Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
16401	Evaluate the Limit	limit as t approaches 0 of ( square root of 1+t- square root of 1-t)/t	$lim_{t \to 0} \frac{\sqrt{1 + t} - \sqrt{1 - t}}{t}$
16402	Find the Derivative - d/d@VAR	f(x)=1/2x^4+6x^3-36x^2+108x-4	$f (x) = \frac{1}{2} x^{4} + 6 x^{3} - 36 x^{2} + 108 x - 4$
16403	Find the Derivative - d/d@VAR	f(x)=1/(2x-3)	$f (x) = \frac{1}{2 x - 3}$
16404	Find the Derivative - d/d@VAR	f(x)=1/( square root of 7-4x)	$f (x) = \frac{1}{\sqrt{7 - 4 x}}$
16405	Find the Derivative - d/d@VAR	f(x)=(12x)/(x^2+4)	$f (x) = \frac{12 x}{x^{2} + 4}$
16406	Find the Derivative - d/d@VAR	f(x)=12^(7x-4)	$f (x) = 12^{7 x - 4}$
16407	Find the Derivative - d/d@VAR	f(x)=(2e^x-1)/(2e^x+1)	$f (x) = \frac{2 e^{x} - 1}{2 e^{x} + 1}$
16408	Find the Derivative - d/d@VAR	f(x)=(2x^2-3x+1)/x+x^(2/3)-x^(1/3)+4	$f (x) = \frac{2 x^{2} - 3 x + 1}{x} + x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4$
16409	Evaluate the Limit	limit as x approaches 4 of (x-5)/((x-4)^2)	$lim_{x \to 4} \frac{x - 5}{{(x - 4)}^{2}}$
16410	Find the Derivative - d/d@VAR	f(x)=1/(4x^2+4)	$f (x) = \frac{1}{4 x^{2} + 4}$
16411	Find the Derivative - d/d@VAR	f(x)=1/(x-7)	$f (x) = \frac{1}{x - 7}$
16412	Find the Derivative - d/d@VAR	f(x)=(1+sin(x))/(1-sin(x))	$f (x) = \frac{1 + \sin (x)}{1 - \sin (x)}$
16413	Find the Derivative - d/d@VAR	f(x)=10/3x^3-51/2x^2+5x+13	$f (x) = \frac{10}{3} x^{3} - \frac{51}{2} x^{2} + 5 x + 13$
16414	Find the Derivative - d/d@VAR	f(x)=1/x+1/(x^3)-4/( square root of x)	$f (x) = \frac{1}{x} + \frac{1}{x^{3}} - \frac{4}{\sqrt{x}}$
16415	Find the Derivative - d/d@VAR	f(x)=1/3x^3-5x^2+1	$f (x) = \frac{1}{3} x^{3} - 5 x^{2} + 1$
16416	Find the Derivative - d/d@VAR	f(x)=1/(x+7)	$f (x) = \frac{1}{x + 7}$
16417	Find the Derivative - d/d@VAR	f(x)=1/(x+9)	$f (x) = \frac{1}{x + 9}$
16418	Find the Derivative - d/d@VAR	f(x)=(x^2-3)/(x-2)	$f (x) = \frac{x^{2} - 3}{x - 2}$
16419	Find the Derivative - d/d@VAR	f(x)=(x^2-1)/(2x-3)	$f (x) = \frac{x^{2} - 1}{2 x - 3}$
16420	Find the Derivative - d/d@VAR	f(x)=(x^2+1)/(cos(x))	$f (x) = \frac{x^{2} + 1}{\cos (x)}$
16421	Find the Derivative - d/d@VAR	f(x)=(x^2+7)/(16-x^2)	$f (x) = \frac{x^{2} + 7}{16 - x^{2}}$
16422	Find the Derivative - d/d@VAR	f(x)=(x^2-8)/(x-3)	$f (x) = \frac{x^{2} - 8}{x - 3}$
