Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
16301	Find the Derivative - d/d@VAR	f(x)=4 square root of xsin(x)	$f (x) = 4 \sqrt{x} \sin (x)$
16302	Find the Derivative - d/d@VAR	f(x)=2-x^3	$f (x) = 2 - x^{3}$
16303	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(9x)-1-9x)/(x^2)	$lim_{x \to 0} \frac{e^{9 x} - 1 - 9 x}{x^{2}}$
16304	Find the Derivative - d/d@VAR	f(x)=2x^5	$f (x) = 2 x^{5}$
16305	Find dz/dt	z=(4-t)(9+t^2)^-1	$z = (4 - t) {(9 + t^{2})}^{- 1}$
16306	Find the Derivative - d/d@VAR	f(x)=2x^2-3x+1	$f (x) = 2 x^{2} - 3 x + 1$
16307	Find dy/dx	y=9x^-7-6x^-1	$y = 9 x^{- 7} - 6 x^{- 1}$
16308	Find the Derivative - d/d@VAR	f(x)=1-cos(x)	$f (x) = 1 - \cos (x)$
16309	Find the Derivative - d/d@VAR	f(x)=2 square root of 25-x^2	$f (x) = 2 \sqrt{25 - x^{2}}$
16310	Find the Derivative - d/d@VAR	f(x)=2 square root of x+3e^x	$f (x) = 2 \sqrt{x} + 3 e^{x}$
16311	Find the Derivative - d/d@VAR	f(x)=2x^2+7x- natural log of x^2+1	$f (x) = 2 x^{2} + 7 x - \ln (x^{2} + 1)$
16312	Evaluate the Limit	limit as x approaches 5 of (x^2-9x+20)/(x-5)	$lim_{x \to 5} \frac{x^{2} - 9 x + 20}{x - 5}$
16313	Find the Derivative - d/d@VAR	f(x)=2x^3+3t^2-4t+1000	$f (x) = 2 x^{3} + 3 t^{2} - 4 t + 1000$
16314	Find the Derivative - d/d@VAR	f(x)=2x^3-x^4	$f (x) = 2 x^{3} - x^{4}$
16315	Find the Derivative - d/d@VAR	f(x)=2x^3+42x^2+270x+9	$f (x) = 2 x^{3} + 42 x^{2} + 270 x + 9$
16316	Find the Derivative - d/d@VAR	f(x)=-2x^3+5	$f (x) = - 2 x^{3} + 5$
16317	Find the Derivative - d/d@VAR	f(x)=2x-5	$f (x) = 2 x - 5$
16318	Evaluate the Limit	limit as x approaches -4 of (8x^2+40x+32)/(x+4)	$lim_{x \to - 4} \frac{8 x^{2} + 40 x + 32}{x + 4}$
16319	Find the Derivative - d/d@VAR	f(x)=2x-pi+cos(x)	$f (x) = 2 x - π + \cos (x)$
16320	Evaluate the Limit	limit as x approaches 3 of (x-3)/( square root of x-2- square root of 4-x)	$lim_{x \to 3} \frac{x - 3}{\sqrt{x - 2} - \sqrt{4 - x}}$
16321	Find the Derivative - d/d@VAR	f(x)=2x^4-8x	$f (x) = 2 x^{4} - 8 x$
16322	Find the Derivative - d/d@VAR	f(x)=2sin(3x^2-2)	$f (x) = 2 \sin (3 x^{2} - 2)$
16323	Find the Derivative - d/d@VAR	f(x)=2sin(4x)	$f (x) = 2 \sin (4 x)$
16324	Find the Derivative - d/d@VAR	f(x)=2t	$f (x) = 2 t$
16325	Find the Derivative - d/d@VAR	f(x)=3x^2-3	$f (x) = 3 x^{2} - 3$
16326	Find the Derivative - d/d@VAR	f(x)=3x^3-4x^4	$f (x) = 3 x^{3} - 4 x^{4}$
16327	Find the Derivative - d/d@VAR	f(x)=3x^2-84x	$f (x) = 3 x^{2} - 84 x$
16328	Find the Derivative - d/d@VAR	f(x)=3x^3-2x^2+7	$f (x) = 3 x^{3} - 2 x^{2} + 7$
16329	Find the Derivative - d/d@VAR	f(x)=3x^2- natural log of x	$f (x) = 3 x^{2} - \ln (x)$
16330	Evaluate the Limit	limit as x approaches -5 of f(x)	$lim_{x \to - 5} f (x)$
16331	Find the Derivative - d/d@VAR	f(x)=3t^2sin(t)	$f (x) = 3 t^{2} \sin (t)$
16332	Find the Derivative - d/d@VAR	f(x)=2x square root of x	$f (x) = 2 x \sqrt{x}$
16333	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(5x)	$lim_{x \to 0} \frac{\sin (2 x)}{5 x}$
