Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67101	Find dy/dx	(x+y)^3=x^3+y^3	${(x + y)}^{3} = x^{3} + y^{3}$
67102	Find dy/dx	y=3x^2	$y = 3 x^{2}$
67103	Find dy/dx	sin(xy)=x	$\sin (x y) = x$
67104	Find dy/dx	(4x+4y)^3=64x^3+64y^3	${(4 x + 4 y)}^{3} = 64 x^{3} + 64 y^{3}$
67105	Find Where Increasing/Decreasing	y=x	$y = x$
67106	Find the Tangent Line at (1,1)	y = square root of x , (1,1)	$y = \sqrt{x}$ , $(1, 1)$
67107	Find the Derivative - d/dx	f(x^2)	$f (x^{2})$
67108	Find dx/dy	x^3+y^3=6xy	$x^{3} + y^{3} = 6 x y$
67109	Find dy/dx	2xy^2-3x^2y=6x	$2 x y^{2} - 3 x^{2} y = 6 x$
67110	Find dy/dx	y=(csc(x)+cot(x))^-1	$y = {(\csc (x) + \cot (x))}^{- 1}$
67111	Find the Antiderivative	dx	$d x$
67112	Evaluate the Integral	integral of (e^x+4^(x+2)) with respect to x	$\int (e^{x} + 4^{x + 2}) d x$
67113	Integrate By Parts	integral of e^(-x) with respect to x	$\int e^{- x} d x$
67114	Find the Derivative - d/dx	f(3)	$f (3)$
67115	Find Where Increasing/Decreasing	f(x)=x/(x^2+1)	$f (x) = \frac{x}{x^{2} + 1}$
67116	Find dy/dx	x^3+y^3=9	$x^{3} + y^{3} = 9$
67117	Find the Antiderivative	e	$e$
67118	Find the Slope	-3/2	$- \frac{3}{2}$
67119	Evaluate the Integral	integral from 0 to 2 of (3x^2-1)/(x^2) with respect to x	$\int_{0}^{2} \frac{3 x^{2} - 1}{x^{2}} d x$
67120	Find dy/dx	y=(sec(x))/(1+sec(x))	$y = \frac{\sec (x)}{1 + \sec (x)}$
67121	Find the Derivative - d/dx	y=x^2-1/2cos(x)	$y = x^{2} - \frac{1}{2} \cos (x)$
67122	Find the Antiderivative	f(x)=4x^3-6x^2+2	$f (x) = 4 x^{3} - 6 x^{2} + 2$
67123	Evaluate the Integral	integral of (x+3)/(x^2-16) with respect to x	$\int \frac{x + 3}{x^{2} - 16} d x$
67124	Find dy/dx	y=(csc(x))/(1+csc(x))	$y = \frac{\csc (x)}{1 + \csc (x)}$
67125	Find dy/dx	ycos(x)=3x^2+4y^2	$y \cos (x) = 3 x^{2} + 4 y^{2}$
67126	Use Logarithmic Differentiation to Find the Derivative	y=x^(5x)	$y = x^{5 x}$
67127	Find the Antiderivative	f(x)=x(x-4)	$f (x) = x (x - 4)$
67128	Find dy/dx	(x^2+y^2)^2=4x^2y	${(x^{2} + y^{2})}^{2} = 4 x^{2} y$
67129	Evaluate the Limit	limit as x approaches pi/2 of (cot(x)^2)/(1-sin(x))	$lim_{x \to \frac{π}{2}} \frac{\cot^{2} (x)}{1 - \sin (x)}$
67130	Find the Derivative - d/dx	x^1	$x^{1}$
67131	Integrate By Parts	integral of xsec(x)^2 with respect to x	$\int x \sec^{2} (x) d x$
67132	Find the Linearization at a=π/6	f(x)=sin(x) , a=pi/6	$f (x) = \sin (x)$ , $a = \frac{π}{6}$
67133	Find dy/dx	3y^2+x^2-xy=1	$3 y^{2} + x^{2} - x y = 1$
67134	Find Where Increasing/Decreasing	f(x)=x^(2/3)	$f (x) = x^{\frac{2}{3}}$
67135	Find dy/dx	y=e^(x^2)	$y = e^{x^{2}}$
67136	Integrate By Parts	integral of x^3 natural log of x with respect to x	$\int x^{3} \ln (x) d x$
