Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68901	Find dy/dx	3x^2+4xy+2y^2=2x+15	$3 x^{2} + 4 x y + 2 y^{2} = 2 x + 15$
68902	Find dy/dx	y=-7x(8^(-2x))	$y = - 7 x (8^{- 2 x})$
68903	Integrate Using u-Substitution	integral of x^2 square root of 1+x with respect to x	$\int x^{2} \sqrt{1 + x} d x$
68904	Find Where Increasing/Decreasing	f(x)=-\|1/3(x+3)\|	$f (x) = - \| \frac{1}{3} (x + 3) \|$
68905	Find dy/dx	y=3/(4+x^2)	$y = \frac{3}{4 + x^{2}}$
68906	Evaluate the Integral	integral from 1 to 2 of (4x^3-6x) with respect to x	$\int_{1}^{2} (4 x^{3} - 6 x) d x$
68907	Find the Maximum/Minimum Value	f(x)=4-5sin(2x+pi/4)	$f (x) = 4 - 5 \sin (2 x + \frac{π}{4})$
68908	Find the Tangent Line at (1,0)	y=x-x^3 , (1,0)	$y = x - x^{3}$ , $(1, 0)$
68909	Find the Derivative - d/dx	d/(dx)(4x^4-7x^3+3)	$\frac{d}{d x} (4 x^{4} - 7 x^{3} + 3)$
68910	Find Where Increasing/Decreasing	C(x)=x^(1/5)(x+6)	$C (x) = x^{\frac{1}{5}} (x + 6)$
68911	Find the Maximum/Minimum Value	y=csc(x)	$y = \csc (x)$
68912	Find dy/dx	y = square root of 1-3x^2	$y = \sqrt{1 - 3 x^{2}}$
68913	Evaluate the Limit	limit as x approaches 1 of (x^2+x-2)/((x-1)^2)	$lim_{x \to 1} \frac{x^{2} + x - 2}{{(x - 1)}^{2}}$
68914	Find the Slope of the Tangent Line at (4/3,8/3)	x^3+y^3-6xy=0 , (4/3,8/3)	$x^{3} + y^{3} - 6 x y = 0$ , $(\frac{4}{3}, \frac{8}{3})$
68915	Evaluate the Limit	limit as x approaches 2 of (f(x))/(g(x))	$lim_{x \to 2} \frac{f (x)}{g (x)}$
68916	Integrate By Parts	integral of x^5 natural log of x with respect to x	$\int x^{5} \ln (x) d x$
68917	Solve the Differential Equation	(dy)/(dx)=e^(-y)(2x-3) , y(1)=0	$\frac{d y}{d x} = e^{- y} (2 x - 3)$ , $y (1) = 0$
68918	Find dx/dy	x^(2/3)+y^(2/3)=a^(2/3)	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$
68919	Find the Derivative - d/dx	d/(dx)(x^-3)	$\frac{d}{d x} (x^{- 3})$
68920	Find dy/dx	y=cot(x)	$y = \cot (x)$
68921	Find the Derivative - d/dx	x/1	$\frac{x}{1}$
68922	Find the Turning Points	f(x)=4x^3-x^4+x+5	$f (x) = 4 x^{3} - x^{4} + x + 5$
68923	Find the Derivative - d/dx	1/( square root of x)+ square root of x	$\frac{1}{\sqrt{x}} + \sqrt{x}$
68924	Find dy/dx	y^4+5x=11	$y^{4} + 5 x = 11$
68925	Find the Percentage Rate of Change	y=2200(1.074)^x	$y = 2200 {(1.074)}^{x}$
68926	Find the Derivative - d/dx	d/(dx)(e^(2x))	$\frac{d}{d x} (e^{2 x})$
68927	Find dy/dx	y=5/x	$y = \frac{5}{x}$
68928	Evaluate the Limit	limit as x approaches 0 of (x-1)/(x+1)	$lim_{x \to 0} \frac{x - 1}{x + 1}$
68929	Find dy/dx	5/(x^3)+3 fourth root of y=18	$\frac{5}{x^{3}} + 3 \sqrt[4]{y} = 18$
68930	Integrate Using u-Substitution	integral of xe^x with respect to x	$\int x e^{x} d x$
68931	Find dy/dx	y=2x-6y^2	$y = 2 x - 6 y^{2}$
68932	Find the Derivative - d/dx	-xsin(x)+cos(x)	$- x \sin (x) + \cos (x)$
68933	Find the Derivative - d/dθ	-sin(theta)	$- \sin (θ)$
68934	Find dy/dx	y=(1+x)^(1/x)	$y = {(1 + x)}^{\frac{1}{x}}$
68935	Find the Derivative - d/dx	d/(dx)(-1/(x^4)-5/(x^2))	$\frac{d}{d x} (- \frac{1}{x^{4}} - \frac{5}{x^{2}})$
