Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
70701	Find the Derivative - d/dx	-2cot(x)+6x^4csc(x)	$- 2 \cot (x) + 6 x^{4} \csc (x)$
70702	Find dy/dx	y=x^3 square root of x+1	$y = x^{3} \sqrt{x + 1}$
70703	Evaluate the Limit	limit as x approaches 1/2 of xsec(pix)	$lim_{x \to \frac{1}{2}} x \sec (π x)$
70704	Find dy/dx	y=(x^3)/3-x	$y = \frac{x^{3}}{3} - x$
70705	Find the Derivative - d/dx	cube root of x-1/( cube root of x)	$\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}}$
70706	Find the Derivative - d/dθ	1/theta	$\frac{1}{θ}$
70707	Find the Domain and Range	f(x)=4x if x<0; -4x if x>=0	$f (x) = {\begin{cases} 4 x & x < 0 \\ - 4 x & x \geq 0 \end{cases}$
70708	Evaluate the Integral	integral of ( square root of x^3+ cube root of x^2) with respect to x	$\int (\sqrt{x^{3}} + \sqrt[3]{x^{2}}) d x$
70709	Find the Derivative - d/dt	t+1/t	$t + \frac{1}{t}$
70710	Evaluate the Integral	integral of x square root of 1-x^4 with respect to x	$\int x \sqrt{1 - x^{4}} d x$
70711	Find Where Increasing/Decreasing	f(x)=(x^3)/3-5x^2+21x+1	$f (x) = \frac{x^{3}}{3} - 5 x^{2} + 21 x + 1$
70712	Find the Center and Radius	(x-0)^2+(y-0)^2=49	${(x - 0)}^{2} + {(y - 0)}^{2} = 49$
70713	Evaluate the Limit	limit as x approaches infinity of ((4+5x)(2-x))/((2+x)(1-x))	$lim_{x \to \infty} \frac{(4 + 5 x) (2 - x)}{(2 + x) (1 - x)}$
70714	Find the Derivative - d/dx	square root of 49x^-9	$\sqrt{49 x^{- 9}}$
70715	Find dx/dy	xy=6	$x y = 6$
70716	Find the Derivative - d/dx	y=-7x(8^(-2x))	$y = - 7 x (8^{- 2 x})$
70717	Integrate Using Trig Substitution	integral of cos(x)^2 with respect to x	$\int \cos^{2} (x) d x$
70718	Find the Derivative - d/dx	(x-y)	$(x - y)$
70719	Evaluate the Limit	limit as x approaches infinity of (8x-5)/( square root of 4x^2+3)	$lim_{x \to \infty} \frac{8 x - 5}{\sqrt{4 x^{2} + 3}}$
70720	Find the Derivative - d/dx	y = natural log of \|csc(x)\|	$y = \ln (\| \csc (x) \|)$
70721	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (e^(3x)+5)^(2/x)	$lim_{x \to \infty} {(e^{3 x} + 5)}^{\frac{2}{x}}$
70722	Evaluate the Integral	integral from e to infinity of 1/(x( natural log of x)^3) with respect to x	$\int_{e}^{\infty} \frac{1}{x \ln^{3} (x)} d x$
70723	Find the Domain and Range	f(x)=-2x-1,x<=2; -x+4,x>2	$f (x) = {\begin{cases} - 2 x - 1, x \leq 2 \\ - x + 4, x > 2 \end{cases}$
70724	Find the Derivative - d/dx	(2y)/x	$\frac{2 y}{x}$
70725	Find the Derivative - d/dx	d/(dx)xe^x	$\frac{d}{d x} x e^{x}$
70726	Find the Derivative - d/dx	(sin(x))/(e^x)	$\frac{(\sin (x))}{e^{x}}$
70727	Find the Derivative - d/dx	1/(e^(-x))	$\frac{1}{e^{- x}}$
70728	Find the Integral	f(x)=25-x^2	$f (x) = 25 - x^{2}$
70729	Evaluate the Integral	integral from 0 to 1 of 30/(6x^2+7x+1) with respect to x	$\int_{0}^{1} \frac{30}{6 x^{2} + 7 x + 1} d x$
70730	Find the Derivative - d/dt	square root of 1-t^2	$\sqrt{1 - t^{2}}$
70731	Find the Derivative - d/dx	(x^3)/12+1/x	$\frac{x^{3}}{12} + \frac{1}{x}$
70732	Find dy/dx	y=(5cos(x))/(1+sin(x))	$y = \frac{5 \cos (x)}{1 + \sin (x)}$
