Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44301	Find the Second Derivative	y=4cot(x)	$y = 4 \cot (x)$
44302	Find the Second Derivative	y=e^(5x)sin(x)	$y = e^{5 x} \sin (x)$
44303	Find the Second Derivative	y=5sec(x)csc(x)	$y = 5 \sec (x) \csc (x)$
44304	Find the Second Derivative	y=x(2x+3)^5	$y = x {(2 x + 3)}^{5}$
44305	Find the Second Derivative	r=1/(3s^2)-8/(5s^4)	$r = \frac{1}{3 s^{2}} - \frac{8}{5 s^{4}}$
44306	Find the Third Derivative	y=14xcos(x)	$y = 14 x \cos (x)$
44307	Find the Fourth Derivative	y=10x^5	$y = 10 x^{5}$
44308	Find the Fourth Derivative	y=8sin(x)	$y = 8 \sin (x)$
44309	Find the Second Derivative	w=5z^2e^z	$w = 5 z^{2} e^{z}$
44310	Find the Second Derivative	4x^2+3y^2=4	$4 x^{2} + 3 y^{2} = 4$
44311	Find the Second Derivative	sin(x)+x^2y=10	$\sin (x) + x^{2} y = 10$
44312	Find the Second Derivative	f(x)=(x^2-3x-28)/(x+4)	$f (x) = \frac{x^{2} - 3 x - 28}{x + 4}$
44313	Find the Second Derivative	f(x)=3x-4x^(7/8)	$f (x) = 3 x - 4 x^{\frac{7}{8}}$
44314	Find the Second Derivative	f(x)=4x-5x^(7/8)	$f (x) = 4 x - 5 x^{\frac{7}{8}}$
44315	Find the Second Derivative	f(x)=4x+11	$f (x) = 4 x + 11$
44316	Find the Second Derivative	v(t) = square root of t^6- square root of t	$v (t) = \sqrt{t^{6}} - \sqrt{t}$
44317	Find the Second Derivative	f(x)=(x^3-4)^4	$f (x) = {(x^{3} - 4)}^{4}$
44318	Find the Third Derivative	f(x)=e^xsin(x)	$f (x) = e^{x} \sin (x)$
44319	Convert to a Decimal	11/10	$\frac{11}{10}$
44320	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (x-3)/(x^2-9)	$lim_{x \to 3} \frac{x - 3}{x^{2} - 9}$
44321	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x^2cot(x)	$lim_{x \to 0} x^{2} \cot (x)$
44322	Evaluate Using L'Hospital's Rule	limit as theta approaches pi/2 of (1-sin(theta))/(1+cos(2theta))	$lim_{θ \to \frac{π}{2}} \frac{1 - \sin (θ)}{1 + \cos (2 θ)}$
44323	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of sec(x)-tan(x)	$lim_{x \to \frac{π}{2}} \sec (x) - \tan (x)$
44324	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (3x^2)/(e^x)	$lim_{x \to \infty} \frac{3 x^{2}}{e^{x}}$
44325	Evaluate the Summation	sum from k=1 to 275 of -5k+12	$\sum_{k = 1}^{275} - 5 k + 12$
44326	Evaluate the Summation	sum from j=1 to 7 of 4^(j-1)	$\sum_{j = 1}^{7} 4^{j - 1}$
44327	Evaluate the Summation	sum from j=0 to 1 of 2j-4	$\sum_{j = 0}^{1} 2 j - 4$
44328	Evaluate the Summation	sum from j=1 to 7 of 1/4j+1	$\sum_{j = 1}^{7} \frac{1}{4} j + 1$
44329	Find Where Increasing/Decreasing Using Derivatives	f(x)=5x^3-10x^2+5x-2	$f (x) = 5 x^{3} - 10 x^{2} + 5 x - 2$
44330	Find Where Increasing/Decreasing Using Derivatives	f(x)=(6x)/(x^2+81)	$f (x) = \frac{6 x}{x^{2} + 81}$
44331	Find Where Increasing/Decreasing Using Derivatives	f(x)=-5x^3+15x+2	$f (x) = - 5 x^{3} + 15 x + 2$