68936	Evaluate the Summation	sum from i=1 to 3 of (ai+b)/(2a)	$\sum_{i = 1}^{3} \frac{a i + b}{2 a}$
68937	Evaluate the Integral	integral of x square root of 5+2x^2 with respect to x	$\int x \sqrt{5 + 2 x^{2}} d x$
68938	Find the Area Between the Curves	y=x^2	$y = x^{2}$
68939	Find dy/dx	sin(y)=x	$\sin (y) = x$
68940	Find the Domain and Range	f(x)=2+2x if x<0; x^2 if x>=0	$f (x) = {\begin{cases} 2 + 2 x & x < 0 \\ x^{2} & x \geq 0 \end{cases}$
68941	Find the Derivative - d/dy	2xy^3	$2 x y^{3}$
68942	Evaluate the Limit	limit as x approaches -1 of (-5x-5)/(2x+2)	$lim_{x \to - 1} \frac{- 5 x - 5}{2 x + 2}$
68943	Find the Derivative - d/dx	4cos(x)+2sin(x)+1	$4 \cos (x) + 2 \sin (x) + 1$
68944	Find dy/dx	e^(xy)=5y	$e^{x y} = 5 y$
68945	Integrate Using Partial Fractions	integral of 1/(x^2-9) with respect to x	$\int \frac{1}{x^{2} - 9} d x$
68946	Find the Derivative - d/dx	1dx	$1 d x$
68947	Find dx/dy	x^2+y^2=5	$x^{2} + y^{2} = 5$
68948	Find dy/dx	x^2+xy-3y=3	$x^{2} + x y - 3 y = 3$
68949	Find the Derivative - d/dx	d/(dx)(1/(x^8))	$\frac{d}{d x} (\frac{1}{x^{8}})$
68950	Find the Derivative - d/dx	cot(x)^3	$\cot^{3} (x)$
68951	Find the Derivative - d/dx	y=(arctan(x))^2	$y = {(\arctan (x))}^{2}$
68952	Find the Derivative - d/dx	e^(x^x)	$e^{x^{x}}$
68953	Find dy/dx	xsin(y)+ysin(x)=1	$x \sin (y) + y \sin (x) = 1$
68954	Find the Derivative - d/dx	cos(x)x^-2	$\cos (x) x^{- 2}$
68955	Find ds/dt	s=5t^3-3t^5	$s = 5 t^{3} - 3 t^{5}$
68956	Find the Derivative - d/dx	y=sinh(cosh(x))	$y = \sinh (\cosh (x))$
68957	Find the Derivative - d/dt	y=bcos(t)+t^2sin(t)	$y = b \cos (t) + t^{2} \sin (t)$
68958	Evaluate the Limit	limit as x approaches 16 of ( square root of 23- square root of x+7)/(x-16)	$lim_{x \to 16} \frac{\sqrt{23} - \sqrt{x + 7}}{x - 16}$
68959	Find the Derivative - d/dx	d/(dx)((2x^5+3x^4-1)/(-2x^7))	$\frac{d}{d x} (\frac{2 x^{5} + 3 x^{4} - 1}{- 2 x^{7}})$
68960	Find the Derivative - d/dx	y=1/(2 cube root of x^2)	$y = \frac{1}{2 \sqrt[3]{x^{2}}}$
68961	Evaluate the Integral	integral of (e^(2x)-e^(-2x))^2 with respect to x	$\int {(e^{2 x} - e^{- 2 x})}^{2} d x$
68962	Integrate Using u-Substitution	integral of x square root of 2x-1 with respect to x	$\int x \sqrt{2 x - 1} d x$
68963	Find the Antiderivative	2cos(x)^2	$2 \cos^{2} (x)$
68964	Evaluate the Integral	integral of e^(ax) with respect to a	$\int e^{a x} d a$
68965	Find the Tangent Line at (6,0)	y = natural log of x^2-6x+1 , (6,0)	$y = \ln (x^{2} - 6 x + 1)$ , $(6, 0)$
68966	Evaluate the Limit	limit as x approaches a of 0/infinity	$lim_{x \to a} \frac{0}{\infty}$
68967	Find dy/dx	2x^3=(3xy+1)^2	$2 x^{3} = {(3 x y + 1)}^{2}$
68968	Evaluate the Limit	limit as x approaches 0 of (4x^2)/(e^(4x)-4x-1)	$lim_{x \to 0} \frac{4 x^{2}}{e^{4 x} - 4 x - 1}$
68969	Find Where Increasing/Decreasing	f(x)=x+4/x	$f (x) = x + \frac{4}{x}$
68970	Find the Derivative - d/dx	y=x^4f(x)	$y = x^{4} f (x)$
