Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
16101	Find the Derivative - d/d@VAR	P(x)=(-1/2x^2+900x)-(5400+500x)	$P (x) = (- \frac{1}{2} x^{2} + 900 x) - (5400 + 500 x)$
16102	Find the Derivative - d/d@VAR	R(x)=2000(1-x/600)^2	$R (x) = 2000 {(1 - \frac{x}{600})}^{2}$
16103	Find the Derivative - d/d@VAR	r(x)=100xe^(-0.1x)	$r (x) = 100 x e^{- 0.1 x}$
16104	Find the Derivative - d/d@VAR	p(y)=(y^-1+y^-2)(3y^-3-5y^-4)	$p (y) = (y^{- 1} + y^{- 2}) (3 y^{- 3} - 5 y^{- 4})$
16105	Find the Derivative - d/d@VAR	S(t)=(50t^2)/(t^2+150)	$S (t) = \frac{50 t^{2}}{t^{2} + 150}$
16106	Find the Derivative - d/d@VAR	s(t)=1/(t^2+3t-1)	$s (t) = \frac{1}{t^{2} + 3 t - 1}$
16107	Find the Derivative - d/d@VAR	s(x)=5e^(-1.5x)cos(2pix)	$s (x) = 5 e^{- 1.5 x} \cos (2 π x)$
16108	Find the Derivative - d/d@VAR	f(x)=tan(3x)^3	$f (x) = \tan^{3} (3 x)$
16109	Find the Derivative - d/d@VAR	f(x)=tan(x)^8	$f (x) = \tan^{8} (x)$
16110	Find the Derivative - d/d@VAR	f(x)=arctan(3x^2)	$f (x) = \arctan (3 x^{2})$
16111	Find the Derivative - d/d@VAR	f(x)=sin(x)^2+sin(x)	$f (x) = \sin^{2} (x) + \sin (x)$
16112	Find the Derivative - d/d@VAR	f(x)=sin(x)^2-cos(x)	$f (x) = \sin^{2} (x) - \cos (x)$
16113	Find the Derivative - d/d@VAR	f(x)=(t+1)/(2^t)	$f (x) = \frac{t + 1}{2^{t}}$
16114	Find the Derivative - d/d@VAR	f(x)=(t-5)/(t^2+10t+25)	$f (x) = \frac{t - 5}{t^{2} + 10 t + 25}$
16115	Find the Derivative - d/d@VAR	f(x)=u^3e^(-u)	$f (x) = u^{3} e^{- u}$
16116	Find the Derivative - d/d@VAR	f(x) = square root of x^3+27	$f (x) = \sqrt{x^{3} + 27}$
16117	Find the Derivative - d/d@VAR	f(x) = square root of 11x-x^5	$f (x) = \sqrt{11 x - x^{5}}$
16118	Find the Derivative - d/d@VAR	f(x) = square root of 3-6x	$f (x) = \sqrt{3 - 6 x}$
16119	Evaluate the Limit	limit as x approaches 0 of (tan(x)-sin(x))/(x^3)	$lim_{x \to 0} \frac{\tan (x) - \sin (x)}{x^{3}}$
16120	Find the Derivative - d/d@VAR	f(x) = square root of 4x^2-12x+9	$f (x) = \sqrt{4 x^{2} - 12 x + 9}$
16121	Evaluate the Limit	limit as x approaches 2 of square root of (3x^2+4)/(3x-2)	$lim_{x \to 2} \sqrt{\frac{3 x^{2} + 4}{3 x - 2}}$
16122	Find the Derivative - d/dx	y=10 root of x	$y = \sqrt[10]{x}$
16123	Find the Derivative - d/d@VAR	f(x) = square root of 64-x^2	$f (x) = \sqrt{64 - x^{2}}$
16124	Find the Derivative - d/d@VAR	f(x)=( natural log of x)/(1+x)	$f (x) = \frac{\ln (x)}{1 + x}$
16125	Find the Derivative - d/d@VAR	f(x)=e^(xy)	$f (x) = e^{x y}$
16126	Find the Derivative - d/d@VAR	f(x) = natural log of (x^2+1)^9	$f (x) = \ln ({(x^{2} + 1)}^{9})$
16127	Find the Derivative - d/d@VAR	f(x)=e^(6-x)	$f (x) = e^{6 - x}$
16128	Find the Derivative - d/d@VAR	f(x)=e^x-6x	$f (x) = e^{x} - 6 x$
16129	Find the Derivative - d/d@VAR	f(x)=e^(cos(2x))	$f (x) = e^{\cos (2 x)}$
16130	Find the Derivative - d/d@VAR	f(x)=e^( log of e^(5x))	$f (x) = e^{\log (e^{5 x})}$
16131	Find the Derivative - d/d@VAR	f(x)=e^( log of sin(3x))	$f (x) = e^{\log (\sin (3 x))}$
16132	Find the Derivative - d/d@VAR	f(x) = log of x^6+4	$f (x) = \log (x^{6} + 4)$
