Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70201	Find dy/dx	y=8x^(3/4)	$y = 8 x^{\frac{3}{4}}$
70202	Find the Concavity	f(x)=-x^5	$f (x) = - x^{5}$
70203	Find the Antiderivative	f(x)=x(x^2-3)	$f (x) = x (x^{2} - 3)$
70204	Evaluate the Limit	limit as x approaches infinity of (8x-14x^2)/(9x^2+20x+4)	$lim_{x \to \infty} \frac{8 x - 14 x^{2}}{9 x^{2} + 20 x + 4}$
70205	Solve the Differential Equation	(dy)/(dx)=(xy+2y-x-2)/(xy-3y+x-3)	$\frac{d y}{d x} = \frac{x y + 2 y - x - 2}{x y - 3 y + x - 3}$
70206	Find the Maximum/Minimum Value	1/x	$\frac{1}{x}$
70207	Find the Derivative - d/dx	(1+x)	$(1 + x)$
70208	Find the Integral	4x^3dx	$4 x^{3} d x$
70209	Evaluate the Integral	integral from 0 to 1 of (2x^3+x)/(x^2+x^4+1) with respect to x	$\int_{0}^{1} \frac{2 x^{3} + x}{x^{2} + x^{4} + 1} d x$
70210	Find the Derivative - d/dx	x^2-2xy	$x^{2} - 2 x y$
70211	Find the Derivative - d/dy	e^(x^2-y^2)	$e^{x^{2} - y^{2}}$
70212	Evaluate the Limit	limit as h approaches 0 of (7e^x-7e^(x+h))/(4h)	$lim_{h \to 0} \frac{7 e^{x} - 7 e^{x + h}}{4 h}$
70213	Integrate Using u-Substitution	integral of x^2 square root of 1-x with respect to x	$\int x^{2} \sqrt{1 - x} d x$
70214	Verify the Differential Equation Solution	y''''+y''''''''=6e^(2x) , y=e^(2x)	$y'' + y'''' = 6 e^{2 x}$ , $y = e^{2 x}$
70215	Find dx/dy	y=2^x	$y = 2^{x}$
70216	Find the Derivative - d/dx	y=a/x-b/(x^2)+c/(x^3)	$y = \frac{a}{x} - \frac{b}{x^{2}} + \frac{c}{x^{3}}$
70217	Evaluate the Integral	integral from 1 to infinity of (e^(- square root of x))/( square root of x) with respect to x	$\int_{1}^{\infty} \frac{e^{- \sqrt{x}}}{\sqrt{x}} d x$
70218	Find the Area Between the Curves	y=x^4 and y=x	$y = x^{4}$ and $y = x$
70219	Find the Derivative Using Product Rule - d/dx	xy	$x y$
70220	Find the Center and Radius	x^2-y^2=4	$x^{2} - y^{2} = 4$
70221	Evaluate the Integral	integral from 0 to 5 of 1/( square root of 9+4x^2) with respect to x	$\int_{0}^{5} \frac{1}{\sqrt{9 + 4 x^{2}}} d x$
70222	Find dx/dy	y=cos(x)	$y = \cos (x)$
70223	Evaluate the Integral	integral of (x^-1-x^-2+x^-3)/(x^2) with respect to x	$\int \frac{x^{- 1} - x^{- 2} + x^{- 3}}{x^{2}} d x$
70224	Evaluate the Limit	limit as x approaches infinity of (x^4-2x^2)/(1+4x^4)	$lim_{x \to \infty} \frac{x^{4} - 2 x^{2}}{1 + 4 x^{4}}$
70225	Verify the Differential Equation Solution	y''''=(3y)/x , y=3x	$y'' = \frac{3 y}{x}$ , $y = 3 x$
70226	Find Where Increasing/Decreasing	f(x)=2(1/2)^x	$f (x) = 2 {(\frac{1}{2})}^{x}$
70227	Evaluate the Limit	limit as x approaches infinity of x/x	$lim_{x \to \infty} \frac{x}{x}$
70228	Evaluate the Limit	limit as h approaches 0 of (2^(3+h)-2^3)/h	$lim_{h \to 0} \frac{2^{3 + h} - 2^{3}}{h}$
70229	Find dy/dx	6x^3y^2=-1	$6 x^{3} y^{2} = - 1$
70230	Integrate Using Trig Substitution	integral of 1/( square root of 9-x^2) with respect to x	$\int \frac{1}{\sqrt{9 - x^{2}}} d x$
70231	Find the Integral	log of x	$\log (x)$
