Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82801	Find the Derivative - d/dx	y=5x-4 square root of x	$y = 5 x - 4 \sqrt{x}$
82802	Find dy/dx	-y-2-2x^2=y^3	$- y - 2 - 2 x^{2} = y^{3}$
82803	Find Where Increasing/Decreasing	f(x)=4x^3	$f (x) = 4 x^{3}$
82804	Find the Derivative - d/dx	-(x+1)sin((x^2)/2)	$- (x + 1) \sin (\frac{x^{2}}{2})$
82805	Find the Derivative - d/dy	natural log of square root of x^2+y^2	$\ln (\sqrt{x^{2} + y^{2}})$
82806	Find dy/dx	xy-y-5-2x^3=0	$x y - y - 5 - 2 x^{3} = 0$
82807	Find the Antiderivative	(2x+1)/(2x-3)	$\frac{2 x + 1}{2 x - 3}$
82808	Find dx/dy	(xy)^x=e	${(x y)}^{x} = e$
82809	Evaluate the Integral	integral of 2/(3 cube root of x) with respect to x	$\int \frac{2}{3 \sqrt[3]{x}} d x$
82810	Find the Second Derivative	x+3(1-x)^(1/3)	$x + 3 {(1 - x)}^{\frac{1}{3}}$
82811	Find dy/dx	x^2+y^2=y	$x^{2} + y^{2} = y$
82812	Evaluate the Integral	integral of 9x^2 square root of x^3-1 with respect to x	$\int 9 x^{2} \sqrt{x^{3} - 1} d x$
82813	Find the Derivative - d/dx	1+1/(2 square root of x+1)	$1 + \frac{1}{2 \sqrt{x + 1}}$
82814	Evaluate the Limit	limit as x approaches 12 of (12-x)/(4x-48)	$lim_{x \to 12} \frac{12 - x}{4 x - 48}$
82815	Find the Derivative - d/dx	d/(dx)(-sin(-x))	$\frac{d}{d x} (- \sin (- x))$
82816	Evaluate the Limit	limit as x approaches 49 of (x( square root of x-7))/(x-49)	$lim_{x \to 49} \frac{x (\sqrt{x} - 7)}{x - 49}$
82817	Evaluate the Integral	-3 integral of 0(x^2-2x+3) with respect to x	$- 3 \int 0 (x^{2} - 2 x + 3) d x$
82818	Evaluate the Limit	limit as x approaches -1/2 of (2x^2-x-1)/(2x^2+3x+1)	$lim_{x \to - \frac{1}{2}} \frac{2 x^{2} - x - 1}{2 x^{2} + 3 x + 1}$
82819	Find the Maximum/Minimum Value	y=-1+3cos(3/2x)	$y = - 1 + 3 \cos (\frac{3}{2} x)$
82820	Find the Maximum/Minimum Value	f(x)=(x+3)(x-3)	$f (x) = (x + 3) (x - 3)$
82821	Find the Maximum/Minimum Value	y=sin(x)+cos(x)	$y = \sin (x) + \cos (x)$
82822	Find the Antiderivative	square root of 1+4x^2	$\sqrt{1 + 4 x^{2}}$
82823	Find dy/dx	y=1/(2 square root of x)	$y = \frac{1}{2 \sqrt{x}}$
82824	Find the Antiderivative	e^x(e^x-1)	$e^{x} (e^{x} - 1)$
82825	Integrate Using u-Substitution	integral of (e^x)/(e^x+1) with respect to x	$\int \frac{e^{x}}{e^{x} + 1} d x$
82826	Find the Integral	x/( square root of x)	$\frac{x}{\sqrt{x}}$
82827	Find the Derivative - d/dx	e^(-x)+2xe^(-x)+x^2e^(-x)	$e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
