Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84301	Find dy/dx	-x^2-y+5y^2=-5	$- x^{2} - y + 5 y^{2} = - 5$
84302	Evaluate the Limit	limit as x approaches 4 of (1+ cube root of x)(2-x^2+3x^3)	$lim_{x \to 4} (1 + \sqrt[3]{x}) (2 - x^{2} + 3 x^{3})$
84303	Evaluate the Integral	integral from 0 to a of 6x square root of a^2-x^2 with respect to x	$\int_{0}^{a} 6 x \sqrt{a^{2} - x^{2}} d x$
84304	Find the Derivative - d/dx	(e^x-1)^2	${(e^{x} - 1)}^{2}$
84305	Find the Derivative - d/dx	(2sin(x))/(sec(x))	$\frac{2 \sin (x)}{\sec (x)}$
84306	Find the Derivative - d/dx	x^2+4^y	$x^{2} + 4^{y}$
84307	Find the Second Derivative	2sin(x)+sin(2x)	$2 \sin (x) + \sin (2 x)$
84308	Integrate By Parts	integral of square root of 1-x^2 with respect to x	$\int \sqrt{1 - x^{2}} d x$
84309	Evaluate the Integral	integral from 0 to infinity of sin(x) with respect to x	$\int_{0}^{\infty} \sin (x) d x$
84310	Find the Tangent Line at (1,-7)	y=x^3-8x , (1,-7)	$y = x^{3} - 8 x$ , $(1, - 7)$
84311	Find dy/dx	y = square root of (4x^2)/(2-2x)	$y = \sqrt{\frac{4 x^{2}}{2 - 2 x}}$
84312	Evaluate the Summation	5 sum from i=1 to 14 of i^2+13	$5 \sum_{i = 1}^{14} i^{2} + 13$
84313	Find dy/dx	y=sinh(5x)^2	$y = \sinh^{2} (5 x)$
84314	Find the Derivative - d/dx	( square root of x^5)/2	$\frac{\sqrt{x^{5}}}{2}$
84315	Find the Integral	1+x^2	$1 + x^{2}$
84316	Find the Derivative - d/dx	2/(x^(1/3))-2	$\frac{2}{x^{\frac{1}{3}}} - 2$
84317	Find the Derivative - d/dx	5xy-x^2-y^2-5	$5 x y - x^{2} - y^{2} - 5$
84318	Evaluate the Integral	integral of (5 square root of x) with respect to x	$\int (5 \sqrt{x}) d x$
84319	Find the Antiderivative	f(x)=(x^3)/2-cos(3x)	$f (x) = \frac{x^{3}}{2} - \cos (3 x)$
84320	Find the Integral	(x^3)/(x^2+1)	$\frac{x^{3}}{x^{2} + 1}$
84321	Evaluate Using Summation Formulas	sum from i=1 to n of 1	$\sum_{i = 1}^{n} 1$
84322	Find the Maximum/Minimum Value	4(x-1)(x+3)	$4 (x - 1) (x + 3)$
84323	Evaluate the Integral	integral of tan(5x)^4 with respect to x	$\int \tan^{4} (5 x) d x$
84324	Find the Antiderivative	f(x)=(2x^2+5)/(x^2+1)	$f (x) = \frac{2 x^{2} + 5}{x^{2} + 1}$
84325	Find the Inflection Points	y=x^2e^x	$y = x^{2} e^{x}$
84326	Evaluate the Integral	integral from 0 to 1 of 1/((x-1)^(1/3)) with respect to x	$\int_{0}^{1} \frac{1}{{(x - 1)}^{\frac{1}{3}}} d x$
84327	Evaluate Using Summation Formulas	limit as n approaches infinity of sum from i=1 to n of (1+i/n)(2/n)	$lim_{n \to \infty} \sum_{i = 1}^{n} (1 + \frac{i}{n}) (\frac{2}{n})$
84328	Evaluate the Integral	integral from -1 to 1 of e^y-y^2+2 with respect to y	$\int_{- 1}^{1} e^{y} - y^{2} + 2 d y$
84329	Find Where Increasing/Decreasing	h'(x)=(x+5)/(x+1)	$h' (x) = \frac{(x + 5)}{(x + 1)}$
84330	Evaluate the Integral	- integral from 1 to 0 of x with respect to x	$- \int_{1}^{0} x d x$
84331	Evaluate the Limit	limit as x approaches 5 of ( natural log of x- natural log of 5)/(x-5)	$lim_{x \to 5} \frac{\ln (x) - \ln (5)}{x - 5}$
84332	Evaluate the Integral	integral of (3x^3+6+6x) with respect to x	$\int (3 x^{3} + 6 + 6 x) d x$
84333	Find the Inflection Points	3/10x^5+x^4+x^3	$\frac{3}{10} x^{5} + x^{4} + x^{3}$
