Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
50001	Find the Focus	(y+2)^2=8x	${(y + 2)}^{2} = 8 x$
50002	Expand the Trigonometric Expression	(1-sin(x)^2)^2	${(1 - \sin^{2} (x))}^{2}$
50003	Expand the Trigonometric Expression	(1-U^2)^3	${(1 - U^{2})}^{3}$
50004	Expand the Trigonometric Expression	(3+h)^4	${(3 + h)}^{4}$
50005	Expand the Trigonometric Expression	(3-z^2)(z^3-5z+5)	$(3 - z^{2}) (z^{3} - 5 z + 5)$
50006	Expand the Trigonometric Expression	(h+1)^3	${(h + 1)}^{3}$
50007	Expand the Trigonometric Expression	(x+8)^2	${(x + 8)}^{2}$
50008	Expand the Trigonometric Expression	8(h+3)	$8 (h + 3)$
50009	Find the Slope	y=3+9x	$y = 3 + 9 x$
50010	Identify the Sequence	-1.4 , -3.7 , -6 , -8.3	$- 1.4$ , $- 3.7$ , $- 6$ , $- 8.3$
50011	Write as a Single Logarithm	1/2 log of b+6 log of c	$\frac{1}{2} \log (b) + 6 \log (c)$
50012	Write as a Single Logarithm	11 natural log of 8-11 natural log of 1	$11 \ln (8) - 11 \ln (1)$
50013	Write as a Single Logarithm	log base 3 of square root of x- log base 3 of x^2	$\log_{3} (\sqrt{x}) - \log_{3} (x^{2})$
50014	Write as a Single Logarithm	1/2 log of a+9 log of b	$\frac{1}{2} \log (a) + 9 \log (b)$
50015	Find the Concavity	f(x)=2x^4-10x^3-72x^2+100	$f (x) = 2 x^{4} - 10 x^{3} - 72 x^{2} + 100$
50016	Find the Concavity	f(x)=x^3-3x^2+27x-25	$f (x) = x^{3} - 3 x^{2} + 27 x - 25$
50017	Find the Concavity	f(x)=16x^2-1	$f (x) = 16 x^{2} - 1$
50018	Find the Concavity	f(x)=x^3-4x^2-16x+4	$f (x) = x^{3} - 4 x^{2} - 16 x + 4$
50019	Find the Concavity	f(x)=x^3-27x+5	$f (x) = x^{3} - 27 x + 5$
50020	Find the Concavity	f(x)=2x^4+6x^3-12x^2+8	$f (x) = 2 x^{4} + 6 x^{3} - 12 x^{2} + 8$
50021	Find the Derivative of the Integral	y=dcos(t)+t^2sin(t)	$y = d \cos (t) + t^{2} \sin (t)$
50022	Find the Derivative of the Integral	y=3^x log base 3 of x	$y = 3^{x} \log_{3} (x)$
50023	Find the Derivative of the Integral	y = natural log of cot(x)	$y = \ln (\cot (x))$
50024	Find the Derivative of the Integral	integral of (sin(x))/(cos(x)^3) with respect to x	$\int \frac{\sin (x)}{\cos^{3} (x)} d x$
50025	Find the Derivative of the Integral	y=(8-sec(x))/(tan(x))	$y = \frac{8 - \sec (x)}{\tan (x)}$
50026	Find the Derivative of the Integral	f(x) = integral from 0 to x^3 of sin(t^2) with respect to t	$f (x) = \int_{0}^{x^{3}} \sin (t^{2}) d t$
50027	Find the Derivative of the Integral	y=xsin(6/x)	$y = x \sin (\frac{6}{x})$
50028	Find the Derivative of the Integral	y=(5+csc(x))/(9-csc(x))	$y = \frac{5 + \csc (x)}{9 - \csc (x)}$
50029	Find the Derivative of the Integral	(d^99)/(dx^99)sin(x)	$\frac{d^{99}}{d x^{99}} \sin (x)$
50030	Find the Derivative of the Integral	(d^2)/(dx^2)(2sec(x))	$\frac{d^{2}}{d x^{2}} (2 \sec (x))$
50031	Find the Derivative of the Integral	y=2x^2cos(x)cot(x)	$y = 2 x^{2} \cos (x) \cot (x)$
50032	Find the Derivative of the Integral	y = natural log of 8x^2	$y = \ln (8 x^{2})$
50033	Find the Derivative of the Integral	y=(sec(x)+tan(x))(sec(x)-tan(x))	$y = (\sec (x) + \tan (x)) (\sec (x) - \tan (x))$
50034	Find the Derivative of the Integral	integral of (e^(tan(x)))/(cos(x)^2) with respect to x	$\int \frac{e^{\tan (x)}}{\cos^{2} (x)} d x$
