Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43301	Find the Second Derivative	f(x)=(x^3+2)e^x	$f (x) = (x^{3} + 2) e^{x}$
43302	Find the Critical Points	f(x)=1/x- natural log of x	$f (x) = \frac{1}{x} - \ln (x)$
43303	Simplify	(csc(x)^2-1)/(csc(x)^2)	$\frac{\csc^{2} (x) - 1}{\csc^{2} (x)}$
43304	Solve for x	x^2e^x-5xe^x=0	$x^{2} e^{x} - 5 x e^{x} = 0$
43305	Find the Concavity	f(x)=5(x-3)^(5/3)	$f (x) = 5 {(x - 3)}^{\frac{5}{3}}$
43306	Find the Tangent Line at (3p,0)	y=sin(sin(x)) , (3pi,0)	$y = \sin (\sin (x))$ , $(3 π, 0)$
43307	Graph	r=1+cos(theta)	$r = 1 + \cos (θ)$
43308	Graph	x-2sin(x)	$x - 2 \sin (x)$
43309	Evaluate the Summation	sum from n=1 to 8 of 3n-1	$\sum_{n = 1}^{8} 3 n - 1$
43310	Find the Local Maxima and Minima	1/7x^7-x	$\frac{1}{7} x^{7} - x$
43311	Find the Third Derivative	h(x)=x^2e^(11x)	$h (x) = x^{2} e^{11 x}$
43312	Find the Second Derivative	y=8sec(x)	$y = 8 \sec (x)$
43313	Solve for y	x=1/3(y^2+2)^(3/2)	$x = \frac{1}{3} {(y^{2} + 2)}^{\frac{3}{2}}$
43314	Solve for x	x=1/3(y^2+2)^(3/2)	$x = \frac{1}{3} {(y^{2} + 2)}^{\frac{3}{2}}$
43315	Find the Second Derivative	4x cube root of x	$4 x \sqrt[3]{x}$
43316	Find the Second Derivative	e^x-x^8	$e^{x} - x^{8}$
43317	Find Where Increasing/Decreasing Using Derivatives	f(x)=sin(x)+cos(x)	$f (x) = \sin (x) + \cos (x)$
43318	Find the Antiderivative	1/( natural log of x)	$\frac{1}{\ln (x)}$
43319	Find the Second Derivative	h(x)=x^2e^(9x)	$h (x) = x^{2} e^{9 x}$
43320	Evaluate the Summation	sum from i=1 to 8 of 4.9i-2.9	$\sum_{i = 1}^{8} 4.9 i - 2.9$
43321	Evaluate the Summation	sum from i=1 to 8 of 3i-7	$\sum_{i = 1}^{8} 3 i - 7$
43322	Find the Local Maxima and Minima	x^3-6x^2+5	$x^{3} - 6 x^{2} + 5$
43323	Solve for t	3t^2-24t+36=0	$3 t^{2} - 24 t + 36 = 0$
43324	Solve for x	2 natural log of x- natural log of x+2=0	$2 \ln (x) - \ln (x + 2) = 0$
43325	Solve for x	3x^2+18x+32=5	$3 x^{2} + 18 x + 32 = 5$
43326	Solve for x	e^(9-4x)=2	$e^{9 - 4 x} = 2$
43327	Simplify	( fourth root of x)^2	${(\sqrt[4]{x})}^{2}$
43328	Simplify	(( square root of x)/2-1/(2 square root of x))^2	${(\frac{\sqrt{x}}{2} - \frac{1}{2 \sqrt{x}})}^{2}$
43329	Find the Inflection Points	5x^3-15x	$5 x^{3} - 15 x$
43330	Find the Local Maxima and Minima	x^3-2x^2-4x+8	$x^{3} - 2 x^{2} - 4 x + 8$
43331	Find the Third Derivative	(3x-2)^4	${(3 x - 2)}^{4}$
43332	Solve for x	e^(-1/x)=e^(1/8)	$e^{- \frac{1}{x}} = e^{\frac{1}{8}}$