84334	Find the Integral	2/(x^5)dx	$\frac{2}{x^{5}} d x$
84335	Find the Percentage Rate of Change	y=0.5(3/4)^t	$y = 0.5 {(\frac{3}{4})}^{t}$
84336	Find the Third Derivative	y=2x natural log of 5x^2	$y = 2 x \ln (5 x^{2})$
84337	Find the Derivative - d/dh	2pirh	$2 π r h$
84338	Evaluate the Integral	integral from pi/4 to pi/2 of sin(x)^3cos(x) square root of 2sin(x)^2-1 with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{2}} \sin^{3} (x) \cos (x) \sqrt{2 \sin^{2} (x) - 1} d x$
84339	Find dz/dx	z=3x^2-6y^2+xy+5y-9	$z = 3 x^{2} - 6 y^{2} + x y + 5 y - 9$
84340	Find dy/dx	Derive y=1/( cube root of x)-2/( square root of x^5)+ fifth root of x^2	Derive $y = \frac{1}{\sqrt[3]{x}} - \frac{2}{\sqrt{x^{5}}} + \sqrt[5]{x^{2}}$
84341	Find the Derivative - d/dx	(f(x))/(e^x)	$\frac{f (x)}{e^{x}}$
84342	Find dy/dx	y^2-4xy+arctan(x)=4	$y^{2} - 4 x y + \arctan (x) = 4$
84343	Find the Antiderivative	1^x	$1^{x}$
84344	Evaluate the Limit	limit as x approaches pi/2 of 7tan(x)	$lim_{x \to \frac{π}{2}} 7 \tan (x)$
84345	Find the Antiderivative	S(t)=t^2-t/2+ square root of t	$S (t) = t^{2} - \frac{t}{2} + \sqrt{t}$
84346	Find dy/dx	(x^3+3y)^6=x	${(x^{3} + 3 y)}^{6} = x$
84347	Evaluate the Integral	integral of 3x^2(x+6)^2 with respect to x	$\int 3 x^{2} {(x + 6)}^{2} d x$
84348	Find the Antiderivative	(x^3+1)^2	${(x^{3} + 1)}^{2}$
84349	Evaluate the Limit	limit as x approaches 0 of \|x/(x+1)\|	$lim_{x \to 0} \| \frac{x}{x + 1} \|$
84350	Find dy/dx	1-3y^2-xy^3=-x	$1 - 3 y^{2} - x y^{3} = - x$
84351	Evaluate the Integral	integral from e^49 to e^64 of 1/(x square root of natural log of x) with respect to x	$\int_{e^{49}}^{e^{64}} \frac{1}{x \sqrt{\ln (x)}} d x$
84352	Solve the Differential Equation	y''-y=0	$y'' - y = 0$
84353	Evaluate the Limit	limit as x approaches negative infinity of (3x^3-10)/(x+4)	$lim_{x \to - \infty} \frac{3 x^{3} - 10}{x + 4}$
84354	Find the Derivative - d/dx	square root of 3sin(x)+cos(x)	$\sqrt{3} \sin (x) + \cos (x)$
84355	Find the Antiderivative	f(x)=cot(x)(-8sin(x)-10csc(x))	$f (x) = \cot (x) (- 8 \sin (x) - 10 \csc (x))$
84356	Evaluate the Limit	limit as x approaches infinity of -1+x^2-x^3+3x^4	$lim_{x \to \infty} - 1 + x^{2} - x^{3} + 3 x^{4}$
84357	Find Where Increasing/Decreasing	f(x)=-1/4e^(x-3)	$f (x) = - \frac{1}{4} e^{x - 3}$
84358	Evaluate the Integral	integral from 0 to 1 of 2/7x^3+1/5x^2+1/2x with respect to x	$\int_{0}^{1} \frac{2}{7} x^{3} + \frac{1}{5} x^{2} + \frac{1}{2} x d x$
84359	Find the Derivative - d/dx	xe^x-x	$x e^{x} - x$
84360	Find the Derivative - d/dy	2ye^(y^2)	$2 y e^{y^{2}}$
84361	Find the Derivative - d/dx	y=(1-cos(4x))/(sin(4x))	$y = \frac{1 - \cos (4 x)}{\sin (4 x)}$
84362	Find the Derivative - d/dx	cube root of x^2(2x-x^2)	$\sqrt[3]{x^{2}} (2 x - x^{2})$
84363	Find the Derivative - d/dx	(x-1)^2(x-2)(x-4)	${(x - 1)}^{2} (x - 2) (x - 4)$
84364	Find the Center and Radius	-x^2-12x+3y^2-24y=0	$- x^{2} - 12 x + 3 y^{2} - 24 y = 0$
84365	Find Where Increasing/Decreasing	f(x)=6x^5-15x^4+10x^3	$f (x) = 6 x^{5} - 15 x^{4} + 10 x^{3}$
84366	Find the Derivative - d/dx	(-x)/(x^2+4)	$\frac{- x}{x^{2} + 4}$
84367	Find the Antiderivative	f(x)=cos(x)-1	$f (x) = \cos (x) - 1$
