Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45101	Find the Second Derivative	y = natural log of sec(2x)+tan(2x)	$y = \ln (\sec (2 x) + \tan (2 x))$
45102	Find the Second Derivative	y=cos(2x)	$y = \cos (2 x)$
45103	Find the Fourth Derivative	y=5x^5	$y = 5 x^{5}$
45104	Find the Fourth Derivative	y=cos(2x)	$y = \cos (2 x)$
45105	Find the Fourth Derivative	y=2x^5-3x^2-5x+1	$y = 2 x^{5} - 3 x^{2} - 5 x + 1$
45106	Write in Exponential Form	log base 16 of 4=1/2	$\log_{16} (4) = \frac{1}{2}$
45107	Find the Third Derivative	-3x^2+2xy=5	$- 3 x^{2} + 2 x y = 5$
45108	Find the Third Derivative	y = square root of 2x^3+3x+10	$y = \sqrt{2 x^{3} + 3 x + 10}$
45109	Find the Third Derivative	y=cos(2x)	$y = \cos (2 x)$
45110	Find the Third Derivative	y=theta^2(2theta+8)	$y = θ^{2} (2 θ + 8)$
45111	Find the Second Derivative	y=2x^5-3x^2-5x+1	$y = 2 x^{5} - 3 x^{2} - 5 x + 1$
45112	Find the Inflection Points	f(x)=5x^3-10x^2+5x-2	$f (x) = 5 x^{3} - 10 x^{2} + 5 x - 2$
45113	Find the Inflection Points	f(x)=4sin(x)+4cos(x)	$f (x) = 4 \sin (x) + 4 \cos (x)$
45114	Find the Inflection Points	f(x)=2x^3-4x^2+2x-2	$f (x) = 2 x^{3} - 4 x^{2} + 2 x - 2$
45115	Find the Inflection Points	f(x)=8-7x^4	$f (x) = 8 - 7 x^{4}$
45116	Find the Inflection Points	f(x)=x^3-5x^2-8x+5	$f (x) = x^{3} - 5 x^{2} - 8 x + 5$
45117	Find the Inflection Points	f(x)=x^3-3x^2+23x-21	$f (x) = x^{3} - 3 x^{2} + 23 x - 21$
45118	Find the Inflection Points	f(x)=16x+16e^x	$f (x) = 16 x + 16 e^{x}$
45119	Find the Inflection Points	f(x)=(x-2)^(5/3)	$f (x) = {(x - 2)}^{\frac{5}{3}}$
45120	Find the Roots (Zeros)	cos(x)=x^3	$\cos (x) = x^{3}$
45121	Find the Area Under the Curve	f(x)=x^2-x-2 , [-5,0]	$f (x) = x^{2} - x - 2$ , $[- 5, 0]$
45122	Find Where Increasing/Decreasing Using Derivatives	f(x)=6x^2(14+x)^2	$f (x) = 6 x^{2} {(14 + x)}^{2}$
45123	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^4-32x+3	$f (x) = x^{4} - 32 x + 3$
45124	Find Where Increasing/Decreasing Using Derivatives	f(x)=5/3x^3-5/2x^2	$f (x) = \frac{5}{3} x^{3} - \frac{5}{2} x^{2}$
45125	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^3-6x^2+3x+8	$f (x) = 3 x^{3} - 6 x^{2} + 3 x + 8$
45126	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x^2)/(x^2+81)	$f (x) = \frac{x^{2}}{x^{2} + 81}$
45127	Evaluate from the Right	limit as x approaches 0 of x^( square root of x)	$lim_{x \to 0} x^{\sqrt{x}}$
45128	Evaluate from the Right	limit as x approaches pi/2 of e^(tan(x))	$lim_{x \to \frac{π}{2}} e^{\tan (x)}$
45129	Apply the Quadratic Formula	12x^2-108x+170	$12 x^{2} - 108 x + 170$
45130	Solve by Factoring	(2x+1)^2=48	${(2 x + 1)}^{2} = 48$
45131	Convert to a Simplified Fraction	2.44948974	$2.44948974$
45132	Find the Fourth Derivative	f(x)=20x^3-32x^2	$f (x) = 20 x^{3} - 32 x^{2}$
45133	Find the Third Derivative	g(x)=8x^4-6x^2+6	$g (x) = 8 x^{4} - 6 x^{2} + 6$
45134	Find the Third Derivative	f(x)=(3x)/(x+1)	$f (x) = \frac{3 x}{(x + 1)}$
