Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69001	Find the Derivative - d/dx	y=7/(3x^-2)	$y = \frac{7}{3 x^{- 2}}$
69002	Find dy/dx	4x^2+3y^2=4	$4 x^{2} + 3 y^{2} = 4$
69003	Integrate Using u-Substitution	integral of 6(2x-1)^-3 with respect to x , u=2x-1	$\int 6 {(2 x - 1)}^{- 3} d x$ , $u = 2 x - 1$
69004	Find the Antiderivative	xy	$x y$
69005	Find the Derivative - d/dh	(f(x+h)-f(x))/h	$\frac{f (x + h) - f (x)}{h}$
69006	Find the Maximum/Minimum Value	f(x)=12x^(2/3)-8x	$f (x) = 12 x^{\frac{2}{3}} - 8 x$
69007	Find dy/dx	y=x^(x^3)	$y = x^{x^{3}}$
69008	Evaluate the Limit	limit as x approaches -5 of (x^2-x)/(5x-5)	$lim_{x \to - 5} \frac{x^{2} - x}{5 x - 5}$
69009	Find the Derivative - d/dx	(1+x^2)^(1/2)	${(1 + x^{2})}^{\frac{1}{2}}$
69010	Find the Derivative - d/dx	(sin(x))/( square root of x)	$\frac{\sin (x)}{\sqrt{x}}$
69011	Use Logarithmic Differentiation to Find the Derivative	y=sin(7x)^( natural log of x)	$y = {\sin (7 x)}^{\ln (x)}$
69012	Find dy/dx	x+y=x^2+y^2	$x + y = x^{2} + y^{2}$
69013	Find dx/dy	y=sin(x)	$y = \sin (x)$
69014	Evaluate the Integral	integral from 0 to 62 of 1/( cube root of (1+2x)^2) with respect to x	$\int_{0}^{62} \frac{1}{\sqrt[3]{{(1 + 2 x)}^{2}}} d x$
69015	Find dx/dy	y=3x	$y = 3 x$
69016	Find dy/dx	x = square root of y+ cube root of y	$x = \sqrt{y} + \sqrt[3]{y}$
69017	Evaluate the Summation	sum from x=0 to 4 of (11x)/5	$\sum_{x = 0}^{4} \frac{11 x}{5}$
69018	Evaluate the Limit	limit as x approaches 0 of (sin(sin(x)))/(sin(x))	$lim_{x \to 0} \frac{\sin (\sin (x))}{\sin (x)}$
69019	Find dy/dx	y=x^(2/x)	$y = x^{\frac{2}{x}}$
69020	Find the Relative Extrema	f(x)=x^2(1-x)^3	$f (x) = x^{2} {(1 - x)}^{3}$
69021	Evaluate the Integral	integral of 8^(x+1) with respect to x	$\int 8^{x + 1} d x$
69022	Evaluate the Integral	integral of (x^3+6x^2-8)/(x^2) with respect to x	$\int \frac{x^{3} + 6 x^{2} - 8}{x^{2}} d x$
69023	Evaluate the Integral	integral of ((4+6h)/( square root of h)) with respect to h	$\int (\frac{4 + 6 h}{\sqrt{h}}) d h$
69024	Evaluate the Integral	integral of 2x natural log of x^2 with respect to x	$\int 2 x \ln (x^{2}) d x$
69025	Find the Derivative - d/dx	d/(dx)(-4x^3-sin(x))	$\frac{d}{d x} (- 4 x^{3} - \sin (x))$
69026	Find the Integral	1/2x	$\frac{1}{2} x$
69027	Find the Derivative - d/du	u=v+cos(v)	$u = v + \cos (v)$
69028	Evaluate the Integral	integral of 3x^2e^(2x) with respect to x	$\int 3 x^{2} e^{2 x} d x$
69029	Evaluate the Integral	integral from 0 to 1 of ((3f(x))x^2+3f(x)+x^2)/(x^2+1) with respect to x	$\int_{0}^{1} \frac{(3 f (x)) x^{2} + 3 f (x) + x^{2}}{x^{2} + 1} d x$
69030	Find the Derivative - d/dx	d/(dx)(( natural log of x)/( square root of x))	$\frac{d}{d x} (\frac{\ln (x)}{\sqrt{x}})$
69031	Find the Antiderivative	y=x^2	$y = x^{2}$
69032	Find the Derivative - d/dx	y=sec(2x^2+4)	$y = \sec (2 x^{2} + 4)$
69033	Find the Derivative - d/dx	1/(3 cube root of x^2)	$\frac{1}{3 \sqrt[3]{x^{2}}}$
69034	Evaluate the Limit	limit as x approaches -1 of (x^2+1)/(-1+x)	$lim_{x \to - 1} \frac{x^{2} + 1}{- 1 + x}$
69035	Find the Derivative - d/dx	y=pi/((2x)^4)	$y = \frac{π}{{(2 x)}^{4}}$
69036	Evaluate the Integral	integral from 1 to 3 of (2x^2-3x+5) with respect to x	$\int_{1}^{3} (2 x^{2} - 3 x + 5) d x$
69037	Find the Center and Radius	x^2-y^2=1	$x^{2} - y^{2} = 1$
69038	Find dr/dθ	r=csc(theta)cot(theta)	$r = \csc (θ) \cot (θ)$
69039	Find the Derivative - d/dx	7cos(x)+3e^x	$7 \cos (x) + 3 e^{x}$
69040	Find Where Increasing/Decreasing	f(x)=x^5-5x^4-x^3+28x^2-2x	$f (x) = x^{5} - 5 x^{4} - x^{3} + 28 x^{2} - 2 x$
