Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
12201	Find the Domain and Range	f(x)=(x^2-2x+1)/(x^3+x-7)	$f (x) = \frac{x^{2} - 2 x + 1}{x^{3} + x - 7}$
12202	Find the Domain and Range	f(x)=(e^x)/(5+e^x)	$f (x) = \frac{e^{x}}{5 + e^{x}}$
12203	Find the Domain and Range	f(x)=8/(x^2+64)	$f (x) = \frac{8}{x^{2} + 64}$
12204	Find the Domain and Range	f(x)=(8x)/(x^2-3x)	$f (x) = \frac{8 x}{x^{2} - 3 x}$
12205	Find the Domain and Range	f(x)=x/(cos(2x))	$f (x) = \frac{x}{\cos (2 x)}$
12206	Find the Domain and Range	f(x)=(x+2)/(x^2-7x-18)	$f (x) = \frac{x + 2}{x^{2} - 7 x - 18}$
12207	Find the Domain and Range	f(x)=(x+3)/(4x-5)	$f (x) = \frac{x + 3}{4 x - 5}$
12208	Find the Domain and Range	f(x)=(x-8)/(x^2-13x+40)	$f (x) = \frac{x - 8}{x^{2} - 13 x + 40}$
12209	Find the Domain and Range	f(x)=(tan(x))/(sin(x))	$f (x) = \frac{\tan (x)}{\sin (x)}$
12210	Find the Domain and Range	f(x)=(3x+6)/(x-2)	$f (x) = \frac{3 x + 6}{x - 2}$
12211	Find the Domain and Range	f(x)=(3x-4)/x	$f (x) = \frac{3 x - 4}{x}$
12212	Find the Domain	f(x)=5x^4-30x^2	$f (x) = 5 x^{4} - 30 x^{2}$
12213	Find the Domain	f(x)=7-8x	$f (x) = 7 - 8 x$
12214	Find the Domain	f(x)=9 natural log of x	$f (x) = 9 \ln (x)$
12215	Find the Domain	f(x)=arcsin(4-2x)	$f (x) = \arcsin (4 - 2 x)$
12216	Find the Domain	square root of 5-x- square root of x^2-4	$\sqrt{5 - x} - \sqrt{x^{2} - 4}$
12217	Find the Domain	f(x)=(x+6)/(x-6)	$f (x) = \frac{x + 6}{x - 6}$
12218	Find the Domain	f(x)=10x^6-13x^5	$f (x) = 10 x^{6} - 13 x^{5}$
12219	Find the Domain	f(x)=2sin(x-4pi)-3	$f (x) = 2 \sin (x - 4 π) - 3$
12220	Find the Domain	f(x)=-0.001x^2+8x-7000	$f (x) = - 0.001 x^{2} + 8 x - 7000$
12221	Find the Domain	f(x)=( square root of x-2+e^x)/(x^2-5)	$f (x) = \frac{\sqrt{x - 2} + e^{x}}{x^{2} - 5}$
12222	Find the Domain	s(x)=sin(x)	$s (x) = \sin (x)$
12223	Find the Domain	f(x)=x+ square root of 4-x^2	$f (x) = x + \sqrt{4 - x^{2}}$
12224	Find the Domain	g(x) = square root of 36-x^2	$g (x) = \sqrt{36 - x^{2}}$
12225	Find the Domain	g(x)=1-2x-x^2	$g (x) = 1 - 2 x - x^{2}$
12226	Find the Domain	g(x)=2/(1-cos(x))	$g (x) = \frac{2}{1 - \cos (x)}$
12227	Find the Domain	f(x)=x/(sin(x))	$f (x) = \frac{x}{\sin (x)}$
12228	Find the Domain	f(x)=3x^2-6x+9	$f (x) = 3 x^{2} - 6 x + 9$
12229	Find the Domain	f(x)=xsin(1/x)	$f (x) = x \sin (\frac{1}{x})$
12230	Find the Domain	f(x)=(1-sin(x))/(2x)	$f (x) = \frac{1 - \sin (x)}{2 x}$
12231	Find the Domain and Range	square root of 16x^6+4a^2x^4	$\sqrt{16 x^{6} + 4 a^{2} x^{4}}$
12232	Find the Domain and Range	f(x)=(( square root of x^2+5x+1)+11)/(5x-2)	$f (x) = \frac{(\sqrt{x^{2} + 5 x + 1}) + 11}{5 x - 2}$
12233	Find the Derivative - d/d@VAR	f(x)=(3x+5)^3	$f (x) = {(3 x + 5)}^{3}$
12234	Find the Derivative - d/d@VAR	f(x)=(3-6^x)^140	$f (x) = {(3 - 6^{x})}^{140}$
12235	Find the Derivative - d/d@VAR	f(x)=(3x^4-8x)^3+ square root of x	$f (x) = {(3 x^{4} - 8 x)}^{3} + \sqrt{x}$
