Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70601	Find dx/dy	y=x^( natural log of x)	$y = x^{\ln (x)}$
70602	Evaluate the Limit	limit as x approaches 0 of (3^x-3^(-x))/(3^x+3^(-x))	$lim_{x \to 0} \frac{3^{x} - 3^{- x}}{3^{x} + 3^{- x}}$
70603	Integrate Using u-Substitution	integral of (3x^2-4x+2)^4(3x-2) with respect to x	$\int {(3 x^{2} - 4 x + 2)}^{4} (3 x - 2) d x$
70604	Evaluate the Integral	integral from 0 to 1 of 14 cube root of 1+7x with respect to x	$\int_{0}^{1} 14 \sqrt[3]{1 + 7 x} d x$
70605	Evaluate the Integral	integral of (-x^5+6e^(-2x)) with respect to x	$\int (- x^{5} + 6 e^{- 2 x}) d x$
70606	Find Where Increasing/Decreasing	f(x)=(x^4)/4-2x^3+4x^2	$f (x) = \frac{x^{4}}{4} - 2 x^{3} + 4 x^{2}$
70607	Evaluate the Integral	integral of (4csc(x)cot(x)+2sec(x)^2) with respect to x	$\int (4 \csc (x) \cot (x) + 2 \sec^{2} (x)) d x$
70608	Evaluate the Integral	integral from pi/4 to pi/3 of (-2sec(x)^2-5cos(x)) with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{3}} (- 2 \sec^{2} (x) - 5 \cos (x)) d x$
70609	Find dy/dx	y^3=x	$y^{3} = x$
70610	Integrate Using u-Substitution	integral of e^(3x) with respect to x	$\int e^{3 x} d x$
70611	Find the Derivative - d/dx	xe^(-x)-2e^(-x)	$x e^{- x} - 2 e^{- x}$
70612	Evaluate the Integral	integral of csc(-7x)*cot(-7x) with respect to x	$\int \csc (- 7 x) \cdot \cot (- 7 x) d x$
70613	Find dx/dy	y^3+y^2-5y-x^2=-4	$y^{3} + y^{2} - 5 y - x^{2} = - 4$
70614	Find the Center and Radius	(x-3/5)+(y-1/2)=4	$(x - \frac{3}{5}) + (y - \frac{1}{2}) = 4$
70615	Evaluate the Limit	limit as x approaches 9 from the left of ( square root of x-3)/(x-9)	$lim_{x \to 9^{-}} \frac{\sqrt{x} - 3}{x - 9}$
70616	Evaluate the Integral	integral of (1/4v^4+v^2+v) with respect to v	$\int (\frac{1}{4} v^{4} + v^{2} + v) d v$
70617	Find the Maximum/Minimum Value	(x^2)/(x-1)	$\frac{x^{2}}{x - 1}$
70618	Find the Maximum/Minimum Value	f(x)=2x^2-x^4	$f (x) = 2 x^{2} - x^{4}$
70619	Evaluate the Integral	integral of e^(-9x^2)x with respect to x	$\int e^{- 9 x^{2}} x d x$
70620	Find the Linearization at a=-3	f(x)=x^3-x^2+5 , a=-3	$f (x) = x^{3} - x^{2} + 5$ , $a = - 3$
70621	Find dz/dx	z=x^2+y^2	$z = x^{2} + y^{2}$
70622	Find Where Increasing/Decreasing	f(x)=1/(1+x^2)	$f (x) = \frac{1}{1 + x^{2}}$
70623	Find dy/dx	y=e^(e^x)	$y = e^{e^{x}}$
70624	Find the Derivative - d/dx	y=(2x+5) square root of 4x-1	$y = (2 x + 5) \sqrt{4 x - 1}$
70625	Find the Linearization at a=-2	f(x)=x^3-x^2+5 , a=-2	$f (x) = x^{3} - x^{2} + 5$ , $a = - 2$
70626	Evaluate the Limit	limit as x approaches 3 of (x^2-x-6)/(4- square root of 5x+1)	$lim_{x \to 3} \frac{x^{2} - x - 6}{4 - \sqrt{5 x + 1}}$
70627	Find the Derivative - d/dx	y=(2x-3)(x+5)	$y = (2 x - 3) (x + 5)$
70628	Find the Derivative - d/dx	square root of 1-4x^2	$\sqrt{1 - 4 x^{2}}$
70629	Find the Derivative - d/dθ	y=pi/3sin(theta)	$y = \frac{π}{3} \sin (θ)$
70630	Find dy/dx	x^2-4xy+2y^2=-4x	$x^{2} - 4 x y + 2 y^{2} = - 4 x$
70631	Evaluate the Integral	integral of 3/(x^2+3x) with respect to x	$\int \frac{3}{x^{2} + 3 x} d x$
70632	Find the Area Under the Curve	A=40 degrees , b=11cm , c=8cm	$A = 40 °$ , $b = 11 cm$ , $c = 8 cm$
70633	Evaluate the Limit	limit as x approaches infinity of (x^2)/(1-x^2)	$lim_{x \to \infty} \frac{x^{2}}{1 - x^{2}}$