67137	Find the Derivative - d/dx	y=x^2 square root of 36-x^2	$y = x^{2} \sqrt{36 - x^{2}}$
67138	Evaluate the Limit	limit as x approaches negative infinity of (x^5+4x^2)/( square root of x^10+8x^7)	$lim_{x \to - \infty} \frac{x^{5} + 4 x^{2}}{\sqrt{x^{10} + 8 x^{7}}}$
67139	Find dy/dx	y^2=x	$y^{2} = x$
67140	Find the Second Derivative	x	$x$
67141	Find dy/dx	y=x^(2x)	$y = x^{2 x}$
67142	Integrate By Parts	integral of x^2e^(3x) with respect to x	$\int x^{2} e^{3 x} d x$
67143	Find dy/dx	2x^2-3y^2=4	$2 x^{2} - 3 y^{2} = 4$
67144	Find dy/dx	ycos(x)=3x^2+2y^2	$y \cos (x) = 3 x^{2} + 2 y^{2}$
67145	Find dx/dy	x^2+y^2=16	$x^{2} + y^{2} = 16$
67146	Find the Derivative - d/dx	ye^(xy)	$y e^{x y}$
67147	Find dy/dx	x^3+y^3=36	$x^{3} + y^{3} = 36$
67148	Find the Slope	-4	$- 4$
67149	Find dy/dx	y=(x^3)/(x-1)	$y = \frac{x^{3}}{x - 1}$
67150	Find the Maximum/Minimum Value	y=x^4-2x^3-11x^2+12x+36	$y = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36$
67151	Evaluate the Integral	integral from 1 to 2 of (3/(x^2)-1) with respect to x	$\int_{1}^{2} (\frac{3}{x^{2}} - 1) d x$
67152	Use Logarithmic Differentiation to Find the Derivative	y=x^( square root of x)	$y = x^{\sqrt{x}}$
67153	Integrate By Parts	integral of x^2e^(2x) with respect to x	$\int x^{2} e^{2 x} d x$
67154	Integrate By Parts	integral of e^xsin(x) with respect to x	$\int e^{x} \sin (x) d x$
67155	Evaluate the Limit	limit as theta approaches pi/2 of (sin(2theta)^2)/(1-sin(theta)^2)	$lim_{θ \to \frac{π}{2}} \frac{\sin^{2} (2 θ)}{1 - \sin^{2} (θ)}$
67156	Find dy/dx	y=x^( natural log of x)	$y = x^{\ln (x)}$
67157	Find the Derivative - d/dY	(D^2Y)/(dx^2)	$\frac{D^{2} Y}{d x^{2}}$
67158	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of 1/x-1/(e^x-1)	$lim_{x \to 0^{+}} \frac{1}{x} - \frac{1}{e^{x} - 1}$
67159	Find the Derivative - d/dx	f(1)	$f (1)$
67160	Find the Derivative - d/dx	f(-2)	$f (- 2)$
67161	Find dy/dx	y=(tan(x))/(1+tan(x))	$y = \frac{\tan (x)}{1 + \tan (x)}$
67162	Find dy/dx	square root of xy=1+x^2y	$\sqrt{x y} = 1 + x^{2} y$
67163	Find dy/dx	x^2-xy-y^2=1	$x^{2} - x y - y^{2} = 1$
67164	Find dy/dx	y^3+y^2-5y-x^2=-4	$y^{3} + y^{2} - 5 y - x^{2} = - 4$
67165	Find dy/dx	2y^2-x^2+x^3y=2	$2 y^{2} - x^{2} + x^{3} y = 2$
67166	Find the Equation of Variation	y=7 , x=-3 , z=-1	$y = 7$ , $x = - 3$ , $z = - 1$
67167	Find dy/dx	cos(x+y)=sin(x)+sin(y)	$\cos (x + y) = \sin (x) + \sin (y)$
67168	Evaluate the Limit	limit as x approaches negative infinity of (5x^2+6x)/( square root of 16x^4-5x^2)	$lim_{x \to - \infty} \frac{5 x^{2} + 6 x}{\sqrt{16 x^{4} - 5 x^{2}}}$
67169	Find dy/dx	-7x^2y^4-4xy^3=x+3	$- 7 x^{2} y^{4} - 4 x y^{3} = x + 3$
67170	Find the Antiderivative	d	$d$