16423	Find the Derivative - d/d@VAR	f(x)=(x^2-9x+39)/(x-7)	$f (x) = \frac{x^{2} - 9 x + 39}{x - 7}$
16424	Find the Derivative - d/d@VAR	f(x)=(e^x)/(sin(x))	$f (x) = \frac{e^{x}}{\sin (x)}$
16425	Find the Derivative - d/d@VAR	f(x)=( fourth root of x^2+1)^3	$f (x) = {(\sqrt[4]{x^{2} + 1})}^{3}$
16426	Find the Derivative - d/d@VAR	f(x)=( log base 7 of x)/(x^4)	$f (x) = \frac{\log_{7} (x)}{x^{4}}$
16427	Find the Derivative - d/d@VAR	f(x)=( log base 9 of x)/(x^3)	$f (x) = \frac{\log_{9} (x)}{x^{3}}$
16428	Find the Derivative - d/d@VAR	f(x)=(x^2)/(9+4x)	$f (x) = \frac{x^{2}}{9 + 4 x}$
16429	Evaluate the Limit	limit as t approaches -6 of (t^2-36)/(2t^2+13t+6)	$lim_{t \to - 6} \frac{t^{2} - 36}{2 t^{2} + 13 t + 6}$
16430	Find the Derivative - d/d@VAR	f(x)=(x^2)/(x-12)	$f (x) = \frac{x^{2}}{x - 12}$
16431	Find the Local Maxima and Minima	f(x)=2x^3-54x	$f (x) = 2 x^{3} - 54 x$
16432	Convert to Interval Notation	x^3<9x	$x^{3} < 9 x$
16433	Find the Derivative - d/d@VAR	f(x)=(x+5)^7(4x-1)^10	$f (x) = {(x + 5)}^{7} {(4 x - 1)}^{10}$
16434	Find the Derivative - d/d@VAR	f(x)=((3x-5)^3)/((2x^2+1)^4)	$f (x) = \frac{{(3 x - 5)}^{3}}{{(2 x^{2} + 1)}^{4}}$
16435	Find the Derivative - d/d@VAR	f(x)=(x+8)^(6/7)	$f (x) = {(x + 8)}^{\frac{6}{7}}$
16436	Find the Derivative - d/dx	y=1/( fourth root of x)	$y = \frac{1}{\sqrt[4]{x}}$
16437	Find the Domain	f(x)=(x+8)/(x-8)	$f (x) = \frac{x + 8}{x - 8}$
16438	Find the Derivative - d/dx	x(x-5)^2	$x {(x - 5)}^{2}$
16439	Find the Derivative - d/d@VAR	f(x)=(e^(4x))/(x^20)	$f (x) = \frac{e^{4 x}}{x^{20}}$
16440	Find the Derivative - d/d@VAR	f(x)=(3x-1)^4	$f (x) = {(3 x - 1)}^{4}$
16441	Find the Derivative - d/d@VAR	f(x)=(3x-4)^5	$f (x) = {(3 x - 4)}^{5}$
16442	Find the Derivative - d/d@VAR	f(x)=(4-e^(-3x))^3	$f (x) = {(4 - e^{- 3 x})}^{3}$
16443	Find the Derivative - d/d@VAR	f(x)=(2x-1)^5	$f (x) = {(2 x - 1)}^{5}$
16444	Find the Derivative - d/d@VAR	f(x)=(x^2+8)^5	$f (x) = {(x^{2} + 8)}^{5}$
16445	Find the Derivative - d/d@VAR	f(x)=(x^3-3)^4	$f (x) = {(x^{3} - 3)}^{4}$
16446	Find the Derivative - d/d@VAR	f(x)=((x-4)/(x+2))^3	$f (x) = {(\frac{x - 4}{x + 2})}^{3}$
16447	Find the Derivative - d/d@VAR	f(x)=(1+ natural log of x)^3	$f (x) = {(1 + \ln (x))}^{3}$
16448	Find the Derivative - d/d@VAR	f(x)=(10x-6)^(1/2)	$f (x) = {(10 x - 6)}^{\frac{1}{2}}$
