Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84901	Find the Relative Extrema	f(x)=6x-x^2	$f (x) = 6 x - x^{2}$
84902	Find the Antiderivative	4 square root of x+5+3/(x^2)	$4 \sqrt{x} + 5 + \frac{3}{x^{2}}$
84903	Integrate Using u-Substitution	integral of sec(x)^2tan(x)^2 with respect to x	$\int \sec^{2} (x) \tan^{2} (x) d x$
84904	Find the Derivative - d/dx	y = square root of 2px	$y = \sqrt{2 p x}$
84905	Find the Second Derivative	(2x)/( square root of 3x-1)	$\frac{2 x}{\sqrt{3 x - 1}}$
84906	Evaluate the Integral	-1/3 integral from 5 to 2 of (x^3-2) with respect to x	$- \frac{1}{3} \int_{5}^{2} (x^{3} - 2) d x$
84907	Evaluate the Integral	integral of 4x^2(3x+1)^2 with respect to x	$\int 4 x^{2} {(3 x + 1)}^{2} d x$
84908	Evaluate the Derivative at (1/2,16)	f(t)=t^-4 ;, (1/2,16)	$f (t) = t^{- 4}$ ;, $(\frac{1}{2}, 16)$
84909	Evaluate the Integral	integral of (3x^5+2)/(4x^2) with respect to x	$\int \frac{3 x^{5} + 2}{4 x^{2}} d x$
84910	Find the Maximum/Minimum Value	y=x^4-4x^3+2	$y = x^{4} - 4 x^{3} + 2$
84911	Find the Antiderivative	1/(x square root of natural log of x+1)	$\frac{1}{x \sqrt{\ln (x) + 1}}$
84912	Find the Maximum/Minimum Value	f(x)=cos(3x)	$f (x) = \cos (3 x)$
84913	Find the Derivative - d/dx	x-xsin(x)	$x - x \sin (x)$
84914	Find dy/dx	y=-(-2x^2+5x+3)^4	$y = - {(- 2 x^{2} + 5 x + 3)}^{4}$
84915	Find the Derivative - d/dx	y=(e^x)/(1+e^x)	$y = \frac{e^{x}}{1 + e^{x}}$
84916	Find the Maximum/Minimum Value	y=x^2e^(-x)	$y = x^{2} e^{- x}$
84917	Evaluate the Integral	integral of (x) with respect to x	$\int (x) d x$
84918	Evaluate the Limit	limit as x approaches 2 of 1=(x^2-4)/(x-2)	$lim_{x \to 2} 1 = \frac{x^{2} - 4}{x - 2}$
84919	Evaluate the Integral	integral from 0 to 1 of (1-8x^3+16x^7) with respect to x	$\int_{0}^{1} (1 - 8 x^{3} + 16 x^{7}) d x$
84920	Evaluate the Limit	limit as x approaches 0 of ((4x+1)^9-1)/(3x)	$lim_{x \to 0} \frac{{(4 x + 1)}^{9} - 1}{3 x}$
84921	Find dy/dx	y=1/(2^(4x))	$y = \frac{1}{2^{4 x}}$
84922	Find the Derivative - d/dx	log of 1+x^2	$\log (1 + x^{2})$
84923	Find the Derivative - d/dx	cube root of 1+3x	$\sqrt[3]{1 + 3 x}$
84924	Evaluate the Limit	limit as x approaches negative infinity of (x^2-5x+4)/(2x^2-8x)	$lim_{x \to - \infty} \frac{x^{2} - 5 x + 4}{2 x^{2} - 8 x}$
84925	Find dy/dx	x^2+5y^3=x+9	$x^{2} + 5 y^{3} = x + 9$
84926	Find dy/dx	y = natural log of \|sin(x)\|	$y = \ln (\| \sin (x) \|)$
84927	Evaluate the Limit	limit as y approaches -2 of (4-3y^2-y^3)/(6-y-y^2)	$lim_{y \to - 2} \frac{4 - 3 y^{2} - y^{3}}{6 - y - y^{2}}$
84928	Find the Percentage Rate of Change	f(t)=16(1.4)^t	$f (t) = 16 {(1.4)}^{t}$
84929	Evaluate the Integral	integral of (7x)/((2x-3)(x+2)) with respect to x	$\int \frac{7 x}{(2 x - 3) (x + 2)} d x$
84930	Evaluate the Integral	integral from 1 to e of (-2 natural log of x)/(x^2) with respect to x	$\int_{1}^{e} \frac{- 2 \ln (x)}{x^{2}} d x$
84931	Evaluate the Integral	integral from 2 to infinity of 1/(x^2) with respect to x	$\int_{2}^{\infty} \frac{1}{x^{2}} d x$
84932	Find the Derivative - d/dx	d/(dx)(f(x)+g(x))	$\frac{d}{d x} (f (x) + g (x))$
84933	Evaluate the Integral	integral of (x^5-4x^-4+6x^3+2x) with respect to x	$\int (x^{5} - 4 x^{- 4} + 6 x^{3} + 2 x) d x$
