Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
12501	Find the Derivative - d/dx	f(x) = log base 6 of square root of x^2+1	$f (x) = \log_{6} (\sqrt{x^{2} + 1})$
12502	Find the Derivative - d/dx	f(x) = log base 9 of x	$f (x) = \log_{9} (x)$
12503	Find the Derivative - d/dx	f(x)=arcsin(e^(-2x))	$f (x) = \arcsin (e^{- 2 x})$
12504	Find the Derivative - d/dx	f(x)=sec(x^2)^4	$f (x) = \sec^{4} (x^{2})$
12505	Find the Derivative - d/dx	f(x)=sin(4x)^3	$f (x) = \sin^{3} (4 x)$
12506	Find the Derivative - d/dx	y=cos((1-e^(5x))/(1+e^(5x)))	$y = \cos (\frac{1 - e^{5 x}}{1 + e^{5 x}})$
12507	Find the Derivative - d/dx	f(x)=8/( square root of x)	$f (x) = \frac{8}{\sqrt{x}}$
12508	Find the Derivative - d/dx	f(x)=8^x	$f (x) = 8^{x}$
12509	Evaluate the Limit	limit as x approaches 0 of ( square root of x+1- square root of 2x+1)/( square root of 3x+4- square root of 2x+4)	$lim_{x \to 0} \frac{\sqrt{x + 1} - \sqrt{2 x + 1}}{\sqrt{3 x + 4} - \sqrt{2 x + 4}}$
12510	Find the Derivative - d/dx	f(x)=800/(1+49e^(-0.17t))	$f (x) = \frac{800}{1 + 49 e^{- 0.17 t}}$
12511	Find the Derivative - d/dx	f(x)=(60x)/((0,1x^2+1))	$f (x) = \frac{60 x}{(0, 1 x^{2} + 1)}$
12512	Find the Derivative - d/dx	f(x)=(7x)/(4-tan(x))	$f (x) = \frac{7 x}{4 - \tan (x)}$
12513	Find the Derivative - d/dx	f(x)=(8(x-t))/(x^2)	$f (x) = \frac{8 (x - t)}{x^{2}}$
12514	Find the Derivative - d/dx	f(x)=(cos(8x)-1)/(sin(9x))	$f (x) = \frac{\cos (8 x) - 1}{\sin (9 x)}$
12515	Evaluate the Limit	limit as x approaches 8 of (x^2-6x-16)/(x-8)	$lim_{x \to 8} \frac{x^{2} - 6 x - 16}{x - 8}$
12516	Find the Derivative - d/dx	f(x)=cot( square root of x)^3	$f (x) = \cot^{3} (\sqrt{x})$
12517	Find the Derivative - d/dx	f(x)=e^(arcsec(x))	$f (x) = e^{arcsec (x)}$
12518	Find the Derivative - d/dx	f(x)=cos(4x)^3	$f (x) = \cos^{3} (4 x)$
12519	Find the Derivative - d/dx	f(x)=cos(x/(x+1))^3	$f (x) = \cos^{3} (\frac{x}{x + 1})$
12520	Find the Derivative - d/dx	f(x)=(cot(x))/(e^x)	$f (x) = \frac{\cot (x)}{e^{x}}$
12521	Evaluate the Limit	limit as x approaches 2 of (x^2-3x+2)/(x^2-4)	$lim_{x \to 2} \frac{x^{2} - 3 x + 2}{x^{2} - 4}$
12522	Find the Derivative - d/dx	f(x)=cot(sin(x))^2	$f (x) = \cot^{2} (\sin (x))$
12523	Find the Derivative - d/dx	f(x)=e^((4x+1)^2)	$f (x) = e^{{(4 x + 1)}^{2}}$
12524	Find the Derivative - d/dx	f(x)=(9+x)/(1-9x)	$f (x) = \frac{9 + x}{1 - 9 x}$
12525	Find the Derivative - d/dx	f(x)=cos(1-2x)^2	$f (x) = \cos^{2} (1 - 2 x)$
12526	Find the Derivative - d/dx	f(x)=e^x-x^3	$f (x) = e^{x} - x^{3}$
12527	Find the Derivative - d/dx	f(x)=e^(sin(2x))	$f (x) = e^{\sin (2 x)}$
12528	Find the Derivative - d/dx	f(x)=e^(kx)	$f (x) = e^{k x}$
12529	Find the Derivative - d/dx	f(x)=e^(-ax)	$f (x) = e^{- a x}$
12530	Find the Derivative - d/dx	f(x)=e^(tan(x))	$f (x) = e^{\tan (x)}$
12531	Find the Derivative - d/dx	f(x)=e^x square root of x	$f (x) = e^{x} \sqrt{x}$
12532	Find the Derivative - d/dx	f(x) = natural log of (ax+b)^3	$f (x) = \ln ({(a x + b)}^{3})$