12236	Find the Derivative - d/d@VAR	f(x)=(2x-7)^11	$f (x) = {(2 x - 7)}^{11}$
12237	Find the Derivative - d/d@VAR	f(x)=(2x-5)^3	$f (x) = {(2 x - 5)}^{3}$
12238	Find the Derivative - d/d@VAR	f(x)=(2x-1)^2	$f (x) = {(2 x - 1)}^{2}$
12239	Find the Derivative - d/d@VAR	f(x)=(2x-1)^4(3x-2)^6	$f (x) = {(2 x - 1)}^{4} {(3 x - 2)}^{6}$
12240	Find the Derivative - d/d@VAR	f(x)=(2x-3)^10	$f (x) = {(2 x - 3)}^{10}$
12241	Find the Derivative - d/d@VAR	f(x)=(2x+7)^3	$f (x) = {(2 x + 7)}^{3}$
12242	Find the Derivative - d/d@VAR	f(x)=((1+cos(2x))/(2cos(x)))^2	$f (x) = {(\frac{1 + \cos (2 x)}{2 \cos (x)})}^{2}$
12243	Find the Derivative - d/d@VAR	f(x)=(x^2+6x-7)^2	$f (x) = {(x^{2} + 6 x - 7)}^{2}$
12244	Find the Derivative - d/d@VAR	f(x)=(x^2+7)^6	$f (x) = {(x^{2} + 7)}^{6}$
12245	Find the Derivative - d/d@VAR	f(x)=(x^2+9)^6	$f (x) = {(x^{2} + 9)}^{6}$
12246	Find the Derivative - d/d@VAR	f(x)=(x^6+1)^5(4x+7)^3	$f (x) = {(x^{6} + 1)}^{5} {(4 x + 7)}^{3}$
12247	Find the Derivative - d/d@VAR	f(x)=(x^2-1)^3	$f (x) = {(x^{2} - 1)}^{3}$
12248	Find the Derivative - d/d@VAR	F(x)=(x^4+3x^2-2)^5	$F (x) = {(x^{4} + 3 x^{2} - 2)}^{5}$
12249	Find the Derivative - d/d@VAR	f(x)=(tan(x)-x)	$f (x) = (\tan (x) - x)$
12250	Find the Derivative - d/d@VAR	f(x)=(u- square root of u)(u+ square root of u)	$f (x) = (u - \sqrt{u}) (u + \sqrt{u})$
12251	Find the Derivative - d/d@VAR	f(x)=(9x^2+4x)(x^3-5x^2)	$f (x) = (9 x^{2} + 4 x) (x^{3} - 5 x^{2})$
12252	Find the Derivative - d/d@VAR	f(x)=(9x^5-6x^-2)sec(x)	$f (x) = (9 x^{5} - 6 x^{- 2}) \sec (x)$
12253	Find the Derivative - d/d@VAR	f(x)=(x+1)cos(x)	$f (x) = (x + 1) \cos (x)$
12254	Find the Derivative - d/d@VAR	f(x)=0.5x0.09365*10	$f (x) = 0.5 x \cdot 0.09 \cdot 365 \cdot 10$
12255	Find the Derivative - d/d@VAR	f(x)=(4x-3)(2x^3-x^2+1)	$f (x) = (4 x - 3) (2 x^{3} - x^{2} + 1)$
12256	Find the Derivative - d/d@VAR	f(x)=(5x^3+6)(2x^7-3)	$f (x) = (5 x^{3} + 6) (2 x^{7} - 3)$
12257	Find the Derivative - d/d@VAR	f(x)=(8x^2-16x+16)e^x	$f (x) = (8 x^{2} - 16 x + 16) e^{x}$
12258	Find the Derivative - d/d@VAR	f(x)=(3x^2-2x+5)(4x^2+3x-1)	$f (x) = (3 x^{2} - 2 x + 5) (4 x^{2} + 3 x - 1)$
12259	Find the Derivative - d/d@VAR	f(x)=(4e^x+cos(x))(e^(3x)-sin(x))	$f (x) = (4 e^{x} + \cos (x)) (e^{3 x} - \sin (x))$
12260	Find the Derivative - d/d@VAR	f(x)=(4x+1)(6x+3)	$f (x) = (4 x + 1) (6 x + 3)$
12261	Find the Derivative - d/d@VAR	f(x)=(x^3+2x)e^x	$f (x) = (x^{3} + 2 x) e^{x}$
12262	Find the Derivative - d/d@VAR	f(x)=(x^2-7)(x-4)	$f (x) = (x^{2} - 7) (x - 4)$
12263	Find the Derivative - d/d@VAR	f(x)=( natural log of (x)^2)	$f (x) = (\ln ({(x)}^{2}))$
12264	Find the Derivative - d/d@VAR	f(x)=( square root of x)( cube root of x)	$f (x) = (\sqrt{x}) (\sqrt[3]{x})$
12265	Find the Derivative - d/d@VAR	f(x)=(x^3+4x)(3x^2+2x-5)	$f (x) = (x^{3} + 4 x) (3 x^{2} + 2 x - 5)$