70232	Evaluate the Limit	f(-1)+ limit as x approaches -1 of g(x)	$f (- 1) + lim_{x \to - 1} g (x)$
70233	Find dy/dx	xy+2x+3y=1	$x y + 2 x + 3 y = 1$
70234	Solve the Differential Equation	(dy)/(dt)+20y=24	$\frac{d y}{d t} + 20 y = 24$
70235	Find the Derivative - d/dx	(cos(x))/(e^x)	$\frac{\cos (x)}{e^{x}}$
70236	Find the Derivative - d/dx	y = square root of xcos(x)	$y = \sqrt{x} \cos (x)$
70237	Find Where Increasing/Decreasing	x/(x^2+9)	$\frac{x}{x^{2} + 9}$
70238	Evaluate the Limit	limit as x approaches 2 of x^2 square root of x^2+5x+2	$lim_{x \to 2} x^{2} \sqrt{x^{2} + 5 x + 2}$
70239	Find the Derivative - d/dx	(9x)/( square root of 3x^3-9)	$\frac{9 x}{\sqrt{3 x^{3} - 9}}$
70240	Evaluate the Integral	integral of (x^2+2) with respect to x	$\int (x^{2} + 2) d x$
70241	Find dy/dx	y=(x^2)/(x+1)	$y = \frac{x^{2}}{x + 1}$
70242	Find the Second Derivative	6y-xy^2=1	$6 y - x y^{2} = 1$
70243	Find the Derivative - d/dx	y = natural log of 1/x	$y = \ln (\frac{1}{x})$
70244	Find dy/dx	y=(-x^2+6x-4)^5	$y = {(- x^{2} + 6 x - 4)}^{5}$
70245	Find dy/dx	y = square root of x-1/( square root of x)	$y = \sqrt{x} - \frac{1}{\sqrt{x}}$
70246	Find dy/dx	y=3x^2-5x	$y = 3 x^{2} - 5 x$
70247	Find the Derivative - d/dx	y=(x^2+a^2)^5	$y = {(x^{2} + a^{2})}^{5}$
70248	Evaluate the Integral	integral of ((-6x^6-4x)/(x^2)-4e^(6x)) with respect to x	$\int (\frac{- 6 x^{6} - 4 x}{x^{2}} - 4 e^{6 x}) d x$
70249	Find dy/dx	e^(x^2-y)=(x^2)/y	$e^{x^{2} - y} = \frac{x^{2}}{y}$
70250	Solve the Differential Equation	(ds)/(dr)=ks	$\frac{d s}{d r} = k s$
70251	Find the Derivative - d/dY	2X+3Y	$2 X + 3 Y$
70252	Find the Derivative - d/dx	(x^2-1)/((x+1)^2)	$\frac{x^{2} - 1}{{(x + 1)}^{2}}$
70253	Find the Area Under the Curve	y=4x-x^2	$y = 4 x - x^{2}$
70254	Find the Tangent Line at (0,7)	y=7e^x+x , (0,7)	$y = 7 e^{x} + x$ , $(0, 7)$
70255	Find the Derivative - d/dx	(x^2e^x)/(x^2+e^x)	$\frac{x^{2} e^{x}}{x^{2} + e^{x}}$
70256	Evaluate the Integral	integral from -1 to 1 of (2x^2-x^3) with respect to x	$\int_{- 1}^{1} (2 x^{2} - x^{3}) d x$
70257	Integrate By Parts	integral of cos(x)^2 with respect to x	$\int \cos^{2} (x) d x$
70258	Find the Derivative - d/dx	( square root of 3x-2)/x	$\frac{\sqrt{3 x - 2}}{x}$
70259	Find the Derivative - d/dx	d/(dx)(1+7/x)^x	$\frac{d}{d x} {(1 + \frac{7}{x})}^{x}$
70260	Find the Maximum/Minimum Value	f(x)=x/(x^2-4)	$f (x) = \frac{x}{x^{2} - 4}$
70261	Find dy/dx	y=cot(2x-2y)	$y = \cot (2 x - 2 y)$
70262	Find the Derivative - d/dx	-4e^x-sin(x)-9	$- 4 e^{x} - \sin (x) - 9$
70263	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (-x^2-x+11)/(7x^2-x+2)	$lim_{x \to \infty} \frac{- x^{2} - x + 11}{7 x^{2} - x + 2}$
70264	Find the Antiderivative	1/( square root of x^2+1)	$\frac{1}{\sqrt{x^{2} + 1}}$
70265	Evaluate the Limit	limit as x approaches e of natural log of x	$lim_{x \to e} \ln (x)$
70266	Evaluate the Limit	limit as x approaches c of cube root of 8	$lim_{x \to c} \sqrt[3]{8}$
70267	Find dy/dx	y=e^(3x^2)	$y = e^{3 x^{2}}$