84934	Integrate Using u-Substitution	integral of e^(cos(x))sin(x) with respect to x	$\int e^{\cos (x)} \sin (x) d x$
84935	Find the Tangent Line at (3,1)	y=3/x at (3,1)	$y = \frac{3}{x}$ at $(3, 1)$
84936	Find the Antiderivative	((1-x)/x)^2	${(\frac{1 - x}{x})}^{2}$
84937	Find the Antiderivative	x+y	$x + y$
84938	Evaluate the Limit	limit as x approaches infinity of 2x( square root of 9+10/x-3)	$lim_{x \to \infty} 2 x (\sqrt{9 + \frac{10}{x}} - 3)$
84939	Find the Slope	1/6x+3/2	$\frac{1}{6} x + \frac{3}{2}$
84940	Find the Slope	f(x)=2(x+3)	$f (x) = 2 (x + 3)$
84941	Evaluate the Integral	integral of 8cos(theta)cos(sin(theta))^5 with respect to theta	$\int 8 \cos (θ) \cos^{5} (\sin (θ)) d θ$
84942	Find dy/dx	y = natural log of x+ square root of 1+x^2	$y = \ln (x + \sqrt{1 + x^{2}})$
84943	Solve the Differential Equation	y'=x+y	$y' = x + y$
84944	Find the Slope	2x-5	$2 x - 5$
84945	Evaluate the Integral	integral of -e^(-2csc(2x))cot(2x)csc(2x) with respect to x	$\int - e^{- 2 \csc (2 x)} \cot (2 x) \csc (2 x) d x$
84946	Find the Derivative - d/dx	tan(x-3)	$\tan (x - 3)$
84947	Find the Maximum/Minimum Value	y=-2cos(-x/2)	$y = - 2 \cos (- \frac{x}{2})$
84948	Find the Integral	(x^3)/((x+1)^2)	$\frac{x^{3}}{{(x + 1)}^{2}}$
84949	Evaluate the Limit	limit as x approaches infinity of (x-2)/( square root of 2x^2-x+1)	$lim_{x \to \infty} \frac{x - 2}{\sqrt{2 x^{2} - x + 1}}$
84950	Find the Second Derivative	2x^10-x^6+5x^2	$2 x^{10} - x^{6} + 5 x^{2}$
84951	Evaluate the Integral	integral of ((5+r)/r)^2 with respect to r	$\int {(\frac{5 + r}{r})}^{2} d r$
84952	Find dy/dx	y=10^(x^2-1)	$y = 10^{x^{2} - 1}$
84953	Evaluate the Limit	limit as x approaches negative infinity of (5x-9)/(4x^3+2x+7)	$lim_{x \to - \infty} \frac{5 x - 9}{4 x^{3} + 2 x + 7}$
84954	Find the Derivative - d/dx	e^x(1+x)	$e^{x} (1 + x)$
84955	Find the Third Derivative	y=-1/2+1/3x^3+3/20x^6+1/24x^-4	$y = - \frac{1}{2} + \frac{1}{3} x^{3} + \frac{3}{20} x^{6} + \frac{1}{24} x^{- 4}$
84956	Use Logarithmic Differentiation to Find the Derivative	y=(x^3+1)^(xe^x)	$y = {(x^{3} + 1)}^{x e^{x}}$
84957	Evaluate the Limit	limit as x approaches infinity of (9x^2-2)/(6-29x)	$lim_{x \to \infty} \frac{9 x^{2} - 2}{6 - 29 x}$
84958	Find the Antiderivative	(x^2)/(2x+2)	$\frac{x^{2}}{2 x + 2}$
84959	Find the Second Derivative	2x^(1/5)+3	$2 x^{\frac{1}{5}} + 3$
84960	Find the Third Derivative	y=5/8x+2/9-1/6x^-3	$y = \frac{5}{8} x + \frac{2}{9} - \frac{1}{6} x^{- 3}$
84961	Evaluate the Limit	limit as x approaches 1 of (x^(1/26)-x^(1/2))/(x^(1/23)-x^(1/2))	$lim_{x \to 1} \frac{x^{\frac{1}{2} \cdot 6} - x^{\frac{1}{2}}}{x^{\frac{1}{2} \cdot 3} - x^{\frac{1}{2}}}$
84962	Find the Maximum/Minimum Value	y=1/(x^2)	$y = \frac{1}{x^{2}}$
84963	Find the Derivative - d/dx	y=(2x+3)^3 square root of 4x^3-1	$y = {(2 x + 3)}^{3} \sqrt{4 x^{3} - 1}$
84964	Find the Tangent Line at (1,-2)	f(x)=-2x^3 at (1,-2)	$f (x) = - 2 x^{3}$ at $(1, - 2)$
84965	Find the Antiderivative	1/x-x^2	$\frac{1}{x} - x^{2}$
84966	Find dx/dy	(1-x)y^1=y^2	$(1 - x) y^{1} = y^{2}$