50035	Find the Derivative of the Integral	f(x) = integral from -2 to x of (t^2-2t) with respect to t	$f (x) = \int_{- 2}^{x} (t^{2} - 2 t) d t$
50036	Find the Derivative of the Integral	integral from x to 5 of sin(t^4) with respect to t	$\int_{x}^{5} \sin (t^{4}) d t$
50037	Find the Derivative of the Integral	y=(2x)/(1-tan(x))	$y = \frac{2 x}{1 - \tan (x)}$
50038	Find the Derivative of the Integral	integral from 1 to 2 of (e^(1/(x^4)))/(x^5) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x^{4}}}}{x^{5}} d x$
50039	Find the Derivative of the Integral	y=sin(x)^5	$y = \sin^{5} (x)$
50040	Find the Derivative of the Integral	y=cos( square root of sin(cot(pix)))	$y = \cos (\sqrt{\sin (\cot (π x))})$
50041	Find the Derivative of the Integral	y=(6x)/(7-cot(x))	$y = \frac{6 x}{7 - \cot (x)}$
50042	Find the Concavity	f(x)=2x^2-2x-8	$f (x) = 2 x^{2} - 2 x - 8$
50043	Find the Concavity	f(x)=x^3-3x^2-9x+4	$f (x) = x^{3} - 3 x^{2} - 9 x + 4$
50044	Find the Concavity	f(x)=x+cos(x)	$f (x) = x + \cos (x)$
50045	Find the Concavity	f(x)=x^2-5x+9	$f (x) = x^{2} - 5 x + 9$
50046	Find the Concavity	f(x)=-x^6+36x^5-36x+11	$f (x) = - x^{6} + 36 x^{5} - 36 x + 11$
50047	Find the Concavity	h(x)=10/(x-6)	$h (x) = \frac{10}{x - 6}$
50048	Find the Concavity	f(x)=x^3-3x^2+24x-22	$f (x) = x^{3} - 3 x^{2} + 24 x - 22$
50049	Find the Concavity	f(x)=10x-10e^(-x)	$f (x) = 10 x - 10 e^{- x}$
50050	Find the Concavity	f(x)=-1/2x^4-128x+6	$f (x) = - \frac{1}{2} x^{4} - 128 x + 6$
50051	Find the Concavity	f(x)=5x^3-10x	$f (x) = 5 x^{3} - 10 x$
50052	Find the Concavity	f(x)=(x+5)^(2/7)	$f (x) = {(x + 5)}^{\frac{2}{7}}$
50053	Find the Concavity	f(x)=x^7 natural log of x	$f (x) = x^{7} \ln (x)$
50054	Find the Concavity	f(x)=x+3cos(x)	$f (x) = x + 3 \cos (x)$
50055	Find the Concavity	f(x)=sin(x)-cos(x)	$f (x) = \sin (x) - \cos (x)$
50056	Find the Slope	4x+5y=7	$4 x + 5 y = 7$
50057	Find the Slope	y=1/3x-8	$y = \frac{1}{3} x - 8$
50058	Find the Slope	(4-2x)/3=y	$\frac{4 - 2 x}{3} = y$
50059	Find the Slope	y=6-2x	$y = 6 - 2 x$
50060	Find the Slope	y=9x-1	$y = 9 x - 1$
50061	Find the Slope	x-2y=2	$x - 2 y = 2$
50062	Find the Slope	y=-1/2x+2	$y = - \frac{1}{2} x + 2$
50063	Identify the Sequence	1 , -4 , 16 , -64	$1$ , $- 4$ , $16$ , $- 64$
50064	Identify the Sequence	3/16 , 4/25 , 5/36 , 6/49	$\frac{3}{16}$ , $\frac{4}{25}$ , $\frac{5}{36}$ , $\frac{6}{49}$
50065	Identify the Sequence	-3 , 6 , -9 , 12 , -15	$- 3$ , $6$ , $- 9$ , $12$ , $- 15$
50066	Write as a Single Logarithm	3 log of x-2 log of y	$3 \log (x) - 2 \log (y)$
50067	Find the Derivative of the Integral	y=tan( square root of 3t)	$y = \tan (\sqrt{3 t})$
50068	Find the Derivative of the Integral	y=(2x)/(3-cot(x))	$y = \frac{2 x}{3 - \cot (x)}$
50069	Find the Derivative of the Integral	y=8/( natural log of x)	$y = \frac{8}{\ln (x)}$
50070	Find the Derivative of the Integral	y=9/( natural log of x)	$y = \frac{9}{\ln (x)}$
50071	Find the Derivative of the Integral	F(x) = integral from 2 to x^2 of 1/(t^3) with respect to t	$F (x) = \int_{2}^{x^{2}} \frac{1}{t^{3}} d t$