70268	Evaluate the Integral	integral of (3x^2-8) with respect to x	$\int (3 x^{2} - 8) d x$
70269	Find the Derivative - d/dy	(x+y)	$(x + y)$
70270	Find the Derivative - d/dx	(cos(-x))	$(\cos (- x))$
70271	Find the Tangent Line at x=7	f(x) = square root of x^2+15 , x=7	$f (x) = \sqrt{x^{2} + 15}$ , $x = 7$
70272	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x/(x-2))^x	$lim_{x \to \infty} {(\frac{x}{x - 2})}^{x}$
70273	Evaluate the Integral	integral from 0 to pi/4 of tan(x)sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} \tan (x) \sec^{2} (x) d x$
70274	Evaluate the Limit	limit as x approaches 0 of x/(cos(x))	$lim_{x \to 0} \frac{x}{\cos (x)}$
70275	Find the Derivative - d/dx	arccsc(e^x)	$arccsc (e^{x})$
70276	Integrate By Parts	integral of te^(-3t) with respect to t	$\int t e^{- 3 t} d t$
70277	Find the Antiderivative	theta	$θ$
70278	Evaluate the Limit	limit as x approaches 9 of (x-9)/( square root of x-3- square root of 6)	$lim_{x \to 9} \frac{x - 9}{\sqrt{x - 3} - \sqrt{6}}$
70279	Find the Derivative - d/dx	(x+1)(x-1)	$(x + 1) (x - 1)$
70280	Find the Derivative - d/dx	e^((-x^2)/2)	$e^{\frac{- x^{2}}{2}}$
70281	Find the Center and Radius	8x+x^2-2y+y^2-64=0	$8 x + x^{2} - 2 y + y^{2} - 64 = 0$
70282	Evaluate the Summation	sum from n=1 to infinity of n	$\sum_{n = 1}^{\infty} n$
70283	Find dr/dθ	r=sin(theta)tan(theta)	$r = \sin (θ) \tan (θ)$
70284	Find the Tangent Line at (2,8)	f(x)=x^3 at (2,8)	$f (x) = x^{3}$ at $(2, 8)$
70285	Find the Derivative - d/dt	(cot(t))/(e^t)	$\frac{\cot (t)}{e^{t}}$
70286	Find the Second Derivative	natural log of 2x+4	$\ln (2 x + 4)$
70287	Find the Slope of the Tangent Line at (-1,1)	(x^2+y^2)^2=4x^2y , (-1,1)	${(x^{2} + y^{2})}^{2} = 4 x^{2} y$ , $(- 1, 1)$
70288	Find the Derivative - d/dx	xcos(xy)	$x \cos (x y)$
70289	Evaluate the Integral	integral of x^2y with respect to x	$\int x^{2} y d x$
70290	Evaluate the Integral	integral from 1 to e of ( natural log of x)/(x^3) with respect to x	$\int_{1}^{e} \frac{\ln (x)}{x^{3}} d x$
70291	Evaluate the Limit	limit as x approaches 4 of square root of (x^2-3x+4)/(2x^2-x-1)	$lim_{x \to 4} \sqrt{\frac{x^{2} - 3 x + 4}{2 x^{2} - x - 1}}$
70292	Find dy/dx	y=(4cos(x))/(1+sin(x))	$y = \frac{4 \cos (x)}{1 + \sin (x)}$
70293	Evaluate the Limit	limit as x approaches c of 8/12	$lim_{x \to c} \frac{8}{12}$
70294	Find the Normal Line at (0,7)	y=x^4+7e^x , (0,7)	$y = x^{4} + 7 e^{x}$ , $(0, 7)$
70295	Find dy/dx	y+x^3y^4=-1	$y + x^{3} y^{4} = - 1$
70296	Find the Maximum/Minimum Value	f(x)=1/3x^3+x^2-3x	$f (x) = \frac{1}{3} x^{3} + x^{2} - 3 x$
70297	Evaluate the Limit	limit as x approaches c of (f(x))^2	$lim_{x \to c} {(f (x))}^{2}$
70298	Find Where Increasing/Decreasing	y=(x^3)/49-3x	$y = \frac{x^{3}}{49} - 3 x$
70299	Evaluate the Limit	limit as x approaches a of f(x)+g(x)	$lim_{x \to a} f (x) + g (x)$
70300	Use Logarithmic Differentiation to Find the Derivative	f(x)=x^(6x)	$f (x) = x^{6 x}$