84967	Find the Concavity	f(x)=x^(4/3)+4x^(1/3)	$f (x) = x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}$
84968	Evaluate the Integral	integral of (1/x)^2 with respect to x	$\int {(\frac{1}{x})}^{2} d x$
84969	Find the Derivative - d/dx	(1+ natural log of x)/(x^2)	$\frac{1 + \ln (x)}{x^{2}}$
84970	Find the Inflection Points	1/10x^5-x^4	$\frac{1}{10} x^{5} - x^{4}$
84971	Find the Center and Radius	x^2+y^2+x-4y=60	$x^{2} + y^{2} + x - 4 y = 60$
84972	Find dx/dy	3x^2+2xy+y^2=2	$3 x^{2} + 2 x y + y^{2} = 2$
84973	Find dy/dx	sin(4x+5y^2)=5x	$\sin (4 x + 5 y^{2}) = 5 x$
84974	Find the Antiderivative	(9x^2)/( square root of 1-x^3)	$\frac{9 x^{2}}{\sqrt{1 - x^{3}}}$
84975	Evaluate the Limit	limit as x approaches 1/3 of (-9x^2)/(2-3x)	$lim_{x \to \frac{1}{3}} \frac{- 9 x^{2}}{2 - 3 x}$
84976	Find dy/dx	square root of x+3y=5x	$\sqrt{x + 3 y} = 5 x$
84977	Evaluate the Integral	integral from 0 to a of x^2 with respect to x	$\int_{0}^{a} x^{2} d x$
84978	Evaluate the Integral	integral from 2 to 3 of (3-x) with respect to x	$\int_{2}^{3} (3 - x) d x$
84979	Integrate By Parts	integral of (x^2)/(x+1) with respect to x	$\int \frac{x^{2}}{x + 1} d x$
84980	Evaluate the Limit	limit as x approaches infinity of (x^3-x+7)/( square root of 9x^6+1)	$lim_{x \to \infty} \frac{x^{3} - x + 7}{\sqrt{9 x^{6} + 1}}$
84981	Find the Antiderivative	(5 square root of x)/x	$\frac{5 \sqrt{x}}{x}$
84982	Find the Antiderivative	f(x)=3x^2-pix	$f (x) = 3 x^{2} - π x$
84983	Evaluate the Integral	integral from e to e^e of 1/(x natural log of x) with respect to x	$\int_{e}^{e^{e}} \frac{1}{x \ln (x)} d x$
84984	Integrate By Parts	integral of 1/(x^3) with respect to x	$\int \frac{1}{x^{3}} d x$
84985	Find the Second Derivative	5 natural log of x^5	$5 \ln (x^{5})$
84986	Evaluate the Limit	limit as x approaches -pi/6 of 4cos(x)-3tan(-2x)	$lim_{x \to - \frac{π}{6}} 4 \cos (x) - 3 \tan (- 2 x)$
84987	Evaluate Using L'Hospital's Rule	limit as x approaches -2 of (4cos(x+2)-x^2)/(4e^(-4-2x)-x^2)	$lim_{x \to - 2} \frac{4 \cos (x + 2) - x^{2}}{4 e^{- 4 - 2 x} - x^{2}}$
84988	Find dy/dx	-y^2+5=x^2	$- y^{2} + 5 = x^{2}$
84989	Evaluate the Summation	7 sum from p=0 to 5 of 6-p^2	$7 \sum_{p = 0}^{5} 6 - p^{2}$
84990	Find the Derivative - d/dx	square root of x^2+y	$\sqrt{x^{2} + y}$
84991	Evaluate the Summation	sum from p=2 to 8 of -9p+p^2	$\sum_{p = 2}^{8} - 9 p + p^{2}$
84992	Integrate Using u-Substitution	integral of 1/(x^3) with respect to x	$\int \frac{1}{x^{3}} d x$
84993	Find the Antiderivative	x^3 square root of x^2+9	$x^{3} \sqrt{x^{2} + 9}$
84994	Find the Derivative - d/dx	10^(x^3-4x^2+9)	$10^{x^{3} - 4 x^{2} + 9}$
84995	Find the Derivative - d/dx	1/x natural log of x	$\frac{1}{x} \ln (x)$
84996	Find the Antiderivative	x/( square root of 2x^2+3)	$\frac{x}{\sqrt{2 x^{2} + 3}}$
84997	Evaluate the Integral	integral from pi/3 to pi/2 of sin(x) with respect to x	$\int_{\frac{π}{3}}^{\frac{π}{2}} \sin (x) d x$
84998	Find the Derivative - d/dk	kx	$k x$
84999	Evaluate the Limit	limit as x approaches infinity of 4/(x+5)	$lim_{x \to \infty} \frac{4}{x + 5}$
85000	Evaluate the Integral	integral from 1 to 2 of (x^2-1)/(x+1) with respect to x	$\int_{1}^{2} \frac{x^{2} - 1}{x + 1} d x$