70634	Evaluate the Limit	limit as x approaches 1/2 of -5e^(-x^4-1/4)	$lim_{x \to \frac{1}{2}} - 5 e^{- x^{4} - \frac{1}{4}}$
70635	Determine if Continuous	f(x)=(4x^2+2x-6)/2	$f (x) = \frac{4 x^{2} + 2 x - 6}{2}$
70636	Find the Maximum/Minimum Value	f(x)=x^3-5x	$f (x) = x^{3} - 5 x$
70637	Find the Derivative - d/dx	-4/(x^3)+1/x	$\frac{- 4}{x^{3}} + \frac{1}{x}$
70638	Evaluate the Integral	integral from 0 to 2 of g(x) with respect to x	$\int_{0}^{2} g (x) d x$
70639	Find dy/dx	x^2+5x+9xy-y^2=4	$x^{2} + 5 x + 9 x y - y^{2} = 4$
70640	Find the Derivative - d/dx	log of square root of x	$\log (\sqrt{x})$
70641	Find the Derivative - d/dx	natural log of xdx	$\ln (x d x)$
70642	Evaluate the Integral	integral of (2-1/(p^2))^2 with respect to p	$\int {(2 - \frac{1}{p^{2}})}^{2} d p$
70643	Evaluate the Integral	integral of (x^2-2x+4) with respect to x	$\int (x^{2} - 2 x + 4) d x$
70644	Find the Domain and Range	f(x)=-x if x<0; x if x>=0	$f (x) = {\begin{cases} - x & x < 0 \\ x & x \geq 0 \end{cases}$
70645	Evaluate the Limit	limit as x approaches negative infinity of (-6x^3+7x+7)/(8x^3-8x+5)	$lim_{x \to - \infty} \frac{- 6 x^{3} + 7 x + 7}{8 x^{3} - 8 x + 5}$
70646	Find the Derivative - d/dx	1/2sin(2x)	$\frac{1}{2} \sin (2 x)$
70647	Find Where Increasing/Decreasing	f(x)=4	$f (x) = 4$
70648	Find dy/dx	y=2 square root of x-1/(2 square root of x)	$y = 2 \sqrt{x} - \frac{1}{2 \sqrt{x}}$
70649	Find the Tangent Line at (-1,-2)	f(x)=2x^3 at (-1,-2)	$f (x) = 2 x^{3}$ at $(- 1, - 2)$
70650	Find the Derivative - d/dx	( square root of x+1/( square root of x))^2	${(\sqrt{x} + \frac{1}{\sqrt{x}})}^{2}$
70651	Find Where Increasing/Decreasing	f(x)=(x^4)/4-3x^3+9x^2	$f (x) = \frac{x^{4}}{4} - 3 x^{3} + 9 x^{2}$
70652	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (1+x)^(1/x)	$lim_{x \to 0^{+}} {(1 + x)}^{\frac{1}{x}}$
70653	Find the Derivative - d/dk	kys	$k y s$
70654	Evaluate the Integral	integral of (sin(x)+cos(x)) with respect to x	$\int (\sin (x) + \cos (x)) d x$
70655	Find the Derivative - d/dx	d/(dx)(6 natural log of x)	$\frac{d}{d x} (6 \ln (x))$
70656	Integrate Using u-Substitution	integral of (cos(x))/(sin(x)^2) with respect to x	$\int \frac{\cos (x)}{\sin^{2} (x)} d x$
70657	Find the Tangent Line at (0,4)	y=4e^x+x , (0,4)	$y = 4 e^{x} + x$ , $(0, 4)$
70658	Evaluate the Limit	limit as x approaches infinity of x^x	$lim_{x \to \infty} x^{x}$
70659	Integrate Using Trig Substitution	integral of square root of x^2+4 with respect to x	$\int \sqrt{x^{2} + 4} d x$
70660	Find the Derivative - d/dx	y=x*e^x	$y = x \cdot e^{x}$
70661	Find the Derivative - d/dy	(2x)/(x^2+y^2)	$\frac{2 x}{x^{2} + y^{2}}$
70662	Find the Derivative - d/dx	y=x^(cot(x))	$y = x^{\cot (x)}$
70663	Evaluate the Integral	integral of (2x)/4 with respect to x	$\int \frac{2 x}{4} d x$
70664	Find the Derivative - d/db	y=bcos(t)+t^2sin(t)	$y = b \cos (t) + t^{2} \sin (t)$
70665	Use Logarithmic Differentiation to Find the Derivative	y = natural log of e^x+xe^x	$y = \ln (e^{x} + x e^{x})$
70666	Evaluate the Integral	integral of x/x with respect to x	$\int \frac{x}{x} d x$
70667	Find the Integral	x square root of 2x-1dx	$x \sqrt{2 x - 1} d x$
70668	Find the Derivative - d/dk	y=k square root of x+x square root of k	$y = k \sqrt{x} + x \sqrt{k}$