82828	Find the Antiderivative	1/(2 square root of x)dx	$\frac{1}{2 \sqrt{x}} d x$
82829	Find the Derivative - d/dx	y=1/( cube root of x^2)	$y = \frac{1}{\sqrt[3]{x^{2}}}$
82830	Find dy/dx	5x^2-4=-4y^2	$5 x^{2} - 4 = - 4 y^{2}$
82831	Evaluate the Summation	sum from n=1 to infinity of 1/( square root of n)	$\sum_{n = 1}^{\infty} \frac{1}{\sqrt{n}}$
82832	Find the Antiderivative	f(x)=cos(-5x)	$f (x) = \cos (- 5 x)$
82833	Evaluate the Integral	integral of (x^5-4x^-4+6x^3-2x) with respect to x	$\int (x^{5} - 4 x^{- 4} + 6 x^{3} - 2 x) d x$
82834	Evaluate the Integral	integral of (15/(x^4)+8/(x^5)) with respect to x	$\int (\frac{15}{x^{4}} + \frac{8}{x^{5}}) d x$
82835	Find dy/dx	-y=y^3-y^2+3x^3	$- y = y^{3} - y^{2} + 3 x^{3}$
82836	Find the Derivative - d/dx	7-(1.01)^(-x^2)	$7 - {(1.01)}^{- x^{2}}$
82837	Find the Antiderivative	x* square root of x^2+1	$x \cdot \sqrt{x^{2} + 1}$
82838	Evaluate the Limit	limit as x approaches -1 of (x^3-7x-6)/(x^3+3x^2+2x)	$lim_{x \to - 1} \frac{x^{3} - 7 x - 6}{x^{3} + 3 x^{2} + 2 x}$
82839	Evaluate the Integral	integral from 1 to 4 of (2 cube root of x+5 square root of x-4x^4) with respect to x	$\int_{1}^{4} (2 \sqrt[3]{x} + 5 \sqrt{x} - 4 x^{4}) d x$
82840	Find the Derivative - d/dx	fourth root of x^3cos(x)	$\sqrt[4]{x^{3}} \cos (x)$
82841	Find dy/dx	-1=-xy+2y^2	$- 1 = - x y + 2 y^{2}$
82842	Integrate Using u-Substitution	integral of (sin(x))/(cos(x)^2) with respect to x	$\int \frac{\sin (x)}{\cos^{2} (x)} d x$
82843	Find the Derivative - d/dx	-cos( square root of x)	$- \cos (\sqrt{x})$
82844	Find the Derivative - d/dx	2^(x^2+3)	$2^{x^{2} + 3}$
82845	Find the Derivative - d/dx	(x+1)/(4^x)	$\frac{x + 1}{4^{x}}$
82846	Find dx/dy	x=(y^4)/4+1/(8y^2)	$x = \frac{y^{4}}{4} + \frac{1}{8 y^{2}}$
82847	Integrate Using u-Substitution	f(x) = integral of (x+1)^3 with respect to x	$f (x) = \int {(x + 1)}^{3} d x$
82848	Evaluate the Integral	integral of ((2r-1)cos( square root of 3(2r-1)^2+6))/( square root of 3(2r-1)^2+6) with respect to r	$\int \frac{(2 r - 1) \cos (\sqrt{3 {(2 r - 1)}^{2} + 6})}{\sqrt{3 {(2 r - 1)}^{2} + 6}} d r$
82849	Find the Derivative - d/dx	(8-2x)/(3y^2)	$\frac{8 - 2 x}{3 y^{2}}$
82850	Evaluate the Integral	integral from npi to (n+2)pi of 7cos(x) with respect to x	$\int_{n π}^{(n + 2) π} 7 \cos (x) d x$
82851	Find Where Increasing/Decreasing	-((x-2)^2)/((x-1)^2)	$- \frac{{(x - 2)}^{2}}{{(x - 1)}^{2}}$