16133	Find the Derivative - d/d@VAR	f(x)=( natural log of x)/(x^9)	$f (x) = \frac{\ln (x)}{x^{9}}$
16134	Find the Derivative - d/d@VAR	f(x)=arcsin(x^2+2)	$f (x) = \arcsin (x^{2} + 2)$
16135	Find the Derivative - d/d@VAR	f(x)=(sec(x))/(1+sec(x))	$f (x) = \frac{\sec (x)}{1 + \sec (x)}$
16136	Find the Inflection Points	x square root of 9-x	$x \sqrt{9 - x}$
16137	Find the Derivative - d/d@VAR	f(x)=x/( square root of x-y)	$f (x) = \frac{x}{\sqrt{x - y}}$
16138	Find the Derivative - d/d@VAR	f(x)=x/( square root of 2-x^2)	$f (x) = \frac{x}{\sqrt{2 - x^{2}}}$
16139	Find the Critical Points	x^4-4x^3+10	$x^{4} - 4 x^{3} + 10$
16140	Find the Concavity	f(x)=4x^3-48x	$f (x) = 4 x^{3} - 48 x$
16141	Find the Derivative - d/d@VAR	f(x)=x/((3x-8)^6)	$f (x) = \frac{x}{{(3 x - 8)}^{6}}$
16142	Find the Derivative - d/d@VAR	f(x)=x/((6x-5)^9)	$f (x) = \frac{x}{{(6 x - 5)}^{9}}$
16143	Find the Derivative - d/d@VAR	f(x)=x/((7x-6)^8)	$f (x) = \frac{x}{{(7 x - 6)}^{8}}$
16144	Find the Derivative - d/d@VAR	f(x) = fourth root of x^2+2x+1	$f (x) = \sqrt[4]{x^{2} + 2 x + 1}$
16145	Find the Derivative - d/d@VAR	f(x) = cube root of 2x^2-x	$f (x) = \sqrt[3]{2 x^{2} - x}$
16146	Find the Derivative - d/d@VAR	f(x) = square root of 5x+1	$f (x) = \sqrt{5 x + 1}$
16147	Find the Derivative - d/d@VAR	f(x)=pi^8	$f (x) = π^{8}$
16148	Find the Derivative - d/d@VAR	f(x) = square root of x- square root of a	$f (x) = \sqrt{x} - \sqrt{a}$
16149	Find the Derivative - d/d@VAR	f(x) = square root of x-10 cube root of x	$f (x) = \sqrt{x} - 10 \sqrt[3]{x}$
16150	Find the Derivative - d/dx	x^4-17x^2+16	$x^{4} - 17 x^{2} + 16$
16151	Find the Derivative - d/dx	-9/(x^10)	$- \frac{9}{x^{10}}$
16152	Find the Derivative - d/d@VAR	f(x) = square root of x-6	$f (x) = \sqrt{x - 6}$
16153	Find the Derivative - d/dx	square root of 36-x^2	$\sqrt{36 - x^{2}}$
16154	Find the Derivative - d/d@VAR	f(x)=x^(5/3)-x^(2/3)	$f (x) = x^{\frac{5}{3}} - x^{\frac{2}{3}}$
16155	Find the Derivative - d/d@VAR	f(x)=x^(7/2)e^x	$f (x) = x^{\frac{7}{2}} e^{x}$
16156	Find the Derivative - d/dy	1/3*( square root of y(y-3))	$\frac{1}{3} \cdot (\sqrt{y} (y - 3))$
16157	Find the Derivative - d/dz	(4z+e^(-z^2))^4	${(4 z + e^{- z^{2}})}^{4}$
16158	Find the Derivative - d/d@VAR	f(x)=x^2e^(5x)	$f (x) = x^{2} e^{5 x}$
16159	Find the Derivative - d/d@VAR	f(x)=x^10e^x-7	$f (x) = x^{10} e^{x} - 7$
16160	Find dy/dx	y=x^-8	$y = x^{- 8}$
16161	Find the Derivative - d/d@VAR	f(x)=x^18 natural log of x	$f (x) = x^{18} \ln (x)$
16162	Find dy/dx	y=3x^2-4x	$y = 3 x^{2} - 4 x$
16163	Find the Local Maxima and Minima	x^4-2x^2	$x^{4} - 2 x^{2}$
16164	Find the Derivative - d/d@VAR	f(x)=2e^xcos(x)	$f (x) = 2 e^{x} \cos (x)$
16165	Find the Derivative - d/d@VAR	f(x)=16xe^x	$f (x) = 16 x e^{x}$
16166	Evaluate the Limit	limit as x approaches infinity of (e^x)/(x^2)	$lim_{x \to \infty} \frac{e^{x}}{x^{2}}$
16167	Find the Derivative - d/d@VAR	f(x)=11 square root of x	$f (x) = 11 \sqrt{x}$
