Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
7601	Evaluate the Integral	integral of 7/x with respect to x	$\int \frac{7}{x} d x$
7602	Evaluate the Integral	integral of x^12e^(x^13) with respect to x	$\int x^{12} e^{x^{13}} d x$
7603	Find the Derivative - d/dx	f(x)=3x^2(x^3+1)^7	$f (x) = 3 x^{2} {(x^{3} + 1)}^{7}$
7604	Find the Derivative - d/dx	f(x)=3x^2-5x	$f (x) = 3 x^{2} - 5 x$
7605	Find the Derivative - d/dx	f(x)=3x^2y	$f (x) = 3 x^{2} y$
7606	Find the Derivative - d/dx	f(x)=2x-3x^(2/3)	$f (x) = 2 x - 3 x^{\frac{2}{3}}$
7607	Find the Derivative - d/dx	f(x)=2sec(x)	$f (x) = 2 \sec (x)$
7608	Find the Derivative - d/dx	y=pi^2	$y = π^{2}$
7609	Find the Derivative - d/dx	f(x)=3 natural log of x	$f (x) = 3 \ln (x)$
7610	Find the Derivative - d/dx	f(x)=3sin(x^4)e	$f (x) = 3 \sin (x^{4}) e$
7611	Find the Derivative - d/dx	f(x)=3x^5 natural log of x	$f (x) = 3 x^{5} \ln (x)$
7612	Find the Derivative - d/d@VAR	f(x)=4e^x	$f (x) = 4 e^{x}$
7613	Find the Derivative - d/dx	f(x)=4x(5x+3)^4	$f (x) = 4 x {(5 x + 3)}^{4}$
7614	Find the Derivative - d/dx	f(x)=4x-x^2	$f (x) = 4 x - x^{2}$
7615	Find the Derivative - d/dx	f(x)=4tan(x)	$f (x) = 4 \tan (x)$
7616	Find the Derivative - d/dx	f(x)=5e^(-3x)	$f (x) = 5 e^{- 3 x}$
7617	Find the Derivative - d/dx	f(x)=5e^x-3x^2	$f (x) = 5 e^{x} - 3 x^{2}$
7618	Find the Inflection Points	f(x)=4x^3-48x	$f (x) = 4 x^{3} - 48 x$
7619	Find the Derivative - d/dx	f(x)=6x-x^2	$f (x) = 6 x - x^{2}$
7620	Find the Derivative - d/dx	f(x)=-7(3x^4+2)^-4	$f (x) = - 7 {(3 x^{4} + 2)}^{- 4}$
7621	Find the Derivative - d/dx	f(x)=6 natural log of x	$f (x) = 6 \ln (x)$
7622	Find the Derivative - d/dx	f(x)=5x^2-x+30	$f (x) = 5 x^{2} - x + 30$
7623	Find the Derivative - d/dx	f(x)=2^70	$f (x) = 2^{70}$
7624	Find the Derivative - d/dx	f(x)=(5x+3)/(5x-3)	$f (x) = \frac{5 x + 3}{5 x - 3}$
7625	Find the Derivative - d/dx	f(x)=(4-3x-x^2)/(x^2-1)	$f (x) = \frac{4 - 3 x - x^{2}}{x^{2} - 1}$
7626	Find the Derivative - d/dx	f(x)=4/3*(px^3)	$f (x) = \frac{4}{3} \cdot (p x^{3})$
7627	Find the Derivative - d/dx	y=(x^3-8)^(2/3)	$y = {(x^{3} - 8)}^{\frac{2}{3}}$
7628	Find the Derivative - d/dx	f(x)=e^(6x)	$f (x) = e^{6 x}$
7629	Find the Derivative - d/dx	f(x)=e^(7x)	$f (x) = e^{7 x}$
7630	Find the Derivative - d/dx	f(x)=e^(9x)	$f (x) = e^{9 x}$
7631	Find dy/dx	y^8=x^9	$y^{8} = x^{9}$
7632	Find the Derivative - d/dx	f(x)=e^(x^2-1)	$f (x) = e^{x^{2} - 1}$
7633	Find dy/dx	2xy-y^2=3	$2 x y - y^{2} = 3$
7634	Simplify	(x-4)( square root of x+2)	$(x - 4) (\sqrt{x} + 2)$
7635	Find the Derivative - d/dx	f(x)=(7x)/(2^x)	$f (x) = \frac{7 x}{2^{x}}$
7636	Find the Derivative - d/dx	f(x)=(7x)/(x^2-49)	$f (x) = \frac{7 x}{x^{2} - 49}$
7637	Solve for ?	2sin(theta)-1=0	$2 \sin (θ) - 1 = 0$