84368	Find the Center and Radius	(x-5)2+(y-6)2=81	$(x - 5) \cdot 2 + (y - 6) \cdot 2 = 81$
84369	Find the Derivative - d/dx	(x^3)/3+e^x	$\frac{x^{3}}{3} + e^{x}$
84370	Find the Second Derivative	f(x)=-x^2+2/3x^3+1/2x^-3	$f (x) = - x^{2} + \frac{2}{3} x^{3} + \frac{1}{2} x^{- 3}$
84371	Find the Concavity	1/6x^4+x^3-10x^2	$\frac{1}{6} x^{4} + x^{3} - 10 x^{2}$
84372	Find Where Increasing/Decreasing	f(x)=- log base 2 of x-1	$f (x) = - \log_{2} (x - 1)$
84373	Find the Derivative - d/dx	xcos(pix)+sin(x)	$x \cos (π x) + \sin (x)$
84374	Find the Derivative - d/dx	d/(dx)( natural log of e^(2x))	$\frac{d}{d x} (\ln (e^{2 x}))$
84375	Find the Antiderivative	x^3*e^x	$x^{3} \cdot e^{x}$
84376	Find the Maximum/Minimum Value	e^(-x)(x^2+2x)	$e^{- x} (x^{2} + 2 x)$
84377	Evaluate the Limit	limit as z approaches 3 of z(2z-z^2)	$lim_{z \to 3} z (2 z - z^{2})$
84378	Evaluate the Integral	integral of (2+x^3) with respect to x	$\int (2 + x^{3}) d x$
84379	Find the Derivative - d/dx	- fifth root of x^6	$- \sqrt[5]{x^{6}}$
84380	Evaluate the Integral	integral of (1-x)/(x^2) with respect to x	$\int \frac{1 - x}{x^{2}} d x$
84381	Find the Antiderivative	f(x)=x^(3/4)+8 cube root of x+3x^5	$f (x) = x^{\frac{3}{4}} + 8 \sqrt[3]{x} + 3 x^{5}$
84382	Find the Derivative - d/dx	1/2sec(x)^2	$\frac{1}{2} \sec^{2} (x)$
84383	Find the Derivative - d/dx	-y/(x-1)	$- \frac{y}{x - 1}$
84384	Find the Derivative - d/dx	e^(1/2x^2)	$e^{\frac{1}{2} x^{2}}$
84385	Find the Antiderivative	(x^3)/( square root of x^2+1)	$\frac{x^{3}}{\sqrt{x^{2} + 1}}$
84386	Find the Derivative of the Integral	h(x) = integral from 1 to square root of x of (5z^2)/(z^4+1) with respect to z	$h (x) = \int_{1}^{\sqrt{x}} \frac{5 z^{2}}{z^{4} + 1} d z$
84387	Evaluate the Limit	limit as x approaches 2 of ( square root of x+7+3)/x	$lim_{x \to 2} \frac{\sqrt{x + 7} + 3}{x}$
84388	Evaluate the Limit	limit as x approaches infinity of (x^4)/(3x^2-7x)	$lim_{x \to \infty} \frac{x^{4}}{3 x^{2} - 7 x}$
84389	Find the Derivative - d/dx	4x^4-1/(4x^4)	$4 x^{4} - \frac{1}{4 x^{4}}$
84390	Find the Third Derivative	S(t)=1/3t^3-3.5t^2+10t	$S (t) = \frac{1}{3} t^{3} - 3.5 t^{2} + 10 t$
84391	Find dy/dx	y=(x^3-4)^4sin(3x^3)	$y = {(x^{3} - 4)}^{4} \sin (3 x^{3})$
84392	Determine if Continuous	f(x)=x+2 if x<0; e^x if 0<=x<=1; 2-x if x>1	$f (x) = {\begin{cases} x + 2 & x < 0 \\ e^{x} & 0 \leq x \leq 1 \\ 2 - x & x > 1 \end{cases}$
84393	Find the Derivative - d/dx	D_x((2x+5)/(x^2-1))	$D_{x} (\frac{2 x + 5}{x^{2} - 1})$
84394	Find dy/dx	(4x+y)^4=3y	${(4 x + y)}^{4} = 3 y$
84395	Evaluate the Limit	limit as x approaches -4 of (4x^2+4x-8)/(ax^2+bx+8)=9/5	$lim_{x \to - 4} \frac{4 x^{2} + 4 x - 8}{a x^{2} + b x + 8} = \frac{9}{5}$
84396	Find dy/dx	y=sin(x)+cos(x)	$y = \sin (x) + \cos (x)$
84397	Evaluate the Integral	integral of -2/(x square root of x^2-36) with respect to x	$\int \frac{- 2}{x \sqrt{x^{2} - 36}} d x$
84398	Find the Antiderivative	cube root of 1+7x	$\sqrt[3]{1 + 7 x}$
84399	Find dx/dy	3x^2+5x^2y^2=2y	$3 x^{2} + 5 x^{2} y^{2} = 2 y$
84400	Integrate By Parts	integral of xsin(3x) with respect to x	$\int x \sin (3 x) d x$