16168	Find the Derivative - d/d@VAR	f(x)=-16	$f (x) = - 16$
16169	Find the Derivative - d/d@VAR	f(x)=12+8e^(8x)	$f (x) = 12 + 8 e^{8 x}$
16170	Find the Derivative - d/d@VAR	f(x)=xe^(3x)-e^(x^2)	$f (x) = x e^{3 x} - e^{x^{2}}$
16171	Find the Derivative - d/d@VAR	f(x)=xe^(-4x)	$f (x) = x e^{- 4 x}$
16172	Find the Derivative - d/d@VAR	f(x)=xe^(3x)	$f (x) = x e^{3 x}$
16173	Evaluate the Limit	limit as x approaches 0 of ( square root of x+6- square root of 6)/x	$lim_{x \to 0} \frac{\sqrt{x + 6} - \sqrt{6}}{x}$
16174	Find the Derivative - d/d@VAR	f(x)=xe^(-(x^2)/2)	$f (x) = x e^{- \frac{x^{2}}{2}}$
16175	Evaluate the Limit	limit as x approaches infinity of (e^(3x)+e^(-3x))/(e^(3x)-e^(-3x))	$lim_{x \to \infty} \frac{e^{3 x} + e^{- 3 x}}{e^{3 x} - e^{- 3 x}}$
16176	Find the Derivative - d/d@VAR	f(x)=x^n	$f (x) = x^{n}$
16177	Evaluate the Limit	limit as x approaches pi/4 of (1+tan(x))/(csc(x)+2)	$lim_{x \to \frac{π}{4}} \frac{1 + \tan (x)}{\csc (x) + 2}$
16178	Find the Derivative - d/d@VAR	f(x)=0.775t^2-140.460t+6868.82	$f (x) = 0.775 t^{2} - 140.46 t + 6868.82$
16179	Find the Derivative - d/d@VAR	f(x)=y^3-3y^2-x^2-9y+10x-60	$f (x) = y^{3} - 3 y^{2} - x^{2} - 9 y + 10 x - 60$
16180	Find the Derivative - d/d@VAR	f(x)=1.5x^2-x+3.7	$f (x) = 1.5 x^{2} - x + 3.7$
16181	Find the Derivative - d/d@VAR	f(x)=1.1sin(4t)+0.6cos(t)	$f (x) = 1.1 \sin (4 t) + 0.6 \cos (t)$
16182	Find the Derivative - d/d@VAR	f(x)=1-e^(-3x)	$f (x) = 1 - e^{- 3 x}$
16183	Find the Derivative - d/d@VAR	f(x)=1000(50-3p)	$f (x) = 1000 (50 - 3 p)$
16184	Find the Derivative - d/d@VAR	f(x)=1+a/(x+1)+b/(x-2)	$f (x) = 1 + \frac{a}{x + 1} + \frac{b}{x - 2}$
16185	Find the Derivative - d/d@VAR	f(x)=x^3cos(2x)	$f (x) = x^{3} \cos (2 x)$
16186	Find the Derivative - d/d@VAR	f(x)=x^4e^(8x)	$f (x) = x^{4} e^{8 x}$
16187	Find the Derivative - d/d@VAR	f(x)=x^4-8x^3	$f (x) = x^{4} - 8 x^{3}$
16188	Evaluate the Limit	limit as x approaches infinity of square root of x^4-5x^2-x^2	$lim_{x \to \infty} \sqrt{x^{4} - 5 x^{2}} - x^{2}$
16189	Evaluate the Limit	limit as x approaches 0 of x/(sin(2x))	$lim_{x \to 0} \frac{x}{\sin (2 x)}$
16190	Find the Derivative - d/d@VAR	f(x)=x^7(4-x)^8	$f (x) = x^{7} {(4 - x)}^{8}$
16191	Find the Derivative - d/d@VAR	f(x)=x^9e^(8x)	$f (x) = x^{9} e^{8 x}$
16192	Evaluate	arccot(- square root of 3)	$arccot (- \sqrt{3})$
16193	Find the Derivative - d/d@VAR	f(x)=x^7e^(5x)	$f (x) = x^{7} e^{5 x}$
16194	Find the Derivative - d/dx	y = fifth root of x^4+x^(4e)	$y = \sqrt[5]{x^{4}} + x^{4 e}$
16195	Find the Derivative - d/d@VAR	f(x)=x^5-8x+5	$f (x) = x^{5} - 8 x + 5$
16196	Find the Derivative - d/d@VAR	f(x)=x^5 natural log of 8x	$f (x) = x^{5} \ln (8 x)$
16197	Find the Derivative - d/d@VAR	f(x)=x^4-6	$f (x) = x^{4} - 6$
16198	Find the Derivative - d/d@VAR	f(x)=x^4-5x^2+4	$f (x) = x^{4} - 5 x^{2} + 4$
16199	Find the Derivative - d/d@VAR	f(x)=x^5e^(6x)	$f (x) = x^{5} e^{6 x}$
16200	Find the Derivative - d/d@VAR	f(x)=x^2-10x	$f (x) = x^{2} - 10 x$