7638	Find the Derivative - d/dx	f(x) = log base 3 of x	$f (x) = \log_{3} (x)$
7639	Evaluate the Integral	integral of (sin( natural log of x))/x with respect to x	$\int \frac{\sin (\ln (x))}{x} d x$
7640	Evaluate the Integral	integral of sin(x)^3cos(x)^2 with respect to x	$\int \sin^{3} (x) \cos^{2} (x) d x$
7641	Evaluate	-2sin(pi/6)-4cos(pi/6)	$- 2 \sin (\frac{π}{6}) - 4 \cos (\frac{π}{6})$
7642	Find the Derivative - d/d@VAR	f(x)=8^(-x)	$f (x) = 8^{- x}$
7643	Find the Derivative - d/dx	f(x) = square root of 12x	$f (x) = \sqrt{12 x}$
7644	Find the Derivative - d/dx	f(x) = square root of sin(4x)	$f (x) = \sqrt{\sin (4 x)}$
7645	Find the Derivative - d/dx	f(x)=x/(1+ natural log of x)	$f (x) = \frac{x}{1 + \ln (x)}$
7646	Evaluate the Limit	limit as x approaches 3 of (x^3-13x+12)/(x^3-14x+15)	$lim_{x \to 3} \frac{x^{3} - 13 x + 12}{x^{3} - 14 x + 15}$
7647	Evaluate the Limit	limit as h approaches 0 of ((7+h)^3-343)/h	$lim_{h \to 0} \frac{{(7 + h)}^{3} - 343}{h}$
7648	Find the Derivative - d/dx	f(x) = square root of x+ square root of x	$f (x) = \sqrt{x + \sqrt{x}}$
7649	Find the Derivative - d/dx	y=3e^x+4/( cube root of x)	$y = 3 e^{x} + \frac{4}{\sqrt[3]{x}}$
7650	Find the Derivative - d/dx	f(x)=x^(3/5)(4-x)	$f (x) = x^{\frac{3}{5}} (4 - x)$
7651	Evaluate the Summation	sum from i=0 to 4 of 5^i(1/3)^i	$\sum_{i = 0}^{4} {(5)}^{i} {(\frac{1}{3})}^{i}$
7652	Find the Derivative - d/dx	f(x)=x^(2/3)(20-x)	$f (x) = x^{\frac{2}{3}} (20 - x)$
7653	Evaluate the Summation	sum from n=1 to 15 of n-4	$\sum_{n = 1}^{15} n - 4$
7654	Evaluate the Limit	limit as x approaches infinity of (3-2x)/(x^2+2x+1)	$lim_{x \to \infty} \frac{3 - 2 x}{x^{2} + 2 x + 1}$
7655	Find the Derivative - d/dx	f(x)=x^(5/2)e^x	$f (x) = x^{\frac{5}{2}} e^{x}$
7656	Evaluate the Integral	integral of arcsin(x) with respect to x	$\int \arcsin (x) d x$
7657	Find the Derivative - d/dx	f(x)=x^2-3x+2	$f (x) = x^{2} - 3 x + 2$
7658	Evaluate the Function	f(x) = square root of x^2+11 , x=5	$f (x) = \sqrt{x^{2} + 11}$ , $x = 5$
7659	Evaluate the Function	f(6) = square root of 64-x^2	$f (6) = \sqrt{64 - x^{2}}$
7660	Convert to Interval Notation	tan(x)=1	$\tan (x) = 1$
7661	Evaluate the Function	f(0.5)=(2x+4)/( square root of x)	$f (0.5) = \frac{2 x + 4}{\sqrt{x}}$
7662	Evaluate the Function	s(t)=2t^2+6t , t=2	$s (t) = 2 t^{2} + 6 t$ , $t = 2$
7663	Evaluate the Function	f(x)=5+4x+16/x , x>0	$f (x) = 5 + 4 x + \frac{16}{x}$ , $x > 0$
7664	Evaluate the Integral	integral of fourth root of x with respect to x	$\int \sqrt[4]{x} d x$
7665	Find the Inverse	f(x)=( square root of x)/2+2x^3+2	$f (x) = \frac{\sqrt{x}}{2} + 2 x^{3} + 2$
7666	Find the Inverse	f(x)=x/(x-1)	$f (x) = \frac{x}{x - 1}$
7667	Find the Inverse	f(x) = square root of 1-9x	$f (x) = \sqrt{1 - 9 x}$