16334	Find the Derivative - d/d@VAR	f(x)=5/(6x)	$f (x) = \frac{5}{6 x}$
16335	Find the Derivative - d/d@VAR	f(x)=-5/(x^3)	$f (x) = \frac{- 5}{x^{3}}$
16336	Find the Derivative - d/d@VAR	f(x)=(5(1-sin(x)))/(2cos(x))	$f (x) = \frac{5 (1 - \sin (x))}{2 \cos (x)}$
16337	Find the Derivative - d/d@VAR	f(x)=(4t)/(3 square root of t-2)	$f (x) = \frac{4 t}{3 \sqrt{t - 2}}$
16338	Find the Derivative - d/d@VAR	f(x)=(40t^2)/(t^2+150)	$f (x) = \frac{40 t^{2}}{t^{2} + 150}$
16339	Find the Derivative - d/d@VAR	f(x)=3/(x+2)- square root of x-3	$f (x) = \frac{3}{x + 2} - \sqrt{x - 3}$
16340	Find the Derivative - d/d@VAR	f(x)=360/(1+11000e^(-2.3x))	$f (x) = \frac{360}{1 + 11000 e^{- 2.3 x}}$
16341	Find the Derivative - d/d@VAR	f(x)=(3x-1)/(2x+1)	$f (x) = \frac{3 x - 1}{2 x + 1}$
16342	Find the Derivative - d/d@VAR	f(x)=(3x-6)/(x+1)	$f (x) = \frac{3 x - 6}{x + 1}$
16343	Find the Derivative - d/d@VAR	f(x)=4/( square root of x)-5/x+8/(x^4)	$f (x) = \frac{4}{\sqrt{x}} - \frac{5}{x} + \frac{8}{x^{4}}$
16344	Find the Derivative - d/d@VAR	f(x)=3^xsin(x)	$f (x) = 3^{x} \sin (x)$
16345	Find the Derivative - d/d@VAR	f(x)=(3x-4)/(x^2+1)	$f (x) = \frac{3 x - 4}{x^{2} + 1}$
16346	Find the Derivative - d/d@VAR	f(x)=4/(7x^3)	$f (x) = \frac{4}{7 x^{3}}$
16347	Find the Derivative - d/dx	12	$12$
16348	Find the Derivative - d/d@VAR	f(x)=2/3x^6	$f (x) = \frac{2}{3} x^{6}$
16349	Find the Derivative - d/dx	square root of 1+3x	$\sqrt{1 + 3 x}$
16350	Find the Derivative - d/d@VAR	f(x)=(2 natural log of 5*5^-3)/7-(3(5)^-3)/7	$f (x) = \frac{2 \ln (5) \cdot 5^{- 3}}{7} - \frac{3 {(5)}^{- 3}}{7}$
16351	Find the Derivative - d/d@VAR	f(x) = square root of xsin(x)	$f (x) = \sqrt{x} \sin (x)$
16352	Find the Derivative - d/d@VAR	f(x)=(2sin(x))/(3+cos(x))	$f (x) = \frac{2 \sin (x)}{3 + \cos (x)}$
16353	Find the Derivative - d/d@VAR	f(x)=5x^5 natural log of x	$f (x) = 5 x^{5} \ln (x)$
16354	Find the Derivative - d/d@VAR	f(x)=sec(2x^2)^4	$f (x) = \sec^{4} (2 x^{2})$
16355	Find the Derivative - d/d@VAR	f(x)=3/2x^2	$f (x) = \frac{3}{2} x^{2}$
16356	Find the Derivative - d/d@VAR	f(x)=3/(x-4)	$f (x) = \frac{3}{x - 4}$
16357	Find the Derivative - d/d@VAR	f(x)=(8x-9)/(6x^2+1)	$f (x) = \frac{8 x - 9}{6 x^{2} + 1}$
16358	Solve for t	27/16=t^2	$\frac{27}{16} = t^{2}$
16359	Solve for x	natural log of (x^2)/(1-x) = natural log of x+ natural log of (2x)/(1+x)	$\ln (\frac{x^{2}}{1 - x}) = \ln (x) + \ln (\frac{2 x}{1 + x})$
16360	Find the Derivative - d/d@VAR	f(x)=a^(5x)	$f (x) = a^{5 x}$
16361	Find the Derivative - d/d@VAR	f(x)=(7x-4)/(x-4)	$f (x) = \frac{7 x - 4}{x - 4}$
16362	Find the Derivative - d/d@VAR	f(x)=(7t)/(t^2+1)	$f (x) = \frac{7 t}{t^{2} + 1}$
16363	Find the Derivative - d/d@VAR	f(x)=8/( square root of 4-x)	$f (x) = \frac{8}{\sqrt{4 - x}}$
16364	Find the Inflection Points	(x+1)^2(2x-x^2)	${(x + 1)}^{2} (2 x - x^{2})$