67171	Find the Maximum/Minimum Value	f(x)=1/9x^3-1/3x^2-x+3	$f (x) = \frac{1}{9} x^{3} - \frac{1}{3} x^{2} - x + 3$
67172	Evaluate the Integral	integral of (x+ square root of x) with respect to x	$\int (x + \sqrt{x}) d x$
67173	Integrate By Parts	integral of xe^(-2x) with respect to x	$\int x e^{- 2 x} d x$
67174	Integrate By Parts	integral of ( natural log of x)^2 with respect to x	$\int \ln^{2} (x) d x$
67175	Find the Derivative - d/dx	e^(f(x))=1+x^2	$e^{f (x)} = 1 + x^{2}$
67176	Find the Derivative - d/dθ	y=pi/2sin(theta)-cos(theta)	$y = \frac{π}{2} \sin (θ) - \cos (θ)$
67177	Find dy/dx	(2x+2y)^3=8x^3+8y^3	${(2 x + 2 y)}^{3} = 8 x^{3} + 8 y^{3}$
67178	Find the Slope	2y+4x+10	$2 y + 4 x + 10$
67179	Find dx/dy	y=xe^x	$y = x e^{x}$
67180	Find the Tangent Line at x=5	f(x) = square root of x^2+11 , x=5	$f (x) = \sqrt{x^{2} + 11}$ , $x = 5$
67181	Solve the Differential Equation	(dy)/(dx)=(x+1)^2	$\frac{d y}{d x} = {(x + 1)}^{2}$
67182	Evaluate the Integral	integral of ((4x^6+2x^4)/(x^3)) with respect to x	$\int (\frac{4 x^{6} + 2 x^{4}}{x^{3}}) d x$
67183	Use Logarithmic Differentiation to Find the Derivative	y=cos(x)^x	$y = {\cos (x)}^{x}$
67184	Find Where Increasing/Decreasing	f(x)=x+1/x	$f (x) = x + \frac{1}{x}$
67185	Find dy/dx	y=e^(-x)	$y = e^{- x}$
67186	Find the Derivative - d/dx	ax^2	$a x^{2}$
67187	Find the Center and Radius	(x^2)/25+(y^2)/9=1	$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$
67188	Integrate Using Trig Substitution	integral of (x^3)/( square root of x^2+4) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} + 4}} d x$
67189	Evaluate the Limit	limit as theta approaches -pi/4 of (1+ square root of 2sin(theta))/(cos(2theta))	$lim_{θ \to - \frac{π}{4}} \frac{1 + \sqrt{2} \sin (θ)}{\cos (2 θ)}$
67190	Find dy/dx	(x^2)/(x+y)=y^2+2	$\frac{x^{2}}{x + y} = y^{2} + 2$
67191	Find dy/dx	x=sec(y)	$x = \sec (y)$
67192	Find the Maximum/Minimum Value	p(x)=-1/2x^3+3/2x-1	$p (x) = - \frac{1}{2} x^{3} + \frac{3}{2} x - 1$
67193	Evaluate Using L'Hospital's Rule	limit as x approaches pi/4 of (cos(x)-sin(x))/(tan(x)-1)	$lim_{x \to \frac{π}{4}} \frac{\cos (x) - \sin (x)}{\tan (x) - 1}$
67194	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2-9)	$f (x) = \frac{x^{2}}{x^{2} - 9}$
67195	Find dy/dx	3x^2+2xy+y^2=2	$3 x^{2} + 2 x y + y^{2} = 2$
67196	Find Where Increasing/Decreasing	f(x)=3	$f (x) = 3$
67197	Find dy/dx	x^2-3xy+y^2=1	$x^{2} - 3 x y + y^{2} = 1$
67198	Find the Tangent Line at (25,5)	y = square root of x , (25,5)	$y = \sqrt{x}$ , $(25, 5)$
67199	Evaluate the Integral	integral from 0 to 9 of (1/3x-2) with respect to x	$\int_{0}^{9} (\frac{1}{3} x - 2) d x$
67200	Find dy/dx	x^3+3xy+2y^3=17	$x^{3} + 3 x y + 2 y^{3} = 17$