Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70301	Find the Derivative - d/dx	y=arccot( square root of x)	$y = arccot (\sqrt{x})$
70302	Find the Antiderivative	1/(x^2+x)	$\frac{1}{x^{2} + x}$
70303	Find the Derivative - d/dx	natural log of 1+a/x	$\ln (1 + \frac{a}{x})$
70304	Evaluate the Limit	limit as x approaches -3 of (x^2+6x+9)/(2-2cos(2x+6))	$lim_{x \to - 3} \frac{x^{2} + 6 x + 9}{2 - 2 \cos (2 x + 6)}$
70305	Evaluate the Integral	integral from 2 to 4 of ( square root of x^2-4)/x with respect to x	$\int_{2}^{4} \frac{\sqrt{x^{2} - 4}}{x} d x$
70306	Evaluate the Integral	integral of (a+x)^3 with respect to x	$\int {(a + x)}^{3} d x$
70307	Find the Integral	arccos(x)	$\arccos (x)$
70308	Evaluate the Integral	integral of (2x^3-5x^2-2x-3)/(2x^2+x+1) with respect to x	$\int \frac{2 x^{3} - 5 x^{2} - 2 x - 3}{2 x^{2} + x + 1} d x$
70309	Find the Derivative - d/dx	natural log of \|cos(pi/x)\|	$\ln (\| \cos (\frac{π}{x}) \|)$
70310	Find the Tangent Line at (4,1/2)	f(x)=2/x at (4,1/2)	$f (x) = \frac{2}{x}$ at $(4, \frac{1}{2})$
70311	Evaluate the Integral	integral of x^3e^(-x^4) with respect to x	$\int x^{3} e^{- x^{4}} d x$
70312	Find dy/dx	square root of xy=8+x^2y	$\sqrt{x y} = 8 + x^{2} y$
70313	Evaluate the Integral	integral of (-4x^6+6x^4+3x^3+6) with respect to x	$\int (- 4 x^{6} + 6 x^{4} + 3 x^{3} + 6) d x$
70314	Find the Integral	f(x)=-3cos(x)-2sin(x)	$f (x) = - 3 \cos (x) - 2 \sin (x)$
70315	Find the Derivative - d/dx	y=1/xsin(x)	$y = \frac{1}{x} \sin (x)$
70316	Find Where Increasing/Decreasing	f(x)=-\|x+4\|-\|x+1\|	$f (x) = - \| x + 4 \| - \| x + 1 \|$
70317	Evaluate the Integral	integral from 0 to pi/4 of (sec(theta)tan(theta)) with respect to theta	$\int_{0}^{\frac{π}{4}} (\sec (θ) \tan (θ)) d θ$
70318	Find the Derivative - d/dx	x*cos(x)	$x \cdot \cos (x)$
70319	Find the Derivative - d/dx	e^xx	$e^{x} x$
70320	Evaluate the Summation	sum from n=1 to infinity of 1/n-1/(n+1)	$\sum_{n = 1}^{\infty} \frac{1}{n} - \frac{1}{n + 1}$
70321	Find dy/dx	y = square root of e^x	$y = \sqrt{e^{x}}$
70322	Find the Derivative - d/dx	y = square root of x^3+1	$y = \sqrt{x^{3} + 1}$
70323	Find the Maximum/Minimum Value	f(x)=x+108/(x^2)	$f (x) = x + \frac{108}{x^{2}}$
70324	Find dy/dx	square root of xy=x+3y	$\sqrt{x y} = x + 3 y$
70325	Find the Derivative - d/dz	2z	$2 z$
70326	Find dy/dx	y=1/3(x^2+2)^(3/2)	$y = \frac{1}{3} {(x^{2} + 2)}^{\frac{3}{2}}$
70327	Find the Derivative - d/dx	d/(dx)(sin(2x))	$\frac{d}{d x} (\sin (2 x))$
70328	Evaluate the Integral	integral of (x^3+x^2-x+1)/(x^3) with respect to x	$\int \frac{x^{3} + x^{2} - x + 1}{x^{3}} d x$
70329	Find the Maximum/Minimum Value	-1/2x^3+3/2x-1	$- \frac{1}{2} x^{3} + \frac{3}{2} x - 1$
70330	Verify the Differential Equation Solution	y''''=3x^2 , y=x^3-4	$y'' = 3 x^{2}$ , $y = x^{3} - 4$
70331	Evaluate the Integral	integral of x*f( natural log of x) with respect to x	$\int x \cdot f (\ln (x)) d x$
70332	Evaluate the Integral	integral of ( square root of x-1/x) with respect to x	$\int (\sqrt{x} - \frac{1}{x}) d x$
70333	Find the Derivative - d/dx	x^2+xy	$x^{2} + x y$