12266	Find the Derivative - d/d@VAR	f(x)=(12x^2-24x+24)e^x	$f (x) = (12 x^{2} - 24 x + 24) e^{x}$
12267	Find the Local Maxima and Minima	f(x)=3sin(x)+3cos(x)	$f (x) = 3 \sin (x) + 3 \cos (x)$
12268	Find the Derivative - d/d@VAR	f(x)=(2x-5)	$f (x) = (2 x - 5)$
12269	Find the Derivative - d/d@VAR	f(t)=e^(tsin(2t))	$f (t) = e^{t \sin (2 t)}$
12270	Find the Derivative - d/d@VAR	f(t)=t/(3-t)+5t^3	$f (t) = \frac{t}{3 - t} + 5 t^{3}$
12271	Find the Derivative - d/d@VAR	f(t)=t^3+3t^2+1	$f (t) = t^{3} + 3 t^{2} + 1$
12272	Find the Derivative - d/d@VAR	f(t)=( square root of 2t+1)/((t+1)^3)	$f (t) = \frac{\sqrt{2 t + 1}}{{(t + 1)}^{3}}$
12273	Find the Derivative - d/d@VAR	f(t)=t/(e^t)	$f (t) = \frac{t}{e^{t}}$
12274	Find the Derivative - d/d@VAR	f(t)=-3t^2+2t-4	$f (t) = - 3 t^{2} + 2 t - 4$
12275	Find the Derivative - d/d@VAR	f(t) = natural log of square root of t^3-6	$f (t) = \ln (\sqrt{t^{3} - 6})$
12276	Find the Derivative - d/d@VAR	f(u)=1/( square root of u)	$f (u) = \frac{1}{\sqrt{u}}$
12277	Find the Derivative - d/d@VAR	f(u)=u/(u^2+1)	$f (u) = \frac{u}{u^{2} + 1}$
12278	Find the Derivative - d/d@VAR	f(u)=u/(u^2+2)	$f (u) = \frac{u}{u^{2} + 2}$
12279	Find the Derivative - d/d@VAR	f(t) = square root of 5t^2-t	$f (t) = \sqrt{5 t^{2} - t}$
12280	Find the Derivative - d/d@VAR	f(t)=arcsin(t^9)	$f (t) = \arcsin (t^{9})$
12281	Find the Derivative - d/d@VAR	f(t)=-cos(3x)-1/2	$f (t) = - \cos (3 x) - \frac{1}{2}$
12282	Find the Derivative - d/d@VAR	f(t) = square root of 5-t	$f (t) = \sqrt{5 - t}$
12283	Find the Derivative - d/d@VAR	f(t)=10((2t^2+8t+55)/(t^2+4t+10))	$f (t) = 10 (\frac{2 t^{2} + 8 t + 55}{t^{2} + 4 t + 10})$
12284	Find the Derivative - d/d@VAR	f(t)=3t^p-2t^1.3	$f (t) = 3 t^{p} - 2 t^{1.3}$
12285	Find the Derivative - d/d@VAR	f(x)=e^(2x)	$f (x) = e^{2 x}$
12286	Find the Derivative - d/d@VAR	f(x) = natural log of 3x^2+4x	$f (x) = \ln (3 x^{2} + 4 x)$
12287	Find the Derivative - d/d@VAR	f(x)=x square root of 16-x^2	$f (x) = x \sqrt{16 - x^{2}}$
12288	Find the Derivative - d/d@VAR	f(x)=6e^(4+5x)	$f (x) = 6 e^{4 + 5 x}$
12289	Find the Derivative - d/d@VAR	f(x)=cot(x)	$f (x) = \cot (x)$
12290	Find the Derivative - d/d@VAR	f(x)=4/(x^4)	$f (x) = \frac{4}{x^{4}}$
12291	Find the Inverse	f(x)=6x+15	$f (x) = 6 x + 15$
12292	Find the Domain	f(t)=4/(3-t)	$f (t) = \frac{4}{3 - t}$
12293	Find the Domain	f(x)=x^2+3x-4	$f (x) = x^{2} + 3 x - 4$
12294	Find the Domain	f(x)=3x^3-7x^2-3x+8	$f (x) = 3 x^{3} - 7 x^{2} - 3 x + 8$
12295	Find the Inverse	f(x)=2x^2+5x+4	$f (x) = 2 x^{2} + 5 x + 4$
12296	Find the Inverse	f(x)=2x^3+3x^2-12x	$f (x) = 2 x^{3} + 3 x^{2} - 12 x$
12297	Find the Inverse	f(x)=18-6x	$f (x) = 18 - 6 x$
12298	Find the Inverse	f(x)=x^3-6x^2+12x	$f (x) = x^{3} - 6 x^{2} + 12 x$
12299	Find the Inverse	f(x)=x^5-2	$f (x) = x^{5} - 2$
12300	Find the Inverse	f(x)=x+sin(2x)	$f (x) = x + \sin (2 x)$