16365	Find the Derivative - d/d@VAR	f(x)=7^(sin(x))	$f (x) = 7^{\sin (x)}$
16366	Find the Derivative - d/d@VAR	f(x)=(703(128))/(x^2)	$f (x) = \frac{703 (128)}{x^{2}}$
16367	Find the Derivative - d/d@VAR	f(x)=6/(7x^2)	$f (x) = \frac{6}{7 x^{2}}$
16368	Find the Derivative - d/d@VAR	f(x)=6/(x^3)+5x^3	$f (x) = \frac{6}{x^{3}} + 5 x^{3}$
16369	Find the Derivative - d/d@VAR	f(x)=e^(-1/x)	$f (x) = e^{\frac{- 1}{x}}$
16370	Find the Derivative - d/d@VAR	f(x)=cx^2+6x^-2	$f (x) = c x^{2} + 6 x^{- 2}$
16371	Find the Derivative - d/d@VAR	f(x)=e^(1/(7x))	$f (x) = e^{\frac{1}{7 x}}$
16372	Find the Derivative - d/d@VAR	f(x)=e^(-1/(x^2))	$f (x) = e^{- \frac{1}{x^{2}}}$
16373	Find the Derivative - d/d@VAR	f(x)=e^(cos(x)^5)	$f (x) = e^{\cos^{5} (x)}$
16374	Find the Derivative - d/d@VAR	f(x)=e^( square root of 5x+2)	$f (x) = e^{\sqrt{5 x + 2}}$
16375	Find the Critical Points	4x^3-12x	$4 x^{3} - 12 x$
16376	Find the Derivative - d/d@VAR	f(x)=(cos(x))/(x^5)	$f (x) = \frac{\cos (x)}{x^{5}}$
16377	Find the Derivative - d/d@VAR	f(x)=cos(7x+2)^2	$f (x) = \cos^{2} (7 x + 2)$
16378	Find the Absolute Max and Min over the Interval	f(x)=3x^3-3x^2-3x+2 , [-1,0]	$f (x) = 3 x^{3} - 3 x^{2} - 3 x + 2$ , $[- 1, 0]$
16379	Solve for x	4x^3-12x^2=0	$4 x^{3} - 12 x^{2} = 0$
16380	Find the Derivative - d/d@VAR	f(x)=cos(1+3x)^2	$f (x) = \cos^{2} (1 + 3 x)$
16381	Find the Derivative - d/d@VAR	f(x)=cos(4x)^2	$f (x) = \cos^{2} (4 x)$
16382	Find the Derivative - d/d@VAR	f(x)=e^9	$f (x) = e^{9}$
16383	Find the Derivative - d/d@VAR	f(x)=e^(-7x)+2x+10	$f (x) = e^{- 7 x} + 2 x + 10$
16384	Find the Derivative - d/d@VAR	f(x) = square root of 3	$f (x) = \sqrt{3}$
16385	Find the Derivative - d/d@VAR	f(x)=e^(4x^2)	$f (x) = e^{4 x^{2}}$
16386	Find the Derivative - d/d@VAR	f(x)=e^(3x+1)	$f (x) = e^{3 x + 1}$
16387	Find the Derivative - d/d@VAR	f(x)=e^(-2x) natural log of x	$f (x) = e^{- 2 x} \ln (x)$
16388	Find the Derivative - d/d@VAR	f(x)=e^(-2x)sin(5x)	$f (x) = e^{- 2 x} \sin (5 x)$
16389	Find the Derivative - d/dx	2x-6	$2 x - 6$
16390	Find the Derivative - d/d@VAR	f(x)=e^(10x)	$f (x) = e^{10 x}$
16391	Find the Derivative - d/dx	x/(sin(x))	$\frac{x}{\sin (x)}$
16392	Find the Derivative - d/d@VAR	f(x)=e^(x^2-9)	$f (x) = e^{x^{2} - 9}$
16393	Find the Derivative - d/d@VAR	f(x)=e^(x^3)	$f (x) = e^{x^{3}}$
16394	Find the Derivative - d/d@VAR	f(x)=e^(x^3+3x)	$f (x) = e^{x^{3} + 3 x}$
16395	Find the Derivative - d/d@VAR	f(x)=\|x^2-9\|	$f (x) = \| x^{2} - 9 \|$
16396	Find the Derivative - d/d@VAR	f(x)=\|x^2-4\|	$f (x) = \| x^{2} - 4 \|$
16397	Evaluate the Limit	limit as t approaches 1 of (1-t)/(1- square root of t)	$lim_{t \to 1} \frac{1 - t}{1 - \sqrt{t}}$
16398	Find the Derivative - d/d@VAR	f(x)=(x^3-4x^2+3)/x	$f (x) = \frac{x^{3} - 4 x^{2} + 3}{x}$
16399	Find the Derivative - d/d@VAR	f(x)=(x^5-5x)/5	$f (x) = \frac{x^{5} - 5 x}{5}$
16400	Find the Derivative - d/d@VAR	f(x)=1/(x^2-4)	$f (x) = \frac{1}{x^{2} - 4}$