Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69501	Find dy/dx	y=- square root of x	$y = - \sqrt{x}$
69502	Evaluate the Integral	integral from 1 to 3 of (4x-x^2) with respect to x	$\int_{1}^{3} (4 x - x^{2}) d x$
69503	Find the Tangent Line at x=π/2	y=cos(x) at x=pi/2	$y = \cos (x)$ at $x = \frac{π}{2}$
69504	Find dy/dx	y=x^2tan(x)	$y = x^{2} \tan (x)$
69505	Find the Derivative - d/dx	e^(-(x^2+y^2))	$e^{- (x^{2} + y^{2})}$
69506	Find the Derivative - d/dx	x^2-xcos(x)	$x^{2} - x \cos (x)$
69507	Find the Maximum/Minimum Value	f(x)=(x^2)/(x^2-1)	$f (x) = \frac{x^{2}}{x^{2} - 1}$
69508	Find the Derivative - d/dx	y=xarctanh(x)+ natural log of square root of 1-x^2	$y = x arctanh (x) + \ln (\sqrt{1 - x^{2}})$
69509	Evaluate the Limit	limit as x approaches 2 from the left of ( square root of 4-x^2)/(x-2)	$lim_{x \to 2^{-}} \frac{\sqrt{4 - x^{2}}}{x - 2}$
69510	Find the Derivative - d/dx	d/(dx)xcos(x)	$\frac{d}{d x} x \cos (x)$
69511	Find the Derivative - d/dx	(3x^5)(6x^4+x)^4	$(3 x^{5}) {(6 x^{4} + x)}^{4}$
69512	Find dy/dx	y^2(4-x)=x^2	$y^{2} (4 - x) = x^{2}$
69513	Find the Second Derivative	a	$a$
69514	Evaluate the Limit	limit as x approaches 0 of x^2cos(9/x)	$lim_{x \to 0} x^{2} \cos (\frac{9}{x})$
69515	Evaluate the Integral	integral of (6x)/((5+3x^2)^4) with respect to x	$\int \frac{6 x}{{(5 + 3 x^{2})}^{4}} d x$
69516	Find the Derivative - d/dx	2^( square root of x)	$2^{\sqrt{x}}$
69517	Find dx/dy	x^2-y^2=16	$x^{2} - y^{2} = 16$
69518	Find the Antiderivative	(x-2)^2	${(x - 2)}^{2}$
69519	Find the Derivative - d/dx	d/(dx)(cot(x))=-csc(x)^2	$\frac{d}{d x} (\cot (x)) = - \csc^{2} (x)$
69520	Find the Derivative - d/dx	9cos(x)-7x^2	$9 \cos (x) - 7 x^{2}$
69521	Find dy/dx	y=cos(pix)	$y = \cos (π x)$
69522	Find the Derivative - d/dx	(x^3-cos(x))^5	${(x^{3} - \cos (x))}^{5}$
69523	Evaluate the Limit	limit as x approaches 1 of (x^2-x)/(x^3-x^2+x-1)	$lim_{x \to 1} \frac{x^{2} - x}{x^{3} - x^{2} + x - 1}$
69524	Find the Derivative - d/dx	y=tan(x^2)	$y = \tan (x^{2})$
69525	Find the Derivative - d/dx	-y/(x+2y)	$- \frac{y}{x + 2 y}$
69526	Find the Maximum/Minimum Value	f(x)=(x+3)/(x-3)	$f (x) = \frac{x + 3}{x - 3}$
69527	Evaluate the Limit	limit as h approaches 0 of (cos(pi/6+h)-cos(pi/6))/h	$lim_{h \to 0} \frac{\cos (\frac{π}{6} + h) - \cos (\frac{π}{6})}{h}$
69528	Find Where Increasing/Decreasing	f(x)=-x^(3/4)	$f (x) = - x^{\frac{3}{4}}$
69529	Find the Derivative - d/dx	1/( square root of x^2+y^2)	$\frac{1}{\sqrt{x^{2} + y^{2}}}$
69530	Find dy/dx	e^(2x)=sin(x+3y)	$e^{2 x} = \sin (x + 3 y)$
69531	Evaluate the Limit	limit as x approaches 2 of ((3x-4)^40)/((x^2-2)^36)	$lim_{x \to 2} \frac{{(3 x - 4)}^{40}}{{(x^{2} - 2)}^{36}}$
69532	Find dy/dv	y=(2-v^2)/(2+v^2)	$y = \frac{2 - v^{2}}{2 + v^{2}}$
69533	Find the Second Derivative	e^(7x-4)	$e^{7 x - 4}$
69534	Evaluate the Integral	integral from 1/( square root of 3) to square root of 3 of 7/(1+x^2) with respect to x	$\int_{\frac{1}{\sqrt{3}}}^{\sqrt{3}} \frac{7}{1 + x^{2}} d x$
