Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69901	Find the Derivative - d/dx	cube root of 8x	$\sqrt[3]{8 x}$
69902	Find the Derivative - d/dx	(-x^2)/(y^2)	$\frac{- x^{2}}{y^{2}}$
69903	Find the Absolute Max and Min over the Interval	f(x)=xe^(-x^2) on 0 , 2	$f (x) = x e^{- x^{2}}$ on $0$ , $2$
69904	Evaluate the Limit	limit as x approaches 0 of (sin(x)cos(x))/x	$lim_{x \to 0} \frac{\sin (x) \cos (x)}{x}$
69905	Evaluate the Limit	limit as x approaches 0 of arctan((1-x)/( square root of 3+x))	$lim_{x \to 0} \arctan (\frac{1 - x}{\sqrt{3 + x}})$
69906	Use Logarithmic Differentiation to Find the Derivative	y=cos(6x)^x	$y = {\cos (6 x)}^{x}$
69907	Find Where Increasing/Decreasing	xe^x	$x e^{x}$
69908	Evaluate the Limit	limit as x approaches 0 of x/(e^x)	$lim_{x \to 0} \frac{x}{e^{x}}$
69909	Find dy/dx	y=( natural log of x)^2	$y = \ln^{2} (x)$
69910	Find dy/dx	y^2-4xy+2x^2=10	$y^{2} - 4 x y + 2 x^{2} = 10$
69911	Find the Derivative - d/dx	(x^2-x+1)/(x^2+x+1)	$\frac{x^{2} - x + 1}{x^{2} + x + 1}$
69912	Integrate Using u-Substitution	integral of x^2e^x with respect to x	$\int x^{2} e^{x} d x$
69913	Find the Derivative - d/dx	(1-2x)/(3x^2)	$\frac{1 - 2 x}{3 x^{2}}$
69914	Find the Derivative - d/dy	-(2x+y)/(x+2y)	$- \frac{2 x + y}{x + 2 y}$
69915	Find dx/dy	x=sin(y)	$x = \sin (y)$
69916	Integrate Using Trig Substitution	integral of (x^2)/( square root of 49-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{49 - x^{2}}} d x$
69917	Find Where Increasing/Decreasing	f(x)=-(x^4)/4-3x^3-9x^2	$f (x) = - \frac{x^{4}}{4} - 3 x^{3} - 9 x^{2}$
69918	Evaluate the Integral	integral of (sec(x)^2-csc(x)^2) with respect to x	$\int (\sec^{2} (x) - \csc^{2} (x)) d x$
69919	Find dx/dy	y=e^( square root of x)	$y = e^{\sqrt{x}}$
69920	Find dx/dy	x^2+6xy+12y^2=28	$x^{2} + 6 x y + 12 y^{2} = 28$
69921	Find dy/dx	sin(y)+cos(x)=1	$\sin (y) + \cos (x) = 1$
69922	Find the Derivative - d/dx	y=tan(x)-cot(x)	$y = \tan (x) - \cot (x)$
69923	Evaluate the Integral	integral of (9+ square root of x+x)/x with respect to x	$\int \frac{9 + \sqrt{x} + x}{x} d x$
69924	Find dx/dy	x=y^2	$x = y^{2}$
69925	Find Where Increasing/Decreasing	f(x)=4x	$f (x) = 4 x$
69926	Find the Derivative - d/dx	xe^2	$x e^{2}$
69927	Evaluate the Limit	limit as x approaches 0 from the left of \|x\|	$lim_{x \to 0^{-}} \| x \|$
69928	Find dy/dx	x^3-y^3=x	$x^{3} - y^{3} = x$
69929	Evaluate the Integral	integral from -1 to 3 of (-x^3+3x^2+1) with respect to x	$\int_{- 1}^{3} (- x^{3} + 3 x^{2} + 1) d x$
69930	Evaluate the Integral	integral of (1-cos(x)) with respect to x	$\int (1 - \cos (x)) d x$
69931	Find the Derivative - d/dx	square root of 2x^3	$\sqrt{2 x^{3}}$
69932	Find the Derivative - d/dx	y=(x^2)/( square root of 4-x^2)	$y = \frac{x^{2}}{\sqrt{4 - x^{2}}}$
69933	Find the Derivative - d/dx	x/pi	$\frac{x}{π}$
