Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83001	Find the Derivative - d/dx	natural log of 2x+y	$\ln (2 x + y)$
83002	Evaluate the Integral	integral of (2x^2+5x)/x with respect to x	$\int \frac{2 x^{2} + 5 x}{x} d x$
83003	Find the Derivative - d/dx	natural log of sec(2x)+6tan(x)	$\ln (\sec (2 x) + 6 \tan (x))$
83004	Find the Derivative - d/dx	x^(n+1)	$x^{n + 1}$
83005	Find the Third Derivative	(3-5x)^5	${(3 - 5 x)}^{5}$
83006	Find dy/dx	sin(xy)=x^2	$\sin (x y) = x^{2}$
83007	Evaluate the Limit	limit as x approaches 3 of (3x^2+4x-39)/(x^2-9)	$lim_{x \to 3} \frac{3 x^{2} + 4 x - 39}{x^{2} - 9}$
83008	Find the Tangent Line at (0,-3)	y=-3/((3x^2+1)^3) , (0,-3)	$y = \frac{- 3}{{(3 x^{2} + 1)}^{3}}$ , $(0, - 3)$
83009	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x- square root of 6-x)/(4+x^2)	$lim_{x \to 2} \frac{\sqrt{2 x} - \sqrt{6 - x}}{4 + x^{2}}$
83010	Evaluate the Integral	integral of ((x^6+5x^9-4)/(x^3)) with respect to x	$\int (\frac{x^{6} + 5 x^{9} - 4}{x^{3}}) d x$
83011	Evaluate the Integral	integral of (7+t) square root of t with respect to t	$\int (7 + t) \sqrt{t} d t$
83012	Find dx/dy	x/(y^3)=1	$\frac{x}{y^{3}} = 1$
83013	Find the Derivative - d/dy	(1+x+y)/( square root of 1+x^2+y^2)	$\frac{1 + x + y}{\sqrt{1 + x^{2} + y^{2}}}$
83014	Integrate Using u-Substitution	integral of x^2 square root of x-1 with respect to x	$\int x^{2} \sqrt{x - 1} d x$
83015	Evaluate the Limit	limit as x approaches pi/2 of sin(2x)+tan((5x)/2)	$lim_{x \to \frac{π}{2}} \sin (2 x) + \tan (\frac{5 x}{2})$
83016	Find Where Increasing/Decreasing	f(x)=-x^3+15x^2-75x+125	$f (x) = - x^{3} + 15 x^{2} - 75 x + 125$
83017	Find the Antiderivative	1959*e^(1959x)	$1959 \cdot e^{1959 x}$
83018	Find the Integral	1/( square root of 1-x)	$\frac{1}{\sqrt{1 - x}}$
83019	Evaluate the Integral	integral of (3 square root of x^5)/2 with respect to x	$\int \frac{3 \sqrt{x^{5}}}{2} d x$
83020	Find the Derivative - d/dx	(70x)/((3x^2+8)^2)	$\frac{70 x}{{(3 x^{2} + 8)}^{2}}$
83021	Find the Derivative - d/dr	y=-3r^5-5r^2	$y = - 3 r^{5} - 5 r^{2}$
83022	Evaluate the Integral	integral of (e^t+1/t) with respect to t	$\int (e^{t} + \frac{1}{t}) d t$
83023	Evaluate the Integral	integral from 4 to 8 of 1/(x natural log of x^2) with respect to x	$\int_{4}^{8} \frac{1}{x \ln (x^{2})} d x$
83024	Find the Derivative - d/dx	2x+cos(2x)	$2 x + \cos (2 x)$
83025	Evaluate the Limit	limit as x approaches 0 of square root of 6(x^2+24)	$lim_{x \to 0} \sqrt{6 (x^{2} + 24)}$
83026	Evaluate the Integral	integral of (9x(x^2-10)^8)/5 with respect to x	$\int \frac{9 x {(x^{2} - 10)}^{8}}{5} d x$
83027	Eliminate the Parameter	x=sin(t)^2 and y=cos(t)	$x = \sin^{2} (t)$ and $y = \cos (t)$
83028	Evaluate the Limit	limit as x approaches 0 from the left of csc(x)-cot(x+pi)	$lim_{x \to 0^{-}} \csc (x) - \cot (x + π)$
83029	Find Where Increasing/Decreasing	y=1/2x^3+x^2-3x+1	$y = \frac{1}{2} x^{3} + x^{2} - 3 x + 1$
83030	Find the Derivative - d/dx	y=x/(3-2x^2)	$y = \frac{x}{3 - 2 x^{2}}$
83031	Find the Derivative - d/dx	(x+xy+y)^3	${(x + x y + y)}^{3}$
83032	Find the Antiderivative	e^x+1/x	$e^{x} + \frac{1}{x}$
83033	Find the Antiderivative	f(x)=e	$f (x) = e$