69535	Find dy/dx	e^(5xy)=6y	$e^{5 x y} = 6 y$
69536	Find the Derivative - d/dx	ax^3+bx^2+cx+d	$a x^{3} + b x^{2} + c x + d$
69537	Find the Fourth Derivative	f(x) = square root of x	$f (x) = \sqrt{x}$
69538	Find the Absolute Max and Min over the Interval	f(x)=8x^(3/4)-x on 0 , 4096	$f (x) = 8 x^{\frac{3}{4}} - x$ on $0$ , $4096$
69539	Evaluate the Limit	limit as x approaches 4 of ( square root of x)/(x^2+1)	$lim_{x \to 4} \frac{\sqrt{x}}{x^{2} + 1}$
69540	Find the Derivative - d/dx	e^(tan(x))-2	$e^{\tan (x)} - 2$
69541	Find the Derivative - d/dx	d/(dx)(-5x^2-4cos(x))	$\frac{d}{d x} (- 5 x^{2} - 4 \cos (x))$
69542	Find the Derivative - d/dx	y=(sin(x)-cos(x))/(sin(x)+cos(x))	$y = \frac{\sin (x) - \cos (x)}{\sin (x) + \cos (x)}$
69543	Evaluate Using Summation Formulas	sum from i=1 to n of (4i+3)/(n^2)	$\sum_{i = 1}^{n} \frac{4 i + 3}{n^{2}}$
69544	Find the Derivative - d/dy	yx^2	$y x^{2}$
69545	Find the Derivative - d/dx	e^x-x^e	$e^{x} - x^{e}$
69546	Find dy/dx	y=1/(1+x^2)	$y = \frac{1}{1 + x^{2}}$
69547	Evaluate the Limit	limit as x approaches 0 from the right of square root of x	$lim_{x \to 0^{+}} \sqrt{x}$
69548	Evaluate the Limit	limit as w approaches infinity of (3w^2+5w-2)/(5w^3+4w^2+1)	$lim_{w \to \infty} \frac{3 w^{2} + 5 w - 2}{5 w^{3} + 4 w^{2} + 1}$
69549	Find the Tangent Line at (16,32)	y=8 square root of x , (16,32)	$y = 8 \sqrt{x}$ , $(16, 32)$
69550	Evaluate the Integral	integral from 0 to e of natural log of x with respect to x	$\int_{0}^{e} \ln (x) d x$
69551	Evaluate the Integral	integral of (-6x^3+9x^2+4x-3) with respect to x	$\int (- 6 x^{3} + 9 x^{2} + 4 x - 3) d x$
69552	Use Logarithmic Differentiation to Find the Derivative	y=( square root of x)^x	$y = {(\sqrt{x})}^{x}$
69553	Find dr/ds	r=1/(4s^3)-6/(5s^4)	$r = \frac{1}{4 s^{3}} - \frac{6}{5 s^{4}}$
69554	Find the Derivative - d/dx	(1+x^2)	$(1 + x^{2})$
69555	Find the Derivative - d/dx	y=(x^2-x)(x+4)	$y = (x^{2} - x) (x + 4)$
69556	Find the Derivative - d/dx	(x^2+3)	$(x^{2} + 3)$
69557	Find the Derivative - d/dx	natural log of xcos(x)	$\ln (x) \cos (x)$
69558	Find the Maximum/Minimum Value	f(x)=2^x	$f (x) = 2^{x}$
69559	Evaluate the Limit	limit as x approaches 2 of 3^(x^2-3)	$lim_{x \to 2} 3^{x^{2} - 3}$
69560	Evaluate the Integral	integral from 0 to 3 of (4-x^2) with respect to x	$\int_{0}^{3} (4 - x^{2}) d x$
69561	Find the Maximum/Minimum Value	f(x)=x^2-16 natural log of x^2	$f (x) = x^{2} - 16 \ln (x^{2})$
69562	Integrate By Parts	integral of cos( natural log of x) with respect to x	$\int \cos (\ln (x)) d x$
69563	Find the Derivative - d/dx	y=(x^3)/6+1/(2x)	$y = \frac{x^{3}}{6} + \frac{1}{2 x}$
69564	Find dx/dy	x^3+3x^2y+y^3=8	$x^{3} + 3 x^{2} y + y^{3} = 8$
69565	Evaluate the Summation	sum from n=2 to infinity of 2/(n^2-1)	$\sum_{n = 2}^{\infty} \frac{2}{n^{2} - 1}$
69566	Evaluate the Integral	integral of (2-csc(x)^2) with respect to x	$\int (2 - \csc^{2} (x)) d x$
