\frac{x}{x - \frac{1}{2}}$
15356	Simplify	eighth root of 8	$\sqrt[8]{8}$
15357	Simplify	(x+8)/(x^2-x-72)	$\frac{x + 8}{x^{2} - x - 72}$
15358	Simplify	1 square root of 2	$1 \sqrt{2}$
15359	Simplify	16 square root of x	$16 \sqrt{x}$
15360	Simplify	fifth root of xy^2 cube root of x^4y	$\sqrt[5]{x y^{2}} \sqrt[3]{x^{4} y}$
15361	Simplify	(x(4+x))/((2+x)^2)	$\frac{x (4 + x)}{{(2 + x)}^{2}}$
15362	Simplify	fifth root of 2	$\sqrt[5]{2}$
15363	Simplify	fifth root of square root of 3^-25	$\sqrt[5]{\sqrt{3^{- 25}}}$
15364	Simplify	fifth root of 1/32	$\sqrt[5]{\frac{1}{32}}$
15365	Simplify	cube root of x^(3a+b)	$\sqrt[3]{x^{3 a + b}}$
15366	Simplify	2x square root of x(2 square root of x)	$2 x \sqrt{x} (2 \sqrt{x})$
15367	Simplify	(x-4)/( square root of x-2)	$\frac{x - 4}{\sqrt{x} - 2}$
15368	Simplify	-2 square root of 8k^2	$- 2 \sqrt{8 k^{2}}$
15369	Simplify	2x( square root of x)	$2 x (\sqrt{x})$
15370	Simplify	2736(2/( square root of 3))^7	$2736 {(\frac{2}{\sqrt{3}})}^{7}$
15371	Simplify	5 square root of 64	$5 \sqrt{64}$
15372	Simplify	3e^x square root of x	$3 e^{x} \sqrt{x}$
15373	Simplify	4 square root of t^5	$4 \sqrt{t^{5}}$
15374	Simplify	cos( square root of 2)	$\cos (\sqrt{2})$
15375	Determine if Continuous	f(x) = square root of x-4	$f (x) = \sqrt{x - 4}$
15376	Simplify	arctan( square root of 3/3)	$\arctan (\sqrt{\frac{3}{3}})$
15377	Simplify	cos( square root of 1/2)	$\cos (\sqrt{\frac{1}{2}})$
15378	Simplify	54 square root of 3	$54 \sqrt{3}$
15379	Simplify	arccos(1/( square root of 290))	$\arccos (\frac{1}{\sqrt{290}})$
15380	Simplify	7(8/3) square root of 4-8/3	$7 (\frac{8}{3}) \sqrt{4 - \frac{8}{3}}$
15381	Simplify	9 square root of 399	$9 \sqrt{399}$
15382	Find the Domain	(t)^4-7t+15	${(t)}^{4} - 7 t + 15$
15383	Find the Domain	(x-2)/(x^2-3x+2)	$\frac{x - 2}{x^{2} - 3 x + 2}$
15384	Divide Using Synthetic Division	(4x^3-2x^2-8x+4)/(2x-2)	$\frac{4 x^{3} - 2 x^{2} - 8 x + 4}{2 x - 2}$
15385	Divide Using Synthetic Division	(x^2+3)/(2x^3+7x^2-5x)	$\frac{x^{2} + 3}{2 x^{3} + 7 x^{2} - 5 x}$
15386	Divide Using Long Polynomial Division	(6x^3+23x^2-12x-4)/(3x-2)	$\frac{6 x^{3} + 23 x^{2} - 12 x - 4}{3 x - 2}$
15387	Simplify	sec(x)( cube root of sec(x)^2)	$\sec (x) (\sqrt[3]{\sec^{2} (x)})$
15388	Simplify	sin( cube root of x)	$\sin (\sqrt[3]{x})$
15389	Simplify	t square root of t	$t \sqrt{t}$
15390	Simplify	f''(3) square root of x^2+27	$f'' (3) \sqrt{x^{2} + 27}$
15391	Simplify	(g(t)(t- square root of t))/(t^(1/3))	$\frac{g (t) (t - \sqrt{t})}{t^{\frac{1}{3}}}$
15392	Simplify	t square root of 9-t^2	$t \sqrt{9 - t^{2}}$
15393	Simplify	cube root of 1- square root of x	$\sqrt[3]{1 - \sqrt{x}}$
15394	Simplify	tan( square root of x)	$\tan (\sqrt{x})$
15395	Simplify	y=4e	$y = 4 e$
15396	Find the Domain	(x+1/x+17)/(x+1/x+2)	$\frac{x + \frac{1}{x} + 17}{x + \frac{1}{x} + 2}$
15397	Find the Domain	(x+6)/(x-6)	$\frac{x + 6}{x - 6}$
15398	Find the Domain	(x+2)/(x^2-1)	$\frac{x + 2}{x^{2} - 1}$
15399	Find the Domain	x^2+y^2+z^2-64=0	$x^{2} + y^{2} + z^{2} - 64 = 0$
15400	Find the Domain	(xy-x^2)/(x-9)=7	$\frac{x y - x^{2}}{x - 9} = 7$