44332	Find Where Increasing/Decreasing Using Derivatives	f(x)=7x^4+2x^3	$f (x) = 7 x^{4} + 2 x^{3}$
44333	Evaluate from the Left	limit as x approaches 2 of (x^2-4)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$
44334	Expand Using Sum/Difference Formulas	tan(15 degrees )	$\tan (15 °)$
44335	Find the Tangent Line at the Point	y=5x-4 square root of x , (1,1)	$y = 5 x - 4 \sqrt{x}$ , $(1, 1)$
44336	Find the Tangent Line at the Point	y=5xe^x , (0,0)	$y = 5 x e^{x}$ , $(0, 0)$
44337	Find the Tangent Line at the Point	natural log of x^2-7x+1 , (7,0)	$\ln (x^{2} - 7 x + 1)$ , $(7, 0)$
44338	Find the Tangent Line at the Point	y=18 square root of x , (9,54)	$y = 18 \sqrt{x}$ , $(9, 54)$
44339	Find the Tangent Line at the Point	y=9x-6 square root of x , (1,3)	$y = 9 x - 6 \sqrt{x}$ , $(1, 3)$
44340	Find the Tangent Line at the Point	sin(sin(x)) , (pi,0)	$\sin (\sin (x))$ , $(π, 0)$
44341	Find the Tangent Line at the Point	y=9e^xcos(x) , (0,9)	$y = 9 e^{x} \cos (x)$ , $(0, 9)$
44342	Find the Tangent Line at the Point	y=4x^2+4 , (-3,40)	$y = 4 x^{2} + 4$ , $(- 3, 40)$
44343	Find the Antiderivative	3/2 square root of x	$\frac{3}{2} \sqrt{x}$
44344	Find the Antiderivative	-32	$- 32$
44345	Find the Antiderivative	1/(x^2+2)	$\frac{1}{x^{2} + 2}$
44346	Find the Antiderivative	2e^x-cos(x)	$2 e^{x} - \cos (x)$
44347	Find the Antiderivative	2cos(2x-5)	$2 \cos (2 x - 5)$
44348	Find the Antiderivative	2^x natural log of 2	$2^{x} \ln (2)$
44349	Find the Antiderivative	sin(pi/4x)	$\sin (\frac{π}{4} x)$
44350	Find the Antiderivative	1+2sin((x^2)/2)	$1 + 2 \sin (\frac{x^{2}}{2})$
44351	Find the Roots (Zeros)	x^2-4x-3	$x^{2} - 4 x - 3$
44352	Find the Roots (Zeros)	x^2+2x+10	$x^{2} + 2 x + 10$
44353	Find the Antiderivative	-sin(2x)	$- \sin (2 x)$
44354	Find the Antiderivative	1-sin(x)^2	$1 - \sin^{2} (x)$
44355	Find the Antiderivative	1/(x^(2/3))	$\frac{1}{x^{\frac{2}{3}}}$
44356	Find the Antiderivative	12x^11	$12 x^{11}$
44357	Find the Inflection Points	f(x)=4+15x-2x^3	$f (x) = 4 + 15 x - 2 x^{3}$
44358	Find the Area Between the Curves	y=x^2-5x , y=3x	$y = x^{2} - 5 x$ , $y = 3 x$
44359	Find the Area Between the Curves	y=3x^2 natural log of x , y=12 natural log of x	$y = 3 x^{2} \ln (x)$ , $y = 12 \ln (x)$
44360	Find the Area Between the Curves	x=y^2-4y , x=2y-y^2	$x = y^{2} - 4 y$ , $x = 2 y - y^{2}$
44361	Find the Asymptotes	f(x)=(x^2+4)/(x^2-4)	$f (x) = \frac{x^{2} + 4}{x^{2} - 4}$
44362	Find the Asymptotes	s(t)=(3t)/(sin(t))	$s (t) = \frac{3 t}{\sin (t)}$
44363	Find the Asymptotes	f(x)=(5x)/(x^3-6x^2)	$f (x) = \frac{5 x}{x^{3} - 6 x^{2}}$
44364	Find the Asymptotes	f(x)=(x+3)/(x^3-12x^2+27x)	$f (x) = \frac{x + 3}{x^{3} - 12 x^{2} + 27 x}$
44365	Find the Maximum/Minimum Value	x^2+8x+14	$x^{2} + 8 x + 14$