70334	Find dy/dx	xy^2-2x^3=2	$x y^{2} - 2 x^{3} = 2$
70335	Find the Derivative - d/dx	\|x^2+x\|	$\| x^{2} + x \|$
70336	Find the Derivative - d/dx	square root of x+1/x	$\sqrt{x + \frac{1}{x}}$
70337	Find the Derivative - d/dx	y=1/( square root of a^2-x^2)	$y = \frac{1}{\sqrt{a^{2} - x^{2}}}$
70338	Find the Derivative - d/dx	2 fifth root of x^2	$2 \sqrt[5]{x^{2}}$
70339	Integrate Using Partial Fractions	integral of (x^2+18)/(x^3-9x) with respect to x	$\int \frac{x^{2} + 18}{x^{3} - 9 x} d x$
70340	Evaluate the Limit	limit as x approaches 0.25 from the left of (4x-1)/(\|4x^3-x^2\|)	$lim_{x \to {0.25}^{-}} \frac{4 x - 1}{\| 4 x^{3} - x^{2} \|}$
70341	Find the Derivative - d/dx	(-cos(-x))	$(- \cos (- x))$
70342	Find the Derivative - d/dx	1/(2^x)	$\frac{1}{2^{x}}$
70343	Evaluate the Limit	limit as x approaches 0 of ( square root of 2x+9-3)/x	$lim_{x \to 0} \frac{\sqrt{2 x + 9} - 3}{x}$
70344	Find Where Increasing/Decreasing	f(x)=x+9/x	$f (x) = x + \frac{9}{x}$
70345	Find the Absolute Max and Min over the Interval	f(x)=4x^(3/4)-x on 0 , 256	$f (x) = 4 x^{\frac{3}{4}} - x$ on $0$ , $256$
70346	Evaluate the Limit	limit as x approaches 2 of (3f(x))/(g(x))	$lim_{x \to 2} \frac{3 f (x)}{g (x)}$
70347	Evaluate the Limit	limit as h approaches 0 of (1/(-2+h)+1/2)/h	$lim_{h \to 0} \frac{\frac{1}{- 2 + h} + \frac{1}{2}}{h}$
70348	Evaluate the Integral	integral of ( square root of 1-x^2)/(x^2) with respect to x	$\int \frac{\sqrt{1 - x^{2}}}{x^{2}} d x$
70349	Find dx/dy	y=e^(-x)sin(x)	$y = e^{- x} \sin (x)$
70350	Find the Maximum/Minimum Value	f(x)=3	$f (x) = 3$
70351	Find the Area Between the Curves	f(x)=12x+x^2-x^3 , g(x)=0	$f (x) = 12 x + x^{2} - x^{3}$ , $g (x) = 0$
70352	Evaluate the Limit	limit as x approaches c of cube root of 27	$lim_{x \to c} \sqrt[3]{27}$
70353	Evaluate the Limit	limit as x approaches 1 from the right of x^(1/(1-x))	$lim_{x \to 1^{+}} x^{\frac{1}{1 - x}}$
70354	Find the Integral	x^(-3/2)	$x^{- \frac{3}{2}}$
70355	Find the Derivative - d/dx	(2x-1)^5(x+1)	${(2 x - 1)}^{5} (x + 1)$
70356	Solve the Differential Equation	y''''=y	$y'' = y$
70357	Find the Derivative - d/dx	x^2-1/(x^2)	$x^{2} - \frac{1}{x^{2}}$
70358	Find the Derivative - d/dx	-1/(x^2)+1	$- \frac{1}{x^{2}} + 1$
70359	Find dy/dx	square root of xy=7+x^2y	$\sqrt{x y} = 7 + x^{2} y$
70360	Find Where Increasing/Decreasing	f(x) = square root of 16-x^2	$f (x) = \sqrt{16 - x^{2}}$
70361	Evaluate the Limit	limit as x approaches 2 of 1/(x-2)-6/(x^2+2x-8)	$lim_{x \to 2} \frac{1}{x - 2} - \frac{6}{x^{2} + 2 x - 8}$
70362	Find the Derivative - d/dx	pix^2y	$π x^{2} y$
70363	Find the Maximum/Minimum Value	f(x)=3x^4-16x^3+18x^2	$f (x) = 3 x^{4} - 16 x^{3} + 18 x^{2}$
70364	Find dy/dx	y=arccos(1/x)	$y = \arccos (\frac{1}{x})$
70365	Evaluate the Integral	integral of (2x^3+2x-3) with respect to x	$\int (2 x^{3} + 2 x - 3) d x$
70366	Find the Derivative - d/dx	(3x^2)/(2y)	$\frac{3 x^{2}}{2 y}$
70367	Evaluate the Limit	limit as x approaches 4 of (x^2-16)/( square root of x-2)	$lim_{x \to 4} \frac{x^{2} - 16}{\sqrt{x - 2}}$