12533	Find the Local Maxima and Minima	x^4-50x^2+625	$x^{4} - 50 x^{2} + 625$
12534	Evaluate from the Left	limit as x approaches 2 of f(x)	$lim_{x \to 2} f (x)$
12535	Find the Derivative - d/dx	f(x)=ee^x	$f (x) = e e^{x}$
12536	Find the Derivative - d/dx	f(x) = natural log of (x^4+1)^2	$f (x) = \ln ({(x^{4} + 1)}^{2})$
12537	Find the Derivative - d/dx	f(x)=e^(-13x)	$f (x) = e^{- 13 x}$
12538	Find the Derivative - d/dx	f(x)=e^(x^3+4x)	$f (x) = e^{x^{3} + 4 x}$
12539	Find the Derivative - d/dx	f(x)=e^(x^5-9)	$f (x) = e^{x^{5} - 9}$
12540	Find the Derivative - d/dx	f(x)=e^(1/2x)	$f (x) = e^{\frac{1}{2} x}$
12541	Find the Derivative - d/dx	f(x)=e^(1/(2x))	$f (x) = e^{\frac{1}{2 x}}$
12542	Find the Derivative - d/dx	f(x)=e^(1/(3x))	$f (x) = e^{\frac{1}{3 x}}$
12543	Find the Derivative - d/dx	f(x)=e^(-3/(t^6))	$f (x) = e^{- \frac{3}{t^{6}}}$
12544	Find Where Increasing/Decreasing Using Derivatives	x^2-x- natural log of x	$x^{2} - x - \ln (x)$
12545	Find the Derivative - d/dx	f(x)=e^(7xsin(2x))	$f (x) = e^{7 x \sin (2 x)}$
12546	Find the Derivative - d/dx	f(x)=e^7	$f (x) = e^{7}$
12547	Evaluate the Derivative at @EQ	y=3x-2 , y=x^2	$y = 3 x - 2$ , $y = x^{2}$
12548	Find the Derivative - d/dx	f(x)=e^(-15x)	$f (x) = e^{- 15 x}$
12549	Find the Derivative - d/dx	f(x)=e^(2x)sin(3x)	$f (x) = e^{2 x} \sin (3 x)$
12550	Find the Derivative - d/dx	f(x)=4/x+2^(x-6)-x+5^5	$f (x) = \frac{4}{x} + 2^{x - 6} - x + 5^{5}$
12551	Find the Derivative - d/dx	f(x)=(4sin(x))/(3+cos(x))	$f (x) = \frac{4 \sin (x)}{3 + \cos (x)}$
12552	Find the Derivative - d/dx	f(x)=4/( cube root of 3t^2+t)	$f (x) = \frac{4}{\sqrt[3]{3 t^{2} + t}}$
12553	Find the Derivative - d/dx	f(x)=4/(6x+7)	$f (x) = \frac{4}{6 x + 7}$
12554	Find the Derivative - d/dx	f(x)=(4x^2-2x^2)/(2x)	$f (x) = \frac{4 x^{2} - 2 x^{2}}{2 x}$
12555	Find the Derivative - d/dx	f(x)=4/(x^6)	$f (x) = \frac{4}{x^{6}}$
12556	Find the Derivative - d/dx	f(x)=(4x-3)/(6x-5)	$f (x) = \frac{4 x - 3}{6 x - 5}$
12557	Find the Derivative - d/dx	f(x)=(4x)/(x^2-36)	$f (x) = \frac{4 x}{x^{2} - 36}$
12558	Find the Derivative - d/dx	f(x)=(4x-8)/(5x^4)	$f (x) = \frac{4 x - 8}{5 x^{4}}$
12559	Find the Derivative - d/dx	f(x)=(6x)/( natural log of x)	$f (x) = \frac{6 x}{\ln (x)}$
12560	Find the Derivative - d/dx	f(x)=(5x-2)/(4x+3)	$f (x) = \frac{5 x - 2}{4 x + 3}$
12561	Find the Derivative - d/dx	f(x)=(5-cos(x))/(5+sin(x))	$f (x) = \frac{5 - \cos (x)}{5 + \sin (x)}$
12562	Find the Derivative - d/dx	f(x)=(550x^2)/( square root of x^2+12)	$f (x) = \frac{550 x^{2}}{\sqrt{x^{2} + 12}}$
12563	Find the Derivative - d/dx	f(x)=6/(x^4)	$f (x) = \frac{6}{x^{4}}$
12564	Evaluate the Integral	integral of (2x+1)/((3x-1)(2x+5)) with respect to x	$\int \frac{2 x + 1}{(3 x - 1) (2 x + 5)} d x$
12565	Find the Derivative - d/dx	f(x)=5/8	$f (x) = \frac{5}{8}$
12566	Find the Derivative - d/dx	f(x)=5/(1+2e^(0.5x))	$f (x) = \frac{5}{1 + 2 e^{0.5 x}}$