45135	Find the Third Derivative	f(x)=20x^3-32x^2	$f (x) = 20 x^{3} - 32 x^{2}$
45136	Find the Third Derivative	f(x)=x^5-3x^4+2x^3-x^2+4x-10	$f (x) = x^{5} - 3 x^{4} + 2 x^{3} - x^{2} + 4 x - 10$
45137	Find the Third Derivative	f(x)=6x^-4	$f (x) = 6 x^{- 4}$
45138	Split Using Partial Fraction Decomposition	1/(x^4-1)	$\frac{1}{x^{4} - 1}$
45139	Find the Second Derivative	f(x)=2x^-6	$f (x) = 2 x^{- 6}$
45140	Find the Second Derivative	f(x)=3/( square root of x+9)	$f (x) = \frac{3}{\sqrt{x + 9}}$
45141	Find the Second Derivative	f(x)=(x^2-3x-4)/(x+1)	$f (x) = \frac{x^{2} - 3 x - 4}{x + 1}$
45142	Find the Second Derivative	f(x)=6x+11	$f (x) = 6 x + 11$
45143	Find the Second Derivative	f(x)=18x^(1/2)	$f (x) = 18 x^{\frac{1}{2}}$
45144	Find the Second Derivative	f(x)=(2x)/(9x^2-16)	$f (x) = \frac{2 x}{9 x^{2} - 16}$
45145	Find the Second Derivative	f(x)=x^(7/3)+56x^(4/3)	$f (x) = x^{\frac{7}{3}} + 56 x^{\frac{4}{3}}$
45146	Find the Second Derivative	f(x)=x^5-3x^4+2x^3-x^2+4x-10	$f (x) = x^{5} - 3 x^{4} + 2 x^{3} - x^{2} + 4 x - 10$
45147	Split Using Partial Fraction Decomposition	y/(y^2-y-2)	$\frac{y}{y^{2} - y - 2}$
45148	Split Using Partial Fraction Decomposition	(7x-19)/(x^2-6x+9)	$\frac{7 x - 19}{x^{2} - 6 x + 9}$
45149	Find the Second Derivative	f(x)=sin(8x^2)	$f (x) = \sin (8 x^{2})$
45150	Find the Second Derivative	f(x)=4x+15	$f (x) = 4 x + 15$
45151	Find the Second Derivative	f(x)=5arctan(x^2)	$f (x) = 5 \arctan (x^{2})$
45152	Find the Second Derivative	f(x)=sin(5x^2)	$f (x) = \sin (5 x^{2})$
45153	Find the Second Derivative	f(x)=5x^-4	$f (x) = 5 x^{- 4}$
45154	Find the Second Derivative	f(x)=5x^3 natural log of 6x	$f (x) = 5 x^{3} \ln (6 x)$
45155	Find the Second Derivative	f(x)=sec(pi/4)	$f (x) = \sec (\frac{π}{4})$
45156	Find the Second Derivative	g(t)=8cos(t)-9sin(t)	$g (t) = 8 \cos (t) - 9 \sin (t)$
45157	Find the Second Derivative	f(x)=6e^x-x^3	$f (x) = 6 e^{x} - x^{3}$
45158	Find the Second Derivative	f(x)=8x+17	$f (x) = 8 x + 17$
45159	Find the Second Derivative	p(x)=300x^3-25x^2+500x	$p (x) = 300 x^{3} - 25 x^{2} + 500 x$
45160	Find the Second Derivative	f(x)=8x+11	$f (x) = 8 x + 11$
45161	Find the Second Derivative	f(x)=9sin(3x)	$f (x) = 9 \sin (3 x)$
45162	Find the Third Derivative	f(x)=7x^-3	$f (x) = 7 x^{- 3}$
45163	Find the Third Derivative	P(x)=300x^3-25x^2+500x	$P (x) = 300 x^{3} - 25 x^{2} + 500 x$
45164	Find the Third Derivative	f(x)=(x-3)/(x-6)	$f (x) = \frac{x - 3}{x - 6}$
45165	Find the Third Derivative	f(x)=3 square root of x+27 cube root of x^2+5/( fifth root of x^3)	$f (x) = 3 \sqrt{x} + 27 \sqrt[3]{x^{2}} + \frac{5}{\sqrt[5]{x^{3}}}$
45166	Find the Fourth Derivative	f(x)=6e^x-x^3	$f (x) = 6 e^{x} - x^{3}$
45167	Find the x and y Intercepts	x^2+y^2-2x-6y-26=0	$x^{2} + y^{2} - 2 x - 6 y - 26 = 0$
45168	Find the Horizontal Tangent Line	y=(x^2-120)e^x	$y = (x^{2} - 120) e^{x}$