7668	Find the Domain	f(x)=e^(2x)	$f (x) = e^{2 x}$
7669	Find the Domain	f(x) = square root of 49-x^2	$f (x) = \sqrt{49 - x^{2}}$
7670	Find the Domain	( square root of 3-x)/( square root of x^2-1)	$\frac{\sqrt{3 - x}}{\sqrt{x^{2} - 1}}$
7671	Evaluate the Integral	integral of xcos(x^2) with respect to x	$\int x \cos (x^{2}) d x$
7672	Find the Derivative - d/d@VAR	f(x)=4x^2-3x+3	$f (x) = 4 x^{2} - 3 x + 3$
7673	Find the Derivative - d/d@VAR	f(x)=xtan(x)	$f (x) = x \tan (x)$
7674	Find the Derivative - d/d@VAR	f(u)=14/( square root of u)	$f (u) = \frac{14}{\sqrt{u}}$
7675	Find the Derivative - d/d@VAR	f(t)=e^(4tsin(2t))	$f (t) = e^{4 t \sin (2 t)}$
7676	Find the Derivative - d/d@VAR	y(x)=cos( square root of sin(cot(pix)))	$y (x) = \cos (\sqrt{\sin (\cot (π x))})$
7677	Find the Derivative - d/d@VAR	f(x)=x^3+5x	$f (x) = x^{3} + 5 x$
7678	Find the Derivative - d/d@VAR	f(x)=(sin(x)+cos(x))sec(x)	$f (x) = (\sin (x) + \cos (x)) \sec (x)$
7679	Find the Derivative - d/d@VAR	f(x)=(x-1)e^(3x+2)	$f (x) = (x - 1) e^{3 x + 2}$
7680	Find the Derivative - d/d@VAR	f(x)=(3x^2-4)^5	$f (x) = {(3 x^{2} - 4)}^{5}$
7681	Find the Derivative - d/d@VAR	f(x)=(4-3x)^2	$f (x) = {(4 - 3 x)}^{2}$
7682	Find the Domain	f(x)=4-x	$f (x) = 4 - x$
7683	Find the Domain and Range	f(x)=(x^3)/(x^2-1)	$f (x) = \frac{x^{3}}{x^{2} - 1}$
7684	Find the Domain and Range	f(x)=(x^2-3)/(x-2)	$f (x) = \frac{x^{2} - 3}{x - 2}$
7685	Find the Derivative - d/d@VAR	f(x)=\|x-1\|	$f (x) = \| x - 1 \|$
7686	Find the Derivative - d/d@VAR	f(x)=(x^2)/(x^2-9)	$f (x) = \frac{x^{2}}{x^{2} - 9}$
7687	Find the Derivative - d/d@VAR	f(x)=(e^(3x))/(x^12)	$f (x) = \frac{e^{3 x}}{x^{12}}$
7688	Find the Derivative - d/d@VAR	f(x)=(4x-9)^3	$f (x) = {(4 x - 9)}^{3}$
7689	Find the Derivative - d/d@VAR	f(x)=(7x+1)^2	$f (x) = {(7 x + 1)}^{2}$
7690	Find the Derivative - d/d@VAR	f(x)=5/( square root of x)	$f (x) = \frac{5}{\sqrt{x}}$
7691	Find the Derivative - d/d@VAR	f(x)=5/4x^(4/5)	$f (x) = \frac{5}{4} x^{\frac{4}{5}}$
7692	Find the Derivative - d/d@VAR	f(x)=-5/x	$f (x) = - \frac{5}{x}$
7693	Find the Derivative - d/d@VAR	f(x)=1/(cos(x))	$f (x) = \frac{1}{\cos (x)}$
7694	Find the Derivative - d/d@VAR	f(x)=(1+x^2)/(1-x^2)	$f (x) = \frac{1 + x^{2}}{1 - x^{2}}$
7695	Find the Derivative - d/d@VAR	f(x)=1/2*tan(x^4)	$f (x) = \frac{1}{2} \cdot \tan (x^{4})$
7696	Find the Derivative - d/d@VAR	f(x)=2^40	$f (x) = 2^{40}$
7697	Find the Derivative - d/d@VAR	f(x)=2/(x^3)	$f (x) = \frac{2}{x^{3}}$
7698	Find the Derivative - d/d@VAR	f(x) = square root of x-6 cube root of x	$f (x) = \sqrt{x} - 6 \sqrt[3]{x}$
7699	Find the Derivative - d/d@VAR	f(x) = square root of 9-x	$f (x) = \sqrt{9 - x}$
7700	Find the Derivative - d/d@VAR	f(x) = square root of cos(x)	$f (x) = \sqrt{\cos (x)}$