69934	Find the Domain and Range	f(x)=-3/2\|x\|+5 if x<=4; -2x+3 if x>4	$f (x) = {\begin{cases} - \frac{3}{2} \| x \| + 5 & x \leq 4 \\ - 2 x + 3 & x > 4 \end{cases}$
69935	Evaluate the Integral	integral from -1 to 4 of (6x+k) with respect to x=0	$\int_{- 1}^{4} (6 x + k) d x = 0$
69936	Find the Derivative - d/dx	(3+x^2cot(x^2))^-3	${(3 + x^{2} \cot (x^{2}))}^{- 3}$
69937	Find the Derivative - d/dx	e^x-1-x	$e^{x} - 1 - x$
69938	Evaluate the Limit	limit as x approaches 0 of (1/((x+2)^2)-1/4)/x	$lim_{x \to 0} \frac{\frac{1}{{(x + 2)}^{2}} - \frac{1}{4}}{x}$
69939	Find dw/dz	w=2z^2e^z	$w = 2 z^{2} e^{z}$
69940	Find the Derivative - d/dx	x+y+z	$x + y + z$
69941	Find the Tangent Line at (-1,2)	y^2=5x^4-x^2 , (-1,2)	$y^{2} = 5 x^{4} - x^{2}$ , $(- 1, 2)$
69942	Evaluate the Limit	limit as x approaches infinity of x- square root of x^2+x	$lim_{x \to \infty} x - \sqrt{x^{2} + x}$
69943	Find dy/dx	(xy)^2+3x=y^2	${(x y)}^{2} + 3 x = y^{2}$
69944	Find the Arc Length	x=1/3 square root of y(y-3) , 1<=y<=9	$x = \frac{1}{3} \sqrt{y} (y - 3)$ , $1 \leq y \leq 9$
69945	Find the Tangent Line at (0,9)	y=9e^x+x , (0,9)	$y = 9 e^{x} + x$ , $(0, 9)$
69946	Find the Derivative - d/dx	y=(x^5-2x)^2	$y = {(x^{5} - 2 x)}^{2}$
69947	Find the Derivative - d/dθ	3theta	$3 θ$
69948	Evaluate the Integral	integral from 0 to infinity of xe^(-2x) with respect to x	$\int_{0}^{\infty} x e^{- 2 x} d x$
69949	Evaluate the Integral	integral of (3x^2) with respect to x	$\int (3 x^{2}) d x$
69950	Evaluate the Integral	integral from -1 to 2 of (4x-6x^2) with respect to x	$\int_{- 1}^{2} (4 x - 6 x^{2}) d x$
69951	Find the Domain and Range	f(x)=-x^2+3 , x>=0	$f (x) = - x^{2} + 3$ , $x \geq 0$
69952	Determine if Continuous	f(x)=x^3,x<=2; ax^2,x>2	$f (x) = {\begin{cases} x^{3}, x \leq 2 \\ a x^{2}, x > 2 \end{cases}$
69953	Find the Derivative - d/dθ	y=sin(theta+tan(theta+cos(theta)))	$y = \sin (θ + \tan (θ + \cos (θ)))$
69954	Evaluate the Limit	limit as x approaches 0 of 2^x+3^x+16x	$lim_{x \to 0} 2^{x} + 3^{x} + 16 x$
69955	Find dy/dx	4x^3+7xy^2=2y^3	$4 x^{3} + 7 x y^{2} = 2 y^{3}$
69956	Find dy/dx	y^2=2x	$y^{2} = 2 x$
69957	Find dy/dx	cos(y)+sin(x)=1	$\cos (y) + \sin (x) = 1$
69958	Find the Derivative - d/dX	X^3-4	$X^{3} - 4$
69959	Find the Integral	(7x^3+4x^2)dx	$(7 x^{3} + 4 x^{2}) d x$
69960	Find the Tangent Line at (-4,-1/2)	f(x)=2/x at (-4,-1/2)	$f (x) = \frac{2}{x}$ at $(- 4, - \frac{1}{2})$
69961	Find the Derivative Using Chain Rule - d/dx	x^( square root of x)	$x^{\sqrt{x}}$
69962	Evaluate the Limit	limit as x approaches infinity of (x^2)/(5-x^3)	$lim_{x \to \infty} \frac{x^{2}}{5 - x^{3}}$
69963	Find dy/dx	y=(sin(x))/x	$y = \frac{\sin (x)}{x}$
69964	Find the Derivative - d/dx	1/(x^n)	$\frac{1}{x^{n}}$
69965	Evaluate the Summation	sum from i=1 to 22 of (i^3)/3	$\sum_{i = 1}^{22} \frac{i^{3}}{3}$