70733	Find the Fourth Derivative	x^4	$x^{4}$
70734	Find the Derivative of the Integral	h(x) = integral from 1 to e^x of 9 natural log of t with respect to t	$h (x) = \int_{1}^{e^{x}} 9 \ln (t) d t$
70735	Integrate By Parts	integral of e^(2x) with respect to x	$\int e^{2 x} d x$
70736	Evaluate the Integral	integral from -2 to 3 of (-3\|x\|) with respect to x	$\int_{- 2}^{3} (- 3 \| x \|) d x$
70737	Solve the Differential Equation	y''''=xy^2	$y'' = x y^{2}$
70738	Find the Derivative - d/du	uv	$u v$
70739	Find the Maximum/Minimum Value	(x^2)/(x^2+3)	$\frac{x^{2}}{x^{2} + 3}$
70740	Evaluate the Limit	limit as x approaches infinity of (x^2-9)/(x(x^2+1))	$lim_{x \to \infty} \frac{x^{2} - 9}{x (x^{2} + 1)}$
70741	Evaluate the Integral	integral of [(sin(x))/(cos(x)^2)+x] with respect to x	$\int [\frac{\sin (x)}{\cos^{2} (x)} + x] d x$
70742	Find the Derivative - d/dx	5e^x-9sin(x)	$5 e^{x} - 9 \sin (x)$
70743	Find the Tangent Line at (1,-1)	f(x)=-x^3 at (1,-1)	$f (x) = - x^{3}$ at $(1, - 1)$
70744	Find the Tangent Line at x=4	f(x) = square root of x^2+9 , x=4	$f (x) = \sqrt{x^{2} + 9}$ , $x = 4$
70745	Find dy/dx	y = natural log of e^x+xe^x	$y = \ln (e^{x} + x e^{x})$
70746	Find dy/dx	y=(sec(x)+tan(x))(sec(x)-tan(x))	$y = (\sec (x) + \tan (x)) (\sec (x) - \tan (x))$
70747	Find the Second Derivative	g(x)=(x^2+4)/(4-x^2)	$g (x) = \frac{x^{2} + 4}{4 - x^{2}}$
70748	Find the Derivative - d/dx	2^(2^x)	$2^{2^{x}}$
70749	Find the Derivative - d/dx	y=sin(e^x)	$y = \sin (e^{x})$
70750	Find the Derivative - d/dx	y=(x^3-3x^2+4)/(x^2)	$y = \frac{x^{3} - 3 x^{2} + 4}{x^{2}}$
70751	Evaluate the Limit	limit as x approaches -2 of x^2+2t-1	$lim_{x \to - 2} x^{2} + 2 t - 1$
70752	Find the Tangent Line at P=(π/3,-1)	y=sec(x)-6cos(x) , P=(pi/3,-1)	$y = \sec (x) - 6 \cos (x)$ , $P = (\frac{π}{3}, - 1)$
70753	Evaluate the Integral	integral of (-6x+2)(-3x^2+2x+5)^3 with respect to x	$\int (- 6 x + 2) {(- 3 x^{2} + 2 x + 5)}^{3} d x$
70754	Find the Absolute Max and Min over the Interval	P(x)=-x^3+27/2x^2-60x+100 , x>=5	$P (x) = - x^{3} + \frac{27}{2} x^{2} - 60 x + 100$ , $x \geq 5$
70755	Find the Derivative - d/dx	d/(dx)(5 natural log of x)	$\frac{d}{d x} (5 \ln (x))$
70756	Find the Tangent Line at (3,1)	2(x^2+y^2)^2=25(x^2-y^2) , (3,1)	$2 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$ , $(3, 1)$
70757	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (3x+1)^(cot(x))	$lim_{x \to 0^{+}} {(3 x + 1)}^{\cot (x)}$
70758	Evaluate the Limit	limit as x approaches negative infinity of (e^(-x))/x	$lim_{x \to - \infty} \frac{e^{- x}}{x}$
70759	Find dx/dy	y=x/(e^x)	$y = \frac{x}{e^{x}}$
70760	Determine if Continuous	f(x)=e^x	$f (x) = e^{x}$
70761	Find the Slope	f(x)=3x	$f (x) = 3 x$
70762	Find dy/dx	y^4-4y^2=x^4-9x^2	$y^{4} - 4 y^{2} = x^{4} - 9 x^{2}$
70763	Find dy/dx	y=arctan(3x)	$y = \arctan (3 x)$
70764	Evaluate the Derivative at a=5	f(x) = square root of 3x+1 , a=5	$f (x) = \sqrt{3 x + 1}$ , $a = 5$