82852	Evaluate the Integral	integral of (-4x^-3-20x^-5) with respect to x	$\int (- 4 x^{- 3} - 20 x^{- 5}) d x$
82853	Find dy/dx	4x+4y^2+x^2=0	$4 x + 4 y^{2} + x^{2} = 0$
82854	Evaluate the Limit	limit as x approaches -1 of (-5x^3+5x^2+2)/(4x-2)	$lim_{x \to - 1} \frac{- 5 x^{3} + 5 x^{2} + 2}{4 x - 2}$
82855	Evaluate the Limit	limit as x approaches 0 of (1-e^x)/( natural log of 2-e^x)	$lim_{x \to 0} \frac{1 - e^{x}}{\ln (2 - e^{x})}$
82856	Find dy/dx	y=2sin(x)	$y = 2 \sin (x)$
82857	Evaluate the Integral	integral from 0 to 3 of (x-1)^2+2 with respect to x	$\int_{0}^{3} {(x - 1)}^{2} + 2 d x$
82858	Evaluate the Summation	7 sum from d=2 to 5 of d+2	$7 \sum_{d = 2}^{5} d + 2$
82859	Evaluate the Limit	limit as x approaches -1/2 of (x+2x^2)/(x^2-1/4)	$lim_{x \to - \frac{1}{2}} \frac{x + 2 x^{2}}{x^{2} - \frac{1}{4}}$
82860	Evaluate from the Left	limit as x approaches 0 from the left of x/(\|x\|)=-1	$lim_{x \to 0^{-}} \frac{x}{\| x \|} = - 1$
82861	Evaluate the Integral	integral of (8sin( square root of x)^3)/( square root of x) with respect to x	$\int \frac{8 \sin^{3} (\sqrt{x})}{\sqrt{x}} d x$
82862	Evaluate the Integral	integral of (2+3x)x with respect to x	$\int (2 + 3 x) x d x$
82863	Find dy/dx	y=1-x*e^y	$y = 1 - x \cdot e^{y}$
82864	Find dy/dx	y=3x^2+2x-1	$y = 3 x^{2} + 2 x - 1$
82865	Find the Antiderivative	f(x)=2/(x^3)+cos(x)	$f (x) = \frac{2}{x^{3}} + \cos (x)$
82866	Find the Antiderivative	f(x)=1/(cos(x)^2)-2/3	$f (x) = \frac{1}{\cos^{2} (x)} - \frac{2}{3}$
82867	Use Logarithmic Differentiation to Find the Derivative	y=x^(9sin(x))	$y = x^{9 \sin (x)}$
82868	Find the Derivative - d/dx	sin(2x^3+3x)^2	$\sin^{2} (2 x^{3} + 3 x)$
82869	Find dy/dx	-3y^2-y+5x^2=-3y^3	$- 3 y^{2} - y + 5 x^{2} = - 3 y^{3}$
82870	Evaluate the Integral	integral of (2+y^2)^2 with respect to y	$\int {(2 + y^{2})}^{2} d y$
82871	Evaluate the Integral	integral from npi to (n+2)pi of 9cos(x) with respect to x	$\int_{n π}^{(n + 2) π} 9 \cos (x) d x$
82872	Find the Antiderivative	(x-1)/( cube root of x)	$\frac{x - 1}{\sqrt[3]{x}}$
82873	Evaluate the Integral	integral of 3^(2-5x) with respect to x	$\int 3^{2 - 5 x} d x$
82874	Integrate Using u-Substitution	integral of sin(3x) with respect to x	$\int \sin (3 x) d x$
82875	Evaluate the Limit	limit as x approaches 0 of (e^(x^2)-cos(x))/(x^2)	$lim_{x \to 0} \frac{e^{x^{2}} - \cos (x)}{x^{2}}$
82876	Find the Derivative - d/dt	20(1+e^(10-t))^-1	$20 {(1 + e^{10 - t})}^{- 1}$