69966	Find dx/dy	y=e^(3x)	$y = e^{3 x}$
69967	Find the Derivative - d/dx	2xcsc(x)sec(x)	$2 x \csc (x) \sec (x)$
69968	Find the Tangent Line at x=3	f(x) = square root of x^2+55 , x=3	$f (x) = \sqrt{x^{2} + 55}$ , $x = 3$
69969	Find the Derivative - d/dx	y=( square root of x)^(5x)	$y = {(\sqrt{x})}^{5 x}$
69970	Find Where Increasing/Decreasing	f(x)=x/(1+x^2)	$f (x) = \frac{x}{1 + x^{2}}$
69971	Find the Inflection Points	F(x)=x^4-2x^2+1	$F (x) = x^{4} - 2 x^{2} + 1$
69972	Find the Derivative - d/dθ	-cos(theta)	$- \cos (θ)$
69973	Find dy/dt	y=t( natural log of 4t)^2	$y = t \ln^{2} (4 t)$
69974	Solve the Differential Equation	(dy)/(dx)=-2x+3x^2	$\frac{d y}{d x} = - 2 x + 3 x^{2}$
69975	Find dx/dy	y=2 square root of x	$y = 2 \sqrt{x}$
69976	Integrate Using u-Substitution	integral of e^(x^2) with respect to x	$\int e^{x^{2}} d x$
69977	Find the Derivative - d/dx	k square root of x	$k \sqrt{x}$
69978	Find dr/ds	r=1/(2s)-6/(5s^4)	$r = \frac{1}{2 s} - \frac{6}{5 s^{4}}$
69979	Find Where Increasing/Decreasing	f(x)=(x-1)/(x^2)	$f (x) = \frac{x - 1}{x^{2}}$
69980	Evaluate the Integral	integral of (-4x^(3/2)+3x^(2/3)-4x^2) with respect to x	$\int (- 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 x^{2}) d x$
69981	Find the Volume	y=x^2 , x=2	$y = x^{2}$ , $x = 2$
69982	Find the Derivative - d/dt	sin((pit)/2)	$\sin (\frac{π t}{2})$
69983	Solve the Differential Equation	(dy)/(dx)=6x^2y^2	$\frac{d y}{d x} = 6 x^{2} y^{2}$
69984	Find the Derivative - d/dx	square root of a^2+x^2	$\sqrt{a^{2} + x^{2}}$
69985	Find the Center and Radius	x^2+y^2+x-6y-2=0	$x^{2} + y^{2} + x - 6 y - 2 = 0$
69986	Find the Derivative - d/dx	-(x^3)/(7cos(x))	$- \frac{x^{3}}{7 \cos (x)}$
69987	Find the Antiderivative	f(x)=1/(2 square root of x)	$f (x) = \frac{1}{2 \sqrt{x}}$
69988	Evaluate the Integral	integral of e^(x^3)x^2 with respect to x	$\int e^{x^{3}} x^{2} d x$
69989	Evaluate the Integral	integral of x^5 square root of x^3+4 with respect to x	$\int x^{5} \sqrt{x^{3} + 4} d x$
69990	Find dy/dx	y=tan(4x^2)	$y = \tan (4 x^{2})$
69991	Find dx/dy	x^3-y^3=x	$x^{3} - y^{3} = x$
69992	Find the Tangent Line at x=2	f(x) = square root of x^2+21 , x=2	$f (x) = \sqrt{x^{2} + 21}$ , $x = 2$
69993	Find dy/dx	y=x^(4x)	$y = x^{4 x}$
69994	Find dy/dx	e^(x+y)=y	$e^{x + y} = y$
69995	Find dx/dy	x^2+xy+y^2=7	$x^{2} + x y + y^{2} = 7$
69996	Evaluate the Limit	limit as x approaches infinity of (4x^2+5)/(2x-1)	$lim_{x \to \infty} \frac{4 x^{2} + 5}{2 x - 1}$
69997	Find dy/dx	y=x square root of 4-x^2	$y = x \sqrt{4 - x^{2}}$
69998	Find the Area Under the Curve	y=9-x^2	$y = 9 - x^{2}$
69999	Check if Continuous Over an Interval	f(x)=1/x , [-6,6]	$f (x) = \frac{1}{x}$ , $[- 6, 6]$
70000	Find the Linearization at a=16	f(x) = square root of x , a=16	$f (x) = \sqrt{x}$ , $a = 16$