70368	Evaluate the Integral	integral of 3x(6-x^2) with respect to x	$\int 3 x (6 - x^{2}) d x$
70369	Find the Integral	e^xsin(x)	$e^{x} \sin (x)$
70370	Integrate Using u-Substitution	integral of x/( square root of x-1) with respect to x	$\int \frac{x}{\sqrt{x - 1}} d x$
70371	Find dy/dx	y=tan(x^2-4x)	$y = \tan (x^{2} - 4 x)$
70372	Find the Derivative - d/dx	y=cos(x)x^3	$y = \cos (x) x^{3}$
70373	Find the Maximum/Minimum Value	f(x) = natural log of x^4+27	$f (x) = \ln (x^{4} + 27)$
70374	Find the Maximum/Minimum Value	f(x)=e^(6x)+e^(-x)	$f (x) = e^{6 x} + e^{- x}$
70375	Evaluate the Integral	integral from 1 to 4 of ((x^2)/2-x+3) with respect to x	$\int_{1}^{4} (\frac{x^{2}}{2} - x + 3) d x$
70376	Evaluate the Integral	integral of (sec(x)-cot(x))^2 with respect to x	$\int {(\sec (x) - \cot (x))}^{2} d x$
70377	Find Where Increasing/Decreasing	f''''(x)=(e^(-x)-e^5)(e^x+e^-2)	$f'' (x) = (e^{- x} - e^{5}) (e^{x} + e^{- 2})$
70378	Integrate Using Trig Substitution	integral of 1/(x square root of 9+4x^2) with respect to x	$\int \frac{1}{x \sqrt{9 + 4 x^{2}}} d x$
70379	Find Where Increasing/Decreasing	f(x)=x^5 natural log of x	$f (x) = x^{5} \ln (x)$
70380	Find the Derivative - d/dx	x^5-5^x	$x^{5} - 5^{x}$
70381	Find the Derivative - d/dx	7sin(x)-2x^3	$7 \sin (x) - 2 x^{3}$
70382	Find the Derivative - d/dt	e^(-t)sin(t)	$e^{- t} \sin (t)$
70383	Find dy/dx	3x^4y^2-7xy^3=4-8y	$3 x^{4} y^{2} - 7 x y^{3} = 4 - 8 y$
70384	Find dy/dx	4xy-3y=1	$4 x y - 3 y = 1$
70385	Find the Domain and Range	f(x)=\|x\| if -1<=x<0; x^3 if x>=0	$f (x) = {\begin{cases} \| x \| & - 1 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$
70386	Find the Derivative - d/dx	y=(x^4+3)(-4x^5+5x^4+5)	$y = (x^{4} + 3) (- 4 x^{5} + 5 x^{4} + 5)$
70387	Find the Derivative - d/dt	2/3t^(3/2)	$\frac{2}{3} t^{\frac{3}{2}}$
70388	Find dy/dx	(2y+1)^3-24x=-3	${(2 y + 1)}^{3} - 24 x = - 3$
70389	Evaluate the Limit	limit as x approaches 2 of x^3f(x)	$lim_{x \to 2} x^{3} f (x)$
70390	Find Where Increasing/Decreasing	f(x)=-(x^4)/4-x^3-x^2	$f (x) = - \frac{x^{4}}{4} - x^{3} - x^{2}$
70391	Evaluate the Integral	integral of 1/(x^2+y^2) with respect to x	$\int \frac{1}{x^{2} + y^{2}} d x$
70392	Evaluate the Integral	integral from 4 to infinity of 1/((x-3)^(3/2)) with respect to x	$\int_{4}^{\infty} \frac{1}{{(x - 3)}^{\frac{3}{2}}} d x$
70393	Find dy/dx	y^3=4x	$y^{3} = 4 x$
70394	Find the Derivative - d/dv	y=ae^v+b/v+cv^2	$y = a e^{v} + \frac{b}{v} + c v^{2}$
70395	Evaluate the Limit	limit as x approaches 0 from the right of 5/x-2/(3x^2)	$lim_{x \to 0^{+}} \frac{5}{x} - \frac{2}{3 x^{2}}$
70396	Find the Antiderivative	(7x)/(x^2-x-2)	$\frac{7 x}{x^{2} - x - 2}$
70397	Find Where Increasing/Decreasing	f(x)=(x^4)/4+x^3+x^2	$f (x) = \frac{x^{4}}{4} + x^{3} + x^{2}$
70398	Find the Tangent Line at (-2,-4)	h(x)=(x^2-3)(x^3-2x) , (-2,-4)	$h (x) = (x^{2} - 3) (x^{3} - 2 x)$ , $(- 2, - 4)$
70399	Evaluate the Integral	integral of (9x^5-3x^2+7) with respect to x	$\int (9 x^{5} - 3 x^{2} + 7) d x$
70400	Evaluate the Integral	integral of 19z^3e^z with respect to z	$\int 19 z^{3} e^{z} d z$