83034	Find the Local Maxima and Minima	f(x)=-1/2x^4+8x^3-32x^2-5	$f (x) = - \frac{1}{2} x^{4} + 8 x^{3} - 32 x^{2} - 5$
83035	Evaluate the Limit	limit as x approaches infinity of (x+5)/(2x^2+1)	$lim_{x \to \infty} \frac{x + 5}{2 x^{2} + 1}$
83036	Use Logarithmic Differentiation to Find the Derivative	f(x) = natural log of e^xx^3(x+1)^4	$f (x) = \ln (e^{x} x^{3} {(x + 1)}^{4})$
83037	Find the Derivative - d/dx	x-sin(2x)	$x - \sin (2 x)$
83038	Find the Derivative - d/dy	x^2+y	$x^{2} + y$
83039	Evaluate the Integral	integral of (4x-csc(x)^2) with respect to x	$\int (4 x - \csc^{2} (x)) d x$
83040	Evaluate the Limit	limit as x approaches negative infinity of (3x^7+x^5-15)/(4x^2+32x)	$lim_{x \to - \infty} \frac{3 x^{7} + x^{5} - 15}{4 x^{2} + 32 x}$
83041	Find the Derivative - d/dx	-2 fourth root of x	$- 2 \sqrt[4]{x}$
83042	Find dy/dx	-4y-2=-2xy	$- 4 y - 2 = - 2 x y$
83043	Find the Slope at (1/2,8) Using Implicit Differentiation	f(t)=t^-3 ;, (1/2,8)	$f (t) = t^{- 3}$ ;, $(\frac{1}{2}, 8)$
83044	Evaluate the Limit	limit as x approaches infinity of (-x^2)/(4x+4)	$lim_{x \to \infty} \frac{- x^{2}}{4 x + 4}$
83045	Find Where Increasing/Decreasing	y=2x^3-3x^2-12x	$y = 2 x^{3} - 3 x^{2} - 12 x$
83046	Evaluate the Limit	limit as x approaches -1 of (x^2+6x+5)/(x^2+x)	$lim_{x \to - 1} \frac{x^{2} + 6 x + 5}{x^{2} + x}$
83047	Find the Derivative - d/dx	1/2cos(2x)	$\frac{1}{2} \cos (2 x)$
83048	Find the Derivative - d/dt	rt^(r-1)	$r t^{r - 1}$
83049	Find the Derivative - d/dx	e^xsin(x)+e^xcos(x)	$e^{x} \sin (x) + e^{x} \cos (x)$
83050	Find the Integral	x^2dz	$x^{2} d z$
83051	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)+tan(5x))/(1-cos(x)-tan(x))	$lim_{x \to 0} \frac{1 - \cos (x) + \tan (5 x)}{1 - \cos (x) - \tan (x)}$
83052	Evaluate the Integral	integral from 0 to a of 7x square root of a^2-x^2 with respect to x	$\int_{0}^{a} 7 x \sqrt{a^{2} - x^{2}} d x$
83053	Find the Antiderivative	1/(x^2+5x+6)	$\frac{1}{x^{2} + 5 x + 6}$
83054	Integrate By Parts	integral of 5x natural log of x with respect to x	$\int 5 x \ln (x) d x$
83055	Find the Derivative - d/dx	(3x^2-6x+1)^2	${(3 x^{2} - 6 x + 1)}^{2}$
83056	Find the Antiderivative	(1/3)x^3-5x	$(\frac{1}{3}) x^{3} - 5 x$
83057	Integrate Using u-Substitution	integral of sin( natural log of x) with respect to x	$\int \sin (\ln (x)) d x$
83058	Find the Critical Points	f(x) = square root of x+2-1	$f (x) = \sqrt{x + 2} - 1$
83059	Find the Derivative - d/dx	y=e^(2x^6-8x^5)	$y = e^{2 x^{6} - 8 x^{5}}$
83060	Find the Antiderivative	f(x) = fifth root of x-2e^x	$f (x) = \sqrt[5]{x} - 2 e^{x}$
83061	Find the Derivative - d/dx	(x+y^2) square root of e^x+2/e	$(x + y^{2}) \sqrt{e^{x}} + \frac{2}{e}$
83062	Find dy/dx	2y^3-2-xy=5x^3	$2 y^{3} - 2 - x y = 5 x^{3}$
83063	Evaluate the Summation	sum from x=1 to 4 of x^3+3x^2+3x+1	$\sum_{x = 1}^{4} x^{3} + 3 x^{2} + 3 x + 1$
83064	Find the Antiderivative	1+ square root of x	$1 + \sqrt{x}$
83065	Find the Turning Points	p(x)=(x-7)(x+4)(x-2)	$p (x) = (x - 7) (x + 4) (x - 2)$
83066	Find the Maximum/Minimum Value	y=-1+3sin(x-pi/4)	$y = - 1 + 3 \sin (x - \frac{π}{4})$
83067	Find Where Increasing/Decreasing	f(x)=-1/2 square root of x	$f (x) = - \frac{1}{2} \sqrt{x}$