70669	Find dy/dx	4y^2+xy-2x^2=3	$4 y^{2} + x y - 2 x^{2} = 3$
70670	Find dy/dx	x^2y+2y^3=3x+2y	$x^{2} y + 2 y^{3} = 3 x + 2 y$
70671	Find the Derivative - d/dx	e^xsin(x)+cos(x)	$e^{x} \sin (x) + \cos (x)$
70672	Integrate By Parts	integral of natural log of 2x+1 with respect to x	$\int \ln (2 x + 1) d x$
70673	Find the Derivative - d/dx	y=(x^2+b^2)/(x^2-b^2)	$y = \frac{x^{2} + b^{2}}{x^{2} - b^{2}}$
70674	Solve the Differential Equation	(dy)/(dx)=1/(xy^3)	$\frac{d y}{d x} = \frac{1}{x y^{3}}$
70675	Find the Derivative - d/dθ	tan(ntheta)^2	$\tan^{2} (n θ)$
70676	Evaluate the Integral	integral from -pi/4 to 7pi/4 of (sin(x)+cos(x)) with respect to x	$\int_{- \frac{π}{4}}^{7 \frac{π}{4}} (\sin (x) + \cos (x)) d x$
70677	Find the Second Derivative	(sec(x))	$(\sec (x))$
70678	Evaluate the Integral	integral from e to infinity of 1/(x( natural log of x)^2) with respect to x	$\int_{e}^{\infty} \frac{1}{x \ln^{2} (x)} d x$
70679	Evaluate the Integral	integral of (3/( fifth root of x^2)-2/( fifth root of x)) with respect to x	$\int (\frac{3}{\sqrt[5]{x^{2}}} - \frac{2}{\sqrt[5]{x}}) d x$
70680	Integrate Using u-Substitution	integral of xe^(2x) with respect to x	$\int x e^{2 x} d x$
70681	Evaluate the Integral	integral from a to b of sec(x)^2 with respect to x	$\int_{a}^{b} \sec^{2} (x) d x$
70682	Find dy/dx	y = natural log of x^2+1	$y = \ln (x^{2} + 1)$
70683	Integrate Using u-Substitution	integral of cos(x)^2 with respect to x	$\int \cos^{2} (x) d x$
70684	Find the Derivative - d/dx	(2-1/x)/(x-3)	$\frac{2 - \frac{1}{x}}{x - 3}$
70685	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^(sin(x))	$lim_{x \to 0^{+}} x^{\sin (x)}$
70686	Find the Derivative - d/dx	f(6)	$f (6)$
70687	Evaluate the Integral	integral of (5t^2+7)/(t^(4/3)) with respect to t	$\int \frac{5 t^{2} + 7}{t^{\frac{4}{3}}} d t$
70688	Find the Derivative - d/dx	y=(x^5)/10+1/(6x^3)	$y = \frac{x^{5}}{10} + \frac{1}{6 x^{3}}$
70689	Use Logarithmic Differentiation to Find the Derivative	y=x^2cos(x)	$y = x^{2} \cos (x)$
70690	Evaluate the Integral	integral from negative infinity to 0 of thetae^theta with respect to theta	$\int_{- \infty}^{0} θ e^{θ} d θ$
70691	Evaluate the Limit	limit as x approaches infinity of (5x^3+27)/(20x^2+10x+9)	$lim_{x \to \infty} \frac{5 x^{3} + 27}{20 x^{2} + 10 x + 9}$
70692	Evaluate the Integral	integral from 2 to square root of 5 of x^3(x^2-4)^3 with respect to x	$\int_{2}^{\sqrt{5}} x^{3} {(x^{2} - 4)}^{3} d x$
70693	Find the Derivative - d/dx	2xsin(x)+x^2cos(x)	$2 x \sin (x) + x^{2} \cos (x)$
70694	Find the Second Derivative	f(x)=(x^4)/4-(x^3)/3+(x^2)/2+x-1	$f (x) = \frac{x^{4}}{4} - \frac{x^{3}}{3} + \frac{x^{2}}{2} + x - 1$
70695	Evaluate the Limit	limit as x approaches 2 from the right of square root of x-2	$lim_{x \to 2^{+}} \sqrt{x - 2}$
70696	Evaluate the Integral	integral of 4x^3(4x^4+5) with respect to x	$\int 4 x^{3} (4 x^{4} + 5) d x$
70697	Evaluate the Limit	limit as x approaches 2 from the right of ( square root of x^2-4)/(x-2)	$lim_{x \to 2^{+}} \frac{\sqrt{x^{2} - 4}}{x - 2}$
70698	Find the Derivative - d/da	ae^x	$a e^{x}$
70699	Find dx/dy	x^4(x+y)=y^2(3x-y)	$x^{4} (x + y) = y^{2} (3 x - y)$
70700	Find the Slope	f(x)=3/4x-5	$f (x) = \frac{3}{4} x - 5$