82877	Find the Tangent Line at (-2,-16)	f(x)=2x^3 at (-2,-16)	$f (x) = 2 x^{3}$ at $(- 2, - 16)$
82878	Find the Derivative - d/dx	e^(x-e)+ natural log of x-x/e	$e^{x - e} + \ln (x) - \frac{x}{e}$
82879	Find the Derivative - d/dx	y=(2-3x)/(3+x^2)	$y = \frac{2 - 3 x}{3 + x^{2}}$
82880	Evaluate the Limit	limit as x approaches 6 of (x^2+4)/( square root of 2x+5)	$lim_{x \to 6} \frac{x^{2} + 4}{\sqrt{2 x + 5}}$
82881	Evaluate the Integral	integral of (5+5x+6x^-3) with respect to x	$\int (5 + 5 x + 6 x^{- 3}) d x$
82882	Find the Concavity	-1/5x^5-3x^4-12x^3	$- \frac{1}{5} x^{5} - 3 x^{4} - 12 x^{3}$
82883	Find dy/dx	-x^3y+y^3=x^2	$- x^{3} y + y^{3} = x^{2}$
82884	Evaluate the Limit	limit as x approaches negative infinity of arctan(x^2)	$lim_{x \to - \infty} \arctan (x^{2})$
82885	Evaluate the Limit	limit as x approaches -8 of (4(x+5)^2+1)/(1/(3x+2)+2)	$lim_{x \to - 8} \frac{4 {(x + 5)}^{2} + 1}{\frac{1}{3 x + 2} + 2}$
82886	Evaluate the Limit	limit as x approaches 81 of (x( square root of x-9))/(x-81)	$lim_{x \to 81} \frac{x (\sqrt{x} - 9)}{x - 81}$
82887	Integrate Using u-Substitution	integral of x^2 square root of 2+x with respect to x	$\int x^{2} \sqrt{2 + x} d x$
82888	Find the Derivative - d/dy	4/((2y+1)^2)	$\frac{4}{{(2 y + 1)}^{2}}$
82889	Find the Derivative - d/dx	(12 square root of x)/(4x^3)	$\frac{12 \sqrt{x}}{4 x^{3}}$
82890	Find dy/dx	-xy+4y^2-3=5x^2	$- x y + 4 y^{2} - 3 = 5 x^{2}$
82891	Find the Local Maxima and Minima	f(x) = natural log of x^2-1	$f (x) = \ln (x^{2} - 1)$
82892	Find the Antiderivative	(x^2+x+1)/(x+1)	$\frac{x^{2} + x + 1}{x + 1}$
82893	Evaluate the Integral	integral from 0 to 1 of x^-2 with respect to x	$\int_{0}^{1} x^{- 2} d x$
82894	Evaluate the Integral	integral of 5tan(x)^2 with respect to x	$\int 5 \tan^{2} (x) d x$
82895	Find the Second Derivative	f(x)=1/10x^-4+4/5x^5-3/2x^4+2x^2	$f (x) = \frac{1}{10} x^{- 4} + \frac{4}{5} x^{5} - \frac{3}{2} x^{4} + 2 x^{2}$
82896	Evaluate the Integral	integral of cot(x)^3csc(x)^2 with respect to x	$\int \cot^{3} (x) \csc^{2} (x) d x$
82897	Find the Domain and Range	f(x)=x+1 if -9<=x<3; -x+4 if x>3	$f (x) = {\begin{cases} x + 1 & - 9 \leq x < 3 \\ - x + 4 & x > 3 \end{cases}$
82898	Evaluate the Integral	integral of cos(2-5x)^2 with respect to x	$\int \cos^{2} (2 - 5 x) d x$
82899	Evaluate the Integral	integral of e^((2x)/3) with respect to x	$\int e^{\frac{2 x}{3}} d x$
82900	Find the Derivative - d/dx	y=3 square root of sin(x)	$y = 3 \sqrt{\sin (x)}$