68971	Find dx/dy	y=x^( square root of x)	$y = x^{\sqrt{x}}$
68972	Evaluate the Limit	limit as x approaches 0 of (8x^2-2x)/(2x)	$lim_{x \to 0} \frac{8 x^{2} - 2 x}{2 x}$
68973	Find the Antiderivative	2e^x-8x	$2 e^{x} - 8 x$
68974	Find dy/dx	square root of x+ square root of y=7	$\sqrt{x} + \sqrt{y} = 7$
68975	Find dy/dx	x^2=(4x^2y^3+1)^2	$x^{2} = {(4 x^{2} y^{3} + 1)}^{2}$
68976	Evaluate the Integral	( integral of e^x-1/(9x) with respect to x)dx	$(\int e^{x} - \frac{1}{9 x} d x) d x$
68977	Evaluate the Limit	limit as x approaches 1/2 of (x^3+5x)/(4x-6)	$lim_{x \to \frac{1}{2}} \frac{x^{3} + 5 x}{4 x - 6}$
68978	Evaluate the Integral	integral from 0 to a of 1/((1+x)^2) with respect to x=1/7	$\int_{0}^{a} \frac{1}{{(1 + x)}^{2}} d x = \frac{1}{7}$
68979	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 3x^2+x)/(x^2-1)	$lim_{x \to - \infty} \frac{\sqrt{3 x^{2} + x}}{x^{2} - 1}$
68980	Integrate By Parts	integral of tan(x) with respect to x	$\int \tan (x) d x$
68981	Evaluate the Limit	limit as x approaches 3 of (x^2-2x-3)/(4x-12)	$lim_{x \to 3} \frac{x^{2} - 2 x - 3}{4 x - 12}$
68982	Solve the Differential Equation	(dy)/(dx)=2xy	$\frac{d y}{d x} = 2 x y$
68983	Find dx/dy	x^2+xy-y^2=4	$x^{2} + x y - y^{2} = 4$
68984	Determine if Continuous	f(x)=cx^2+8x if x<3; x^3-cx if x>=3	$f (x) = {\begin{cases} c x^{2} + 8 x & x < 3 \\ x^{3} - c x & x \geq 3 \end{cases}$
68985	Find the Derivative - d/dx	1/(x^2+y^2)	$\frac{1}{x^{2} + y^{2}}$
68986	Integrate By Parts	integral of x^2e^(5x) with respect to x	$\int x^{2} e^{5 x} d x$
68987	Find the Derivative - d/dx	e^xcos(x)+e^xsin(x)	$e^{x} \cos (x) + e^{x} \sin (x)$
68988	Evaluate the Integral	integral of t^2( cube root of t+ square root of t-t^(-1/2)) with respect to t	$\int t^{2} (\sqrt[3]{t} + \sqrt{t} - t^{- \frac{1}{2}}) d t$
68989	Find the Derivative - d/dx	cube root of 1-x	$\sqrt[3]{1 - x}$
68990	Find the Derivative - d/dx	d/(dx)*3x	$\frac{d}{d x} \cdot 3 x$
68991	Find the Linearization at a=0	f(x) = square root of 4-x , a=0	$f (x) = \sqrt{4 - x}$ , $a = 0$
68992	Integrate Using u-Substitution	integral of x square root of x+3 with respect to x	$\int x \sqrt{x + 3} d x$
68993	Find dy/dx	x^2y^2=4	$x^{2} y^{2} = 4$
68994	Find the Derivative - d/dx	(-sin(-x))	$(- \sin (- x))$
68995	Find dy/dx	y=e^(-7x)	$y = e^{- 7 x}$
68996	Evaluate the Limit	limit as x approaches -1 of ( square root of 3x+5- square root of 2)/(3x+3)	$lim_{x \to - 1} \frac{\sqrt{3 x + 5} - \sqrt{2}}{3 x + 3}$
68997	Integrate Using u-Substitution	integral of sin(t) square root of 1+cos(t) with respect to t	$\int \sin (t) \sqrt{1 + \cos (t)} d t$
68998	Find the Derivative - d/dx	d/(dx)( natural log of (2x+3)/(2x-3))	$\frac{d}{d x} (\ln (\frac{2 x + 3}{2 x - 3}))$
68999	Find the Derivative - d/dx	y=(x^2-a^2)/(x-a)	$y = \frac{x^{2} - a^{2}}{x - a}$
69000	Evaluate the Integral	integral from -1 to 1 of (t^3-9t) with respect to t	$\int_{- 1}^{1} (t^{3} - 9 t) d t$