16449	Find the Derivative - d/d@VAR	f(x)=(1-x)^(1/3)	$f (x) = {(1 - x)}^{\frac{1}{3}}$
16450	Find dy/dx	e^(x/y)=9x-y	$e^{\frac{x}{y}} = 9 x - y$
16451	Find dy/dx	y=(3x^2-9x+11)/(2x+4)	$y = \frac{3 x^{2} - 9 x + 11}{2 x + 4}$
16452	Evaluate the Summation	sum from k=3 to 10 of 9-2k	$\sum_{k = 3}^{10} 9 - 2 k$
16453	Find the Derivative - d/d@VAR	f(x)=(4x^2tan(x))/(sec(x))	$f (x) = \frac{4 x^{2} \tan (x)}{\sec (x)}$
16454	Find the Derivative - d/d@VAR	f(x)=(4x-x^2)^100	$f (x) = {(4 x - x^{2})}^{100}$
16455	Find the Derivative - d/d@VAR	f(x)=(4x-6)^2	$f (x) = {(4 x - 6)}^{2}$
16456	Find the Derivative - d/d@VAR	F(x)=(6x+1)^2	$F (x) = {(6 x + 1)}^{2}$
16457	Find the Derivative - d/d@VAR	f(x)=(60+2t)^(2/3)	$f (x) = {(60 + 2 t)}^{\frac{2}{3}}$
16458	Find the Derivative - d/d@VAR	f(x)=(9-x^2)^(2/3)	$f (x) = {(9 - x^{2})}^{\frac{2}{3}}$
16459	Evaluate the Summation	sum from n=1 to infinity of (-144)(1/2)^(n-1)	$\sum_{n = 1}^{\infty} (- 144) {(\frac{1}{2})}^{n - 1}$
16460	Find the Derivative - d/d@VAR	f(x)=(7x+5)^4	$f (x) = {(7 x + 5)}^{4}$
16461	Find the Derivative - d/d@VAR	f(x)=cos(7x)^x	$f (x) = {\cos (7 x)}^{x}$
16462	Find the Derivative - d/d@VAR	f(x)=csc(2x^2+1)^4	$f (x) = \csc^{4} (2 x^{2} + 1)$
16463	Find the Derivative - d/d@VAR	f(x)=( natural log of x)^(sec(x))	$f (x) = {(\ln (x))}^{\sec (x)}$
16464	Find the Derivative - d/d@VAR	f(x)=(x+1)^99	$f (x) = {(x + 1)}^{99}$
16465	Find the Derivative - d/d@VAR	f(x)=(6x+7)(7x-8)	$f (x) = (6 x + 7) (7 x - 8)$
16466	Find the Derivative - d/d@VAR	f(x)=(5-x)(9-x)	$f (x) = (5 - x) (9 - x)$
16467	Find the Derivative - d/d@VAR	f(x)=(5x+6)(6x-7)	$f (x) = (5 x + 6) (6 x - 7)$
16468	Find the Derivative - d/d@VAR	f(x)=(6 square root of x-2)(5 square root of x+7)	$f (x) = (6 \sqrt{x} - 2) (5 \sqrt{x} + 7)$
16469	Find the Derivative - d/d@VAR	f(x)=(4x-2)e^(2x)	$f (x) = (4 x - 2) e^{2 x}$
16470	Find the Derivative - d/d@VAR	f(x)=(3x-5)(2x^3-x^2+1)	$f (x) = (3 x - 5) (2 x^{3} - x^{2} + 1)$
16471	Find the Derivative - d/d@VAR	f(x)=(4x^2-3x+3)*(4x^2+6x-11)	$f (x) = (4 x^{2} - 3 x + 3) \cdot (4 x^{2} + 6 x - 11)$
16472	Find the Derivative - d/d@VAR	f(x)=(3x-2)(2x+1)	$f (x) = (3 x - 2) (2 x + 1)$
16473	Find the Derivative - d/d@VAR	f(x)=(3x-2)(4x^2+3)	$f (x) = (3 x - 2) (4 x^{2} + 3)$
16474	Find the Derivative - d/d@VAR	f(x)=(4x^2-8x+8)e^x	$f (x) = (4 x^{2} - 8 x + 8) e^{x}$