44366	Find the Asymptotes	y=(4e^x)/(e^x-6)	$y = \frac{4 e^{x}}{e^{x} - 6}$
44367	Find the Asymptotes	y=(x^3-x)/(x^2-6x+5)	$y = \frac{x^{3} - x}{x^{2} - 6 x + 5}$
44368	Find the Derivative Using Chain Rule - d/dx	y=(2x+9)^11	$y = {(2 x + 9)}^{11}$
44369	Find Where Increasing/Decreasing Using Derivatives	9cos(x)^2	$9 \cos^{2} (x)$
44370	Find Where Increasing/Decreasing Using Derivatives	sin(x)^2+sin(x)	$\sin^{2} (x) + \sin (x)$
44371	Find Where Increasing/Decreasing Using Derivatives	x^8 natural log of x	$x^{8} \ln (x)$
44372	Find Where Increasing/Decreasing Using Derivatives	2x^3-15x^2-144x	$2 x^{3} - 15 x^{2} - 144 x$
44373	Find the Sum of the Infinite Geometric Series	12 , 4 , 4/3	$12$ , $4$ , $\frac{4}{3}$
44374	Identify the Polar Equation	r=1+cos(theta)	$r = 1 + \cos (θ)$
44375	Identify the Polar Equation	r=5cos(theta)	$r = 5 \cos (θ)$
44376	Find the Tangent Line at (49,7)	y = square root of x , (49,7)	$y = \sqrt{x}$ , $(49, 7)$
44377	Find the Linearization at a=16	f(x) = square root of x , a=16	$f (x) = \sqrt{x}$ , $a = 16$
44378	Find the Tangent Line at (0,5)	y=10/(1+e^(-x)) , (0,5)	$y = \frac{10}{(1 + e^{- x})}$ , $(0, 5)$
44379	Find the Domain	f(x) = square root of 25-x	$f (x) = \sqrt{25 - x}$
44380	Find the Horizontal Tangent Line	49x^2+25y^2+490x-350y+1225=0	$49 x^{2} + 25 y^{2} + 490 x - 350 y + 1225 = 0$
44381	Find the Sum of the Series	5/6 , 8/12 , 4/7	$\frac{5}{6}$ , $\frac{8}{12}$ , $\frac{4}{7}$
44382	Find the Difference Quotient	f(x) = square root of 2x+2	$f (x) = \sqrt{2 x + 2}$
44383	Find the Second Derivative	e^(-9x^2)	$e^{- 9 x^{2}}$
44384	Find the Second Derivative	e^(13x)cos(x)	$e^{13 x} \cos (x)$
44385	Find the Second Derivative	sin(pix)	$\sin (π x)$
44386	Find the Second Derivative	sin(3t)+cos(3t)	$\sin (3 t) + \cos (3 t)$
44387	Find the Second Derivative	x^4-1/x+2	$x^{4} - \frac{1}{x} + 2$
44388	Find the Third Derivative	sin(3t)+cos(3t)	$\sin (3 t) + \cos (3 t)$
44389	Find the Third Derivative	sin(pix)	$\sin (π x)$
44390	Find the Third Derivative	16x^3-32x^2	$16 x^{3} - 32 x^{2}$
44391	Find the Second Derivative	(7+4x)e^(-3x)	$(7 + 4 x) e^{- 3 x}$
44392	Find the Second Derivative	4x^2-4sin(2x)	$4 x^{2} - 4 \sin (2 x)$
44393	Find the Fourth Derivative	sin(pix)	$\sin (π x)$
44394	Find the Concavity	-81/( cube root of x+5)	$- \frac{81}{\sqrt[3]{x + 5}}$
44395	Find the Concavity	2x^4-10x^3-72x^2+100	$2 x^{4} - 10 x^{3} - 72 x^{2} + 100$
44396	Find the Concavity	3x^4-16x^3+18x^2	$3 x^{4} - 16 x^{3} + 18 x^{2}$
44397	Find the Domain	(1-3t)/(2+t)	$\frac{1 - 3 t}{2 + t}$
44398	Find the Domain	x/(1- natural log of x-5)	$\frac{x}{1 - \ln (x - 5)}$
44399	Find the Integral	x^2 natural log of x	$x^{2} \ln (x)$
44400	Find the Critical Points	1/4x^4-1/3x^3-3x^2	$\frac{1}{4} x^{4} - \frac{1}{3} x^{3} - 3 x^{2}$