69567	Find the Derivative - d/dx	y=(x^5+3)*4x^3	$y = (x^{5} + 3) \cdot 4 x^{3}$
69568	Find the Derivative - d/dθ	sin(theta)^3	$\sin^{3} (θ)$
69569	Solve the Differential Equation	(dy)/(dx)=e^(x-y)	$\frac{d y}{d x} = e^{x - y}$
69570	Evaluate the Limit	limit as x approaches infinity of (x^2+2)/(x-1)	$lim_{x \to \infty} \frac{x^{2} + 2}{x - 1}$
69571	Find Where Increasing/Decreasing	f(x)=(x+2)^(2/3)	$f (x) = {(x + 2)}^{\frac{2}{3}}$
69572	Find the Relative Extrema	f(x)=x^3-3x	$f (x) = x^{3} - 3 x$
69573	Evaluate the Integral	integral from -1 to 0 of (x^5-4x^3+4x+4) with respect to x	$\int_{- 1}^{0} (x^{5} - 4 x^{3} + 4 x + 4) d x$
69574	Find the Derivative - d/dx	y=1/x+3/(x^2)+2/(x^3)	$y = \frac{1}{x} + \frac{3}{x^{2}} + \frac{2}{x^{3}}$
69575	Find the Derivative - d/dθ	3sec(theta)	$3 \sec (θ)$
69576	Find the Tangent Line at (0,0)	y=2xe^x , (0,0)	$y = 2 x e^{x}$ , $(0, 0)$
69577	Evaluate the Integral	integral from 0 to 31 of 1/( cube root of (1+4x)^2) with respect to x	$\int_{0}^{31} \frac{1}{\sqrt[3]{{(1 + 4 x)}^{2}}} d x$
69578	Find the Derivative - d/dR	1/R	$\frac{1}{R}$
69579	Find dy/dx	9x^2sin(y)=xy	$9 x^{2} \sin (y) = x y$
69580	Evaluate the Limit	limit as x approaches 2 of (3^x+x^2)/2	$lim_{x \to 2} \frac{3^{x} + x^{2}}{2}$
69581	Find the Derivative - d/dx	d/(dx)(-1/(x^2)-7/x)	$\frac{d}{d x} (- \frac{1}{x^{2}} - \frac{7}{x})$
69582	Find the Derivative - d/dx	square root of -x	$\sqrt{- x}$
69583	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y+3)	$\frac{d y}{d x} = \frac{x^{2}}{y + 3}$
69584	Evaluate the Limit	limit as x approaches c of 4f(x)	$lim_{x \to c} 4 f (x)$
69585	Find the Derivative - d/dx	y=1/(1-x)	$y = \frac{1}{1 - x}$
69586	Find the Tangent Line at (4,1)	y=(x^2-5x+5)^5 at (4,1)	$y = {(x^{2} - 5 x + 5)}^{5}$ at $(4, 1)$
69587	Find the Second Derivative	f(x)=a/(bx^2)	$f (x) = \frac{a}{b x^{2}}$
69588	Integrate By Parts	integral of x^3sin(x) with respect to x	$\int x^{3} \sin (x) d x$
69589	Evaluate the Summation	sum from n=2 to 4 of 3n^2-5n+7	$\sum_{n = 2}^{4} 3 n^{2} - 5 n + 7$
69590	Evaluate the Integral	integral from 1 to 3 of (t^2)/(5-2t) with respect to t	$\int_{1}^{3} \frac{t^{2}}{5 - 2 t} d t$
69591	Evaluate the Integral	integral of x^4csc(5x^5)^2 with respect to x	$\int x^{4} \csc^{2} (5 x^{5}) d x$
69592	Evaluate the Integral	integral of arctan(x/2) with respect to x	$\int \arctan (\frac{x}{2}) d x$
69593	Find the Derivative - d/dx	d/(dx)(-5x^(4/5)+3x^(2/3)+2)	$\frac{d}{d x} (- 5 x^{\frac{4}{5}} + 3 x^{\frac{2}{3}} + 2)$
69594	Find the Derivative - d/da	y=ax^2	$y = a x^{2}$
69595	Find Where Increasing/Decreasing	F(x)=x+3	$F (x) = x + 3$
69596	Find the Maximum/Minimum Value	y=ax^2+bx+c	$y = a x^{2} + b x + c$
69597	Find the Derivative - d/dx	d/(dx)e^(x^2)	$\frac{d}{d x} e^{x^{2}}$
69598	Evaluate the Derivative at a=1	h(x)=x^( square root of x) , a=1	$h (x) = x^{\sqrt{x}}$ , $a = 1$
69599	Find dy/dx	xsin(y)=ycos(x)	$x \sin (y) = y \cos (x)$
69600	Find the Derivative - d/dx	(x^2+2)	$(x^{2} + 2)$