12567	Find the Derivative - d/dx	f(x)=(4x^2)/5	$f (x) = \frac{4 x^{2}}{5}$
12568	Evaluate the Integral	integral of (e^( square root of t))/( square root of t) with respect to t	$\int \frac{e^{\sqrt{t}}}{\sqrt{t}} d t$
12569	Find the Derivative - d/dx	f(x)=(4-xe^x)/(x+e^x)	$f (x) = \frac{4 - x e^{x}}{x + e^{x}}$
12570	Find the Derivative - d/dx	f(x)=(3x)/(x^2-1)	$f (x) = \frac{3 x}{x^{2} - 1}$
12571	Find the Derivative - d/dx	f(x)=(3x-2)/(2x-3)	$f (x) = \frac{3 x - 2}{2 x - 3}$
12572	Find the Derivative - d/dx	f(x)=(3x-4)/(x^3)	$f (x) = \frac{3 x - 4}{x^{3}}$
12573	Find the Derivative - d/dx	f(x)=3/(x-7)	$f (x) = \frac{3}{x - 7}$
12574	Find the Derivative - d/dx	f(x)=3^(5x)	$f (x) = 3^{5 x}$
12575	Find the Derivative - d/dx	f(x)=3^(cot(x))	$f (x) = 3^{\cot (x)}$
12576	Find the Derivative - d/dx	F(x)=3/4x^8	$F (x) = \frac{3}{4} x^{8}$
12577	Find the Derivative - d/dx	f(x)=3^( natural log of cos(x))	$f (x) = 3^{\ln (\cos (x))}$
12578	Find the Derivative - d/dx	f(x)=3^x-3	$f (x) = 3^{x} - 3$
12579	Find the Derivative - d/dx	f(x)=36/((3-x)^2)	$f (x) = \frac{36}{{(3 - x)}^{2}}$
12580	Find the Derivative - d/dx	f(x)=(-3x^5+40x^3+135x)/270	$f (x) = \frac{- 3 x^{5} + 40 x^{3} + 135 x}{270}$
12581	Find the Derivative - d/dx	f(x)=3/( cube root of x)	$f (x) = \frac{3}{\sqrt[3]{x}}$
12582	Find the Derivative - d/dx	f(x)=-3/(sin(7x)^2)	$f (x) = - \frac{3}{\sin^{2} (7 x)}$
12583	Find the Derivative - d/dx	f(x)=24/(x^2+12)	$f (x) = \frac{24}{x^{2} + 12}$
12584	Find the Derivative - d/dx	f(x)=(2 natural log of x)/x	$f (x) = \frac{2 \ln (x)}{x}$
12585	Find the Derivative - d/dx	f(x)=(24x+10)/(x^2+1)	$f (x) = \frac{24 x + 10}{x^{2} + 1}$
12586	Find the Derivative - d/dx	f(x)=(2tan(x))/x	$f (x) = \frac{2 \tan (x)}{x}$
12587	Find the Derivative - d/dx	f(x)=5x natural log of 3x-5x	$f (x) = 5 x \ln (3 x) - 5 x$
12588	Find the Derivative - d/dx	f(x)=6e^(x^2-3x+6)	$f (x) = 6 e^{x^{2} - 3 x + 6}$
12589	Find the Derivative - d/dx	f(x)=6e^(x^3)	$f (x) = 6 e^{x^{3}}$
12590	Find the Derivative - d/dx	f(x)=5xsin(x)cos(x)	$f (x) = 5 x \sin (x) \cos (x)$
12591	Find the Derivative - d/dx	f(x)=6 square root of 8x^2+5x	$f (x) = 6 \sqrt{8 x^{2} + 5 x}$
12592	Find the Derivative - d/dx	f(x)=5x cube root of x-8	$f (x) = 5 x \sqrt[3]{x - 8}$
12593	Find the Derivative - d/dx	f(x)=5sec(x)+tan(x)	$f (x) = 5 \sec (x) + \tan (x)$
12594	Find the Derivative - d/dx	f(x)=5x^6-8x^2	$f (x) = 5 x^{6} - 8 x^{2}$
12595	Find the Derivative - d/dx	f(x)=66x+ natural log of 3x^4+13	$f (x) = 66 x + \ln (3 x^{4} + 13)$
12596	Find the Derivative - d/dx	f(x)=6x^2-3x	$f (x) = 6 x^{2} - 3 x$
12597	Find the Derivative - d/dx	f(x)=6x^2-2x	$f (x) = 6 x^{2} - 2 x$
12598	Find the Derivative - d/dx	f(x)=6x^2-6x+2	$f (x) = 6 x^{2} - 6 x + 2$
12599	Find the Derivative - d/dx	f(x)=6x^3-4x^2+8x+5	$f (x) = 6 x^{3} - 4 x^{2} + 8 x + 5$
12600	Find the Derivative - d/dx	f(x)=6x^2 natural log of 7x^3+10x^2	$f (x) = 6 x^{2} \ln (7 x^{3} + 10 x^{2})$