45169	Find the Horizontal Tangent Line	y=(x^2-80)e^x	$y = (x^{2} - 80) e^{x}$
45170	Find Trig Functions Using Identities	(sec(x)^2-tan(x)^2+tan(x))/(sec(x))	$\frac{\sec^{2} (x) - \tan^{2} (x) + \tan (x)}{\sec (x)}$
45171	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (9x)/(x-1)-9/( natural log of x)	$lim_{x \to 1} \frac{9 x}{x - 1} - \frac{9}{\ln (x)}$
45172	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( square root of x+x^2)/(9x-x^2)	$lim_{x \to \infty} \frac{\sqrt{x} + x^{2}}{9 x - x^{2}}$
45173	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin((9pi)/x)	$lim_{x \to \infty} x \sin (\frac{9 π}{x})$
45174	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(8x))/(sin(3x))	$lim_{x \to 0} \frac{\sin (8 x)}{\sin (3 x)}$
45175	Evaluate Using L'Hospital's Rule	limit as x approaches 4 of (x^2-16)/(x^2-4x)	$lim_{x \to 4} \frac{x^{2} - 16}{x^{2} - 4 x}$
45176	Write as a Function of y	(dy)/(dx)=xy	$\frac{d y}{d x} = x y$
45177	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xtan(7/x)	$lim_{x \to \infty} x \tan (\frac{7}{x})$
45178	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(sin(x)))/(sin(x))	$lim_{x \to 0} \frac{\sin (\sin (x))}{\sin (x)}$
45179	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (7x-sin(7x))/(7x-tan(7x))	$lim_{x \to 0} \frac{7 x - \sin (7 x)}{7 x - \tan (7 x)}$
45180	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of xsin((4pi)/x)	$lim_{x \to \infty} x \sin (\frac{4 π}{x})$
45181	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 from the right of (cos(x))/(1-sin(x))	$lim_{x \to \frac{π}{2}} \frac{(\cos (x))}{1 - \sin (x)}$
45182	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^x)/(x^3)	$lim_{x \to \infty} \frac{e^{x}}{x^{3}}$
45183	Find the Antiderivative	-32x	$- 32 x$
45184	Find the Antiderivative	6/( square root of 1-x^2)	$\frac{6}{\sqrt{1 - x^{2}}}$
45185	Find the Antiderivative	-4sin(x)^2	$- 4 \sin^{2} (x)$
45186	Find the Antiderivative	1/(5x)	$\frac{1}{5 x}$
45187	Find the Antiderivative	sec(x)tan(x)-e^x	$\sec (x) \tan (x) - e^{x}$
45188	Find the Antiderivative	3 cube root of x^2	$3 \sqrt[3]{x^{2}}$
45189	Find the Antiderivative	2x-cos(x)	$2 x - \cos (x)$
45190	Find the Antiderivative	square root of x^5-40	$\sqrt{x^{5}} - 40$
45191	Find the Antiderivative	y^(-1/2)	$y^{- \frac{1}{2}}$
45192	Find the Antiderivative	(cos(2x))/2	$\frac{\cos (2 x)}{2}$
45193	Find the Antiderivative	16x^3-9 square root of x+12x+11	$16 x^{3} - 9 \sqrt{x} + 12 x + 11$
45194	Find the Antiderivative	-3sin(x)	$- 3 \sin (x)$
45195	Find the Antiderivative	(dy)/(y^2)	$\frac{d y}{y^{2}}$
45196	Find the Antiderivative	3sin(x)-2cos(x)	$3 \sin (x) - 2 \cos (x)$
45197	Find the Antiderivative	9x^-3	$9 x^{- 3}$
45198	Find the Antiderivative	x^2-4x+7	$x^{2} - 4 x + 7$
45199	Find the Roots (Zeros)	3x^2-18x+15	$3 x^{2} - 18 x + 15$
45200	Find the Roots (Zeros)	3x^2-3x-6	$3 x^{2} - 3 x - 6$