70765	Find the Maximum/Minimum Value	f(x) = square root of x+1	$f (x) = \sqrt{x + 1}$
70766	Solve the Differential Equation	(dy)/(dx)+3x^2y=x^2	$\frac{d y}{d x} + 3 x^{2} y = x^{2}$
70767	Evaluate the Limit	limit as x approaches 10 of square root of (10x)/(2x+5)	$lim_{x \to 10} \sqrt{\frac{10 x}{2 x + 5}}$
70768	Find dy/dx	7 natural log of x^2y^2=6	$7 \ln (x^{2} y^{2}) = 6$
70769	Find Where Increasing/Decreasing	x^(1/5)(x+6)	$x^{\frac{1}{5}} (x + 6)$
70770	Find the Derivative - d/dt	y=6/5-6/5e^(-20t)	$y = \frac{6}{5} - \frac{6}{5} e^{- 20 t}$
70771	Evaluate the Integral	integral of (x^2-8)/(8x) with respect to x	$\int \frac{x^{2} - 8}{8 x} d x$
70772	Find the Tangent Line at (-2,-8)	y=x^3 , (-2,-8)	$y = x^{3}$ , $(- 2, - 8)$
70773	Find the Derivative - d/dx	y=pi/x	$y = \frac{π}{x}$
70774	Find dy/dx	y=x^2e^(-2x)	$y = x^{2} e^{- 2 x}$
70775	Find dy/dx	y=x/(3-2x^2)	$y = \frac{x}{3 - 2 x^{2}}$
70776	Find dx/dy	y^2=x	$y^{2} = x$
70777	Find the Maximum/Minimum Value	f(x)=x^5-5x	$f (x) = x^{5} - 5 x$
70778	Find the Center and Radius	x^2-y^2=16	$x^{2} - y^{2} = 16$
70779	Find the Tangent Line at (-3√(3),1)	x^(2/3)+y^(2/3)=4 (-3 square root of 3,1)	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ $(- 3 \sqrt{3}, 1)$
70780	Evaluate the Integral	integral from 1 to 32 of x^(-6/5) with respect to x	$\int_{1}^{32} x^{\frac{- 6}{5}} d x$
70781	Find the Derivative - d/dy	ye^(-x)	$y e^{- x}$
70782	Find the Derivative - d/dx	y=-2/x	$y = - \frac{2}{x}$
70783	Integrate Using u-Substitution	integral of sin(x)cos(x) with respect to x	$\int \sin (x) \cos (x) d x$
70784	Find dy/dx	y = square root of 1+tan(x)^2	$y = \sqrt{1 + \tan^{2} (x)}$
70785	Find dy/dx	y-x^2+2x=0	$y - x^{2} + 2 x = 0$
70786	Determine if Continuous	f(x)=3x^2,x>=1; Ax-4,x<1	$f (x) = {\begin{cases} 3 x^{2}, x \geq 1 \\ A x - 4, x < 1 \end{cases}$
70787	Evaluate the Integral	integral of 13z^3e^z with respect to z	$\int 13 z^{3} e^{z} d z$
70788	Find the Derivative - d/dx	2x square root of xsin(x)	$2 x \sqrt{x} \sin (x)$
70789	Find the Derivative - d/dx	y=sin(x)*cos(x)	$y = \sin (x) \cdot \cos (x)$
70790	Find dy/dx	y=xarcsin(x)+ square root of 1-x^2	$y = x \arcsin (x) + \sqrt{1 - x^{2}}$
70791	Find dy/dx	x^5+y^5=30xy	$x^{5} + y^{5} = 30 x y$
70792	Find the Second Derivative	x^n	$x^{n}$
70793	Find dx/dy	y=x^7	$y = x^{7}$
70794	Evaluate the Integral	integral from 0 to pi/6 of (sec(theta)tan(theta)) with respect to theta	$\int_{0}^{\frac{π}{6}} (\sec (θ) \tan (θ)) d θ$
70795	Find the Derivative - d/dx	e^(2x)-e^(-2x)	$e^{2 x} - e^{- 2 x}$
70796	Find the Derivative - d/dx	y=e^xcos(x^2)	$y = e^{x} \cos (x^{2})$
70797	Evaluate the Limit	limit as h approaches 0 of (13-pi/(h^2))/(5-6/(h^2))	$lim_{h \to 0} \frac{13 - \frac{π}{h^{2}}}{5 - \frac{6}{h^{2}}}$
70798	Find the Derivative - d/dv	u/v	$\frac{u}{v}$
70799	Find the Derivative - d/dx	y=arctan(cos(x))	$y = \arctan (\cos (x))$
70800	Evaluate the Integral	integral from a to c of f(x) with respect to x	$\int_{a}^{c} f (x) d x$