83068	Find the Derivative - d/dx	xcos(pix)	$x \cos (π x)$
83069	Find the Inflection Points	1/4x^4+5x^3+75/2x^2	$\frac{1}{4} x^{4} + 5 x^{3} + \frac{75}{2} x^{2}$
83070	Evaluate the Integral	integral of ((x^4)/2+(5x^3)/3-2x) with respect to x	$\int (\frac{x^{4}}{2} + \frac{5 x^{3}}{3} - 2 x) d x$
83071	Find dy/dx	y=x/(2x+1)	$y = \frac{x}{2 x + 1}$
83072	Find the Antiderivative	f(x)=(e^((a+1)x))/a	$f (x) = \frac{e^{(a + 1) x}}{a}$
83073	Evaluate the Integral	integral from 0 to pi/2 of tan(x)^2sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{2}} \tan^{2} (x) \sec^{2} (x) d x$
83074	Find Where Increasing/Decreasing	y=(-x-1)^2+3	$y = {(- x - 1)}^{2} + 3$
83075	Evaluate the Integral	integral from 1 to 4 of (4x^2+ square root of x) with respect to x	$\int_{1}^{4} (4 x^{2} + \sqrt{x}) d x$
83076	Evaluate the Limit	limit as x approaches 0 of ((-4+x)^2-16)/(-2x)	$lim_{x \to 0} \frac{{(- 4 + x)}^{2} - 16}{- 2 x}$
83077	Find the Derivative - d/dx	cos(5x^2-x)	$\cos (5 x^{2} - x)$
83078	Evaluate the Limit	limit as x approaches infinity of (x^-3+3x^-2+1)/(x^-2+x^-1+3)	$lim_{x \to \infty} \frac{x^{- 3} + 3 x^{- 2} + 1}{x^{- 2} + x^{- 1} + 3}$
83079	Find dy/dx	-y^2+3x^3-xy=0	$- y^{2} + 3 x^{3} - x y = 0$
83080	Find the Derivative of the Integral	F(x) = integral from x to 0 of square root of t^2+25 with respect to t	$F (x) = \int_{x}^{0} \sqrt{t^{2} + 25} d t$
83081	Find the Inflection Points	3/10x^5+5x^4	$\frac{3}{10} x^{5} + 5 x^{4}$
83082	Find the Maximum/Minimum Value	f(x)=-4sin(x)	$f (x) = - 4 \sin (x)$
83083	Evaluate the Integral	integral of (sin(2x)) with respect to x	$\int (\sin (2 x)) d x$
83084	Find the Second Derivative	f(x)=6x^(7/2)+4x^(5/2)+2x	$f (x) = 6 x^{\frac{7}{2}} + 4 x^{\frac{5}{2}} + 2 x$
83085	Find Where Increasing/Decreasing	x^4-8x^3+16x^2	$x^{4} - 8 x^{3} + 16 x^{2}$
83086	Find the Maximum/Minimum Value	f(x)=-x^4+3x^2+2x	$f (x) = - x^{4} + 3 x^{2} + 2 x$
83087	Find the Second Derivative	2/15x^6-3x^4	$\frac{2}{15} x^{6} - 3 x^{4}$
83088	Find dy/dx	-2y-y^2-x^2=0	$- 2 y - y^{2} - x^{2} = 0$
83089	Integrate Using u-Substitution	integral from 0 to 5 of square root of y+4 with respect to y	$\int_{0}^{5} \sqrt{y + 4} d y$
83090	Find dy/dx	x-4y+x^3+3y^3=0	$x - 4 y + x^{3} + 3 y^{3} = 0$
83091	Evaluate the Summation	2 sum from m=0 to 3 of -5m+8m^2	$2 \sum_{m = 0}^{3} - 5 m + 8 m^{2}$
83092	Evaluate the Integral	integral of x(x^2-2)*15 with respect to x	$\int x (x^{2} - 2) \cdot 15 d x$
83093	Evaluate the Limit	limit as x approaches 5 of (x-4)(x^2+8)	$lim_{x \to 5} (x - 4) (x^{2} + 8)$
83094	Evaluate the Integral	integral from 1 to 4 of 1/(x square root of 16x^2-5) with respect to x	$\int_{1}^{4} \frac{1}{x \sqrt{16 x^{2} - 5}} d x$
83095	Find the Derivative - d/dx	ae^(-ax)	$a e^{- a x}$
83096	Evaluate the Integral	integral of (2x^13)/(x^14) with respect to x	$\int \frac{2 x^{13}}{x^{14}} d x$
83097	Evaluate the Limit	limit as x approaches 4 of (1-4/x)/(4-x)	$lim_{x \to 4} \frac{1 - \frac{4}{x}}{4 - x}$
83098	Find the Derivative - d/dx	y=4/3pix^3	$y = \frac{4}{3} π x^{3}$
83099	Find the Second Derivative	x- natural log of x	$x - \ln (x)$
83100	Find the Derivative - d/dx	y=7+5cos(0.503(x-6.75))	$y = 7 + 5 \cos (0.503 (x - 6.75))$