43333	Find the Linearization at a=p/6	f(x)=sin(x) , a=pi/6	$f (x) = \sin (x)$ , $a = \frac{π}{6}$
43334	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x^3)/2-6x	$f (x) = \frac{x^{3}}{2} - 6 x$
43335	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x , [0,4]	$f (x) = x^{3} - 3 x$ , $[0, 4]$
43336	Find the Domain and Range	y=e^(-x)-2	$y = e^{- x} - 2$
43337	Find the Derivative Using Chain Rule - d/dx	y=cos(x)^3	$y = \cos^{3} (x)$
43338	Multiply	49*2	$49 \cdot 2$
43339	Find the Critical Points	f(x)=x^3+3x^2-189x	$f (x) = x^{3} + 3 x^{2} - 189 x$
43340	Find the Critical Points	h(t)=t^(3/4)-3t^(1/4)	$h (t) = t^{\frac{3}{4}} - 3 t^{\frac{1}{4}}$
43341	Find the Domain	x/(1- natural log of x-6)	$\frac{x}{1 - \ln (x - 6)}$
43342	Find the Third Derivative	e^xcos(x)	$e^{x} \cos (x)$
43343	Find the Third Derivative	5cos(2x+10)	$5 \cos (2 x + 10)$
43344	Find dy/dx at (4,3)	x^3+y^3=8xy-5 , (4,3)	$x^{3} + y^{3} = 8 x y - 5$ , $(4, 3)$
43345	Solve for x	6x^2+84x+288=0	$6 x^{2} + 84 x + 288 = 0$
43346	Solve for x	e^(2x)=0	$e^{2 x} = 0$
43347	Solve for x	e^(-1/x)=e^(1/2)	$e^{- \frac{1}{x}} = e^{\frac{1}{2}}$
43348	Solve for x	3x^2-18x+24=0	$3 x^{2} - 18 x + 24 = 0$
43349	Find Where Increasing/Decreasing Using Derivatives	f(x)=1/4x^4-1/3x^3-x^2	$f (x) = \frac{1}{4} x^{4} - \frac{1}{3} x^{3} - x^{2}$
43350	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^2(14+x)^2	$f (x) = 2 x^{2} {(14 + x)}^{2}$
43351	Graph	y=f(x-4)	$y = f (x - 4)$
43352	Graph	f(x)=7/2x^2	$f (x) = \frac{7}{2} x^{2}$
43353	Find the Critical Points	f(x)=x-2sin(x)	$f (x) = x - 2 \sin (x)$
43354	Multiply	7*12	$7 \cdot 12$
43355	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^(x^2))/(x^4)	$lim_{x \to \infty} \frac{e^{x^{2}}}{x^{4}}$
43356	Simplify	e^t*e^t	$e^{t} \cdot e^{t}$
43357	Find the Fourth Derivative	(sin(x))	$(\sin (x))$
43358	Find the Third Derivative	x^2 natural log of x	$x^{2} \ln (x)$
43359	Find the Second Derivative	e^x-x^4	$e^{x} - x^{4}$
43360	Find the Second Derivative	H(theta)=thetacos(theta)	$H (θ) = θ \cos (θ)$
43361	Write as a Single Logarithm	1/7 natural log of (x+2)^7+1/2( natural log of x- natural log of (x^2+3x+2)^2)	$\frac{1}{7} \ln ({(x + 2)}^{7}) + \frac{1}{2} (\ln (x) - \ln ({(x^{2} + 3 x + 2)}^{2}))$
43362	Find the Maximum/Minimum Value	f(x)=x^2+8x+16	$f (x) = x^{2} + 8 x + 16$
43363	Solve for y	xy=x^2+2y^3	$x y = x^{2} + 2 y^{3}$
43364	Solve for y	(dy)/(dx)=y	$\frac{d y}{d x} = y$
43365	Solve for k	k=(1+sin(x))/n	$k = \frac{1 + \sin (x)}{n}$