16475	Find the Derivative - d/d@VAR	f(x)=(1+9x^2)(x-x^2)	$f (x) = (1 + 9 x^{2}) (x - x^{2})$
16476	Find the Derivative - d/d@VAR	f(x)=(3x^2+7)(x^2-2x+3)	$f (x) = (3 x^{2} + 7) (x^{2} - 2 x + 3)$
16477	Find the Derivative - d/d@VAR	f(x)=(x-1)	$f (x) = (x - 1)$
16478	Find the 2nd Derivative	y = fifth root of x	$y = \sqrt[5]{x}$
16479	Find the Derivative - d/d@VAR	f(x)=(1/2x)^5	$f (x) = {(\frac{1}{2} x)}^{5}$
16480	Find the Derivative - d/d@VAR	f(x)=(x-3)(2x-1)	$f (x) = (x - 3) (2 x - 1)$
16481	Find the Derivative - d/d@VAR	f(x)=(x^2+1)^6	$f (x) = {(x^{2} + 1)}^{6}$
16482	Find the Derivative - d/d@VAR	f(x)=(x^2+cos(x))^5	$f (x) = {(x^{2} + \cos (x))}^{5}$
16483	Evaluate the Integral	integral of e^(2theta)sin(3theta) with respect to theta	$\int e^{2 θ} \sin (3 θ) d θ$
16484	Find the Derivative - d/d@VAR	f(x)=(5x-1)	$f (x) = (5 x - 1)$
16485	Find the Derivative - d/d@VAR	f(t)=t+cos(t)	$f (t) = t + \cos (t)$
16486	Find the Derivative - d/d@VAR	f(t) = square root of 10t^2-t	$f (t) = \sqrt{10 t^{2} - t}$
16487	Find the Derivative - d/d@VAR	f(t)=tan(e^(3t))+e^(tan(3t))	$f (t) = \tan (e^{3 t}) + e^{\tan (3 t)}$
16488	Find the Derivative - d/d@VAR	f(t)=7e^(8t)	$f (t) = 7 e^{8 t}$
16489	Find the Derivative - d/d@VAR	f(t)=9-1/3t	$f (t) = 9 - \frac{1}{3} t$
16490	Find the Derivative - d/d@VAR	f(t) = square root of cos(3t)	$f (t) = \sqrt{\cos (3 t)}$
16491	Find the Derivative - d/d@VAR	f(t)=2cos(t)+sin(2t)	$f (t) = 2 \cos (t) + \sin (2 t)$
16492	Find the Derivative - d/d@VAR	f(t)=-3t(5t^8-1)^7	$f (t) = - 3 t {(5 t^{8} - 1)}^{7}$
16493	Find the Derivative - d/d@VAR	f(t)=t^3cos(t)	$f (t) = t^{3} \cos (t)$
16494	Find the Derivative - d/d@VAR	f(t)=0.04t^3-0.09t^2	$f (t) = 0.04 t^{3} - 0.09 t^{2}$
16495	Find the Derivative - d/d@VAR	f(t)=25000/(1+11e^(-0.54t))	$f (t) = \frac{25000}{1 + 11 e^{- 0.54 t}}$
16496	Find the Derivative - d/d@VAR	f(t)=5/(t^3)-4/(t^2)+1/t	$f (t) = \frac{5}{t^{3}} - \frac{4}{t^{2}} + \frac{1}{t}$
16497	Find the Derivative - d/d@VAR	f(t)=(8t)/(8+ square root of t)	$f (t) = \frac{8 t}{8 + \sqrt{t}}$
16498	Find the Derivative - d/d@VAR	f(t)=1/2*(3t^2+t)^-3	$f (t) = \frac{1}{2} \cdot {(3 t^{2} + t)}^{- 3}$
16499	Find the Derivative - d/d@VAR	f(t)=(4t)/(4+ square root of t)	$f (t) = \frac{4 t}{4 + \sqrt{t}}$
16500	Find the Derivative - d/d@VAR	f(t)=e^(x^2)+3	$f (t) = e^{x^{2}} + 3$