50072	Find the Derivative of the Integral	(d^106)/(dx^106)(sin(x))	$\frac{d^{106}}{d x^{106}} (\sin (x))$
50073	Find the Derivative of the Integral	y=(6x)/(5-cot(x))	$y = \frac{6 x}{5 - \cot (x)}$
50074	Find the Derivative of the Integral	ysin(16x)=xcos(2y)	$y \sin (16 x) = x \cos (2 y)$
50075	Find the Derivative of the Integral	y=xarcsin(x)+ square root of 1-x^2	$y = x \arcsin (x) + \sqrt{1 - x^{2}}$
50076	Find the Derivative of the Integral	y=e^(6x)sin(5x)	$y = e^{6 x} \sin (5 x)$
50077	Find the Derivative of the Integral	integral from -k to k of square root of k^2-x^2 with respect to x	$\int_{- k}^{k} \sqrt{k^{2} - x^{2}} d x$
50078	Find the Derivative of the Integral	y = square root of natural log of 4x	$y = \sqrt{\ln (4 x)}$
50079	Find the Derivative of the Integral	y=2sin(x)cos(x)	$y = 2 \sin (x) \cos (x)$
50080	Find the Derivative of the Integral	y=tan(7theta)^2	$y = \tan^{2} (7 θ)$
50081	Find the Derivative of the Integral	y = natural log of square root of (x+9)/(x-9)	$y = \ln (\sqrt{\frac{x + 9}{x - 9}})$
50082	Find the Derivative of the Integral	y=(x^2+1)^(sin(x))	$y = {(x^{2} + 1)}^{\sin (x)}$
50083	Find the Derivative of the Integral	y=(6x)/(9-tan(x))	$y = \frac{6 x}{9 - \tan (x)}$
50084	Find the Derivative of the Integral	y=2arcsin( square root of x/2)	$y = 2 \arcsin (\sqrt{\frac{x}{2}})$
50085	Find the Derivative of the Integral	y=7arctan(x- square root of 1+x^2)	$y = 7 \arctan (x - \sqrt{1 + x^{2}})$
50086	Find the Derivative of the Integral	integral from 0 to x of (t^2)/(1+t^3) with respect to t	$\int_{0}^{x} \frac{t^{2}}{1 + t^{3}} d t$
50087	Find the Derivative of the Integral	ysin(2x)=xcos(2y)	$y \sin (2 x) = x \cos (2 y)$
50088	Find the Derivative of the Integral	y=(4-sec(x))/(tan(x))	$y = \frac{4 - \sec (x)}{\tan (x)}$
50089	Find the Derivative of the Integral	(d^90)/(dx^90)(sin(x))	$\frac{d^{90}}{d x^{90}} (\sin (x))$
50090	Find the Derivative of the Integral	y=(sin(4x))/(sin(2x))	$y = \frac{\sin (4 x)}{\sin (2 x)}$
50091	Find the Derivative of the Integral	integral of 3x^2(x^3+1)^6 with respect to x	$\int 3 x^{2} {(x^{3} + 1)}^{6} d x$
50092	Find the Derivative of the Integral	integral from 0 to sin(x) of square root of t with respect to t	$\int_{0}^{\sin (x)} \sqrt{t} d t$
50093	Find the Derivative of the Integral	y=(cos(6x))/((x^3+4)^2)	$y = \frac{\cos (6 x)}{{(x^{3} + 4)}^{2}}$
50094	Find the Derivative of the Integral	y=(4x)/(7-cot(x))	$y = \frac{4 x}{7 - \cot (x)}$
50095	Find the Derivative of the Integral	f(x) = integral from 0 to x of e^(t^2) with respect to t	$f (x) = \int_{0}^{x} e^{t^{2}} d t$
50096	Find the Derivative of the Integral	(d^30)/(dx^30)(sin(x))	$\frac{d^{30}}{d x^{30}} (\sin (x))$
50097	Find the Derivative of the Integral	y=(tan(2x))/(1-cot(2x))	$y = \frac{\tan (2 x)}{1 - \cot (2 x)}$
50098	Find the Derivative of the Integral	y=arccos(e^(8x))	$y = \arccos (e^{8 x})$
50099	Find the Derivative of the Integral	y=(2x)/(5-cot(x))	$y = \frac{2 x}{5 - \cot (x)}$
50100	Find the Derivative of the Integral	y=x^3tan(x)	$y = x^{3} \tan (x)$