43366	Solve for x	y=40000+10000/3x	$y = 40000 + \frac{10000}{3} x$
43367	Solve for x	(dy)/(dx)=y	$\frac{d y}{d x} = y$
43368	Solve for x	k=(1+sin(x))/n	$k = \frac{1 + \sin (x)}{n}$
43369	Solve for n	k=(1+sin(x))/n	$k = \frac{1 + \sin (x)}{n}$
43370	Solve for t	3t^2-18t+24=0	$3 t^{2} - 18 t + 24 = 0$
43371	Solve for y	y=40000+10000/3x	$y = 40000 + \frac{10000}{3} x$
43372	Find the Linearization at a=-1	f(x)=x^4+2x^2 , a=-1	$f (x) = x^{4} + 2 x^{2}$ , $a = - 1$
43373	Find the Critical Points	t^(3/4)-6t^(1/4)	$t^{\frac{3}{4}} - 6 t^{\frac{1}{4}}$
43374	Find the Inflection Points	f(x)=3x^4-20x^3+24x^2	$f (x) = 3 x^{4} - 20 x^{3} + 24 x^{2}$
43375	Convert to a Simplified Fraction	1.73205080	$1.7320508$
43376	Find the Derivative Using Chain Rule - d/dx	(4x-14)^6	${(4 x - 14)}^{6}$
43377	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^2)/(e^x)	$lim_{x \to \infty} \frac{x^{2}}{e^{x}}$
43378	Find the Second Derivative	h(x)=x^2e^(5x)	$h (x) = x^{2} e^{5 x}$
43379	Graph	r=2cos(theta)	$r = 2 \cos (θ)$
43380	Find the Concavity	x/(9x^2-16)	$\frac{x}{9 x^{2} - 16}$
43381	Multiply	19*2	$19 \cdot 2$
43382	Find the Tangent Line at the Point	y=sin(sin(x)) , (3pi,0)	$y = \sin (\sin (x))$ , $(3 π, 0)$
43383	Divide	(x^2-3x+2)/(x+1)	$\frac{x^{2} - 3 x + 2}{x + 1}$
43384	Solve for w	w = square root of k/m	$w = \sqrt{\frac{k}{m}}$
43385	Solve for P0	P=P_0e^(kt)	$P = P_{0} e^{k t}$
43386	Solve for x	3x^2-8x=0	$3 x^{2} - 8 x = 0$
43387	Solve for x	3x^2+24x+57=9	$3 x^{2} + 24 x + 57 = 9$
43388	Solve for x	x=2y-y^2	$x = 2 y - y^{2}$
43389	Solve for y	x=2y-y^2	$x = 2 y - y^{2}$
43390	Find the Antiderivative	1/(cos(x))	$\frac{1}{\cos (x)}$
43391	Find the Antiderivative	4sec(x)tan(x)	$4 \sec (x) \tan (x)$
43392	Find the Antiderivative	y^-2	$y^{- 2}$
43393	Evaluate the Summation	sum from i=1 to 4 of -3*2^(i-1)	$\sum_{i = 1}^{4} - 3 {(2)}^{i - 1}$
43394	Find the Domain	x/(1- natural log of x-8)	$\frac{x}{1 - \ln (x - 8)}$
43395	Find the Inflection Points	f(x)=4x^3-48x-5	$f (x) = 4 x^{3} - 48 x - 5$
43396	Graph	r=sin(2theta)	$r = \sin (2 θ)$
43397	Find the Derivative Using Quotient Rule - d/db	(cx-d)/(ax-b)	$\frac{c x - d}{a x - b}$
43398	Find the Derivative Using Quotient Rule - d/dc	(cx-d)/(ax-b)	$\frac{c x - d}{a x - b}$
43399	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of x)/x	$lim_{x \to \infty} \frac{\ln (x)}{x}$
43400	Convert to a Decimal	(5pi)/6	$\frac{5 π}{6}$