69041	Evaluate the Integral	integral from 0 to 7 of \|x^2-6x+5\| with respect to x	$\int_{0}^{7} \| x^{2} - 6 x + 5 \| d x$
69042	Evaluate the Limit	limit as x approaches -2 from the left of square root of -x-2+4	$lim_{x \to {(- 2)}^{-}} \sqrt{- x - 2} + 4$
69043	Evaluate the Integral	integral of x(x+4)^2 with respect to x	$\int x {(x + 4)}^{2} d x$
69044	Find the Antiderivative	x^2e^x	$x^{2} e^{x}$
69045	Find the Derivative - d/dx	e^(-x)-x	$e^{- x} - x$
69046	Find the Fourth Derivative	2x+3e^(2x)	$2 x + 3 e^{2 x}$
69047	Find the Integral	(dy)/(dx)	$\frac{d y}{d x}$
69048	Find dy/dx	y=sec(x+y)	$y = \sec (x + y)$
69049	Integrate Using Trig Substitution	integral of 1/(x square root of x^2+4) with respect to x	$\int \frac{1}{x \sqrt{x^{2} + 4}} d x$
69050	Find the Maximum/Minimum Value	f(x)=e^x	$f (x) = e^{x}$
69051	Find dy/dt	y=e^(tan(pit))	$y = e^{\tan (π t)}$
69052	Evaluate the Integral	integral of square root of 3x^2 with respect to x	$\int \sqrt{3 x^{2}} d x$
69053	Find the Fourth Derivative	2x^2	$2 x^{2}$
69054	Evaluate the Integral	integral of xy^2 with respect to x	$\int x y^{2} d x$
69055	Evaluate the Limit	limit as x approaches infinity of (e^x+x)^(1/x)	$lim_{x \to \infty} {(e^{x} + x)}^{\frac{1}{x}}$
69056	Evaluate the Integral	integral of 1/3e^(3x) with respect to x	$\int \frac{1}{3} e^{3 x} d x$
69057	Find the Derivative - d/dx	d/(dx)( square root of x^3)	$\frac{d}{d x} (\sqrt{x^{3}})$
69058	Find the Relative Extrema	f(x)=x^4-4x^3	$f (x) = x^{4} - 4 x^{3}$
69059	Find the Critical Points	p(x)=(x^2+2)/(2x-1)	$p (x) = \frac{x^{2} + 2}{2 x - 1}$
69060	Find the Derivative - d/dx	1/5(xy^2+4y)^2	$\frac{1}{5} {(x y^{2} + 4 y)}^{2}$
69061	Find the Derivative - d/dx	y=(6x^3-x)(10-20x)	$y = (6 x^{3} - x) (10 - 20 x)$
69062	Evaluate the Limit	limit as x approaches 0 of (sin(\|x\|))/x	$lim_{x \to 0} \frac{\sin (\| x \|)}{x}$
69063	Evaluate the Integral	integral of 1/( square root of 1+4x) with respect to x	$\int \frac{1}{\sqrt{1 + 4 x}} d x$
69064	Find the Area Between the Curves	y=x^4 and y=8x	$y = x^{4}$ and $y = 8 x$
69065	Evaluate Using L'Hospital's Rule	limit as x approaches 1 from the right of natural log of x^5-1- natural log of x^3-1	$lim_{x \to 1^{+}} \ln (x^{5} - 1) - \ln (x^{3} - 1)$
69066	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (5^x-4^x)/(3^x-2^x)	$lim_{x \to 0} \frac{5^{x} - 4^{x}}{3^{x} - 2^{x}}$
69067	Evaluate the Limit	limit as x approaches infinity of (8x^3-5x^2+13x)/(2x^3+7x^2-18x)	$lim_{x \to \infty} \frac{8 x^{3} - 5 x^{2} + 13 x}{2 x^{3} + 7 x^{2} - 18 x}$
69068	Evaluate the Integral	integral from 0 to infinity of 1/( eighth root of 1+x) with respect to x	$\int_{0}^{\infty} \frac{1}{\sqrt[8]{1 + x}} d x$
69069	Integrate Using Trig Substitution	integral of ( square root of x^2+1)/x with respect to x	$\int \frac{\sqrt{x^{2} + 1}}{x} d x$
69070	Find the Derivative - d/dx	(1/(x-3))^2	${(\frac{1}{x - 3})}^{2}$
69071	Find the Domain and Range	f(x)=x^2-3 , x<=0	$f (x) = x^{2} - 3$ , $x \leq 0$
69072	Find dy/dx	x^2y-2x^3-4=0	$x^{2} y - 2 x^{3} - 4 = 0$
69073	Find the Maximum/Minimum Value	y=(x^3)/3-2x^2-5x	$y = \frac{x^{3}}{3} - 2 x^{2} - 5 x$
69074	Find the Maximum/Minimum Value	y=x+1/x	$y = x + \frac{1}{x}$
69075	Find the Maximum/Minimum Value	f(x)=5^x	$f (x) = 5^{x}$
69076	Find the Antiderivative	g(x)=x^3-3x^2+3x-1	$g (x) = x^{3} - 3 x^{2} + 3 x - 1$
69077	Find the Integral	natural log of xdx	$\ln (x d x)$
69078	Evaluate the Limit	limit as x approaches 3 from the right of 2/(x+3)	$lim_{x \to 3^{+}} \frac{2}{x + 3}$
69079	Find the Derivative - d/dx	cos(ecx)	$\cos (e c x)$
69080	Find the Derivative - d/dx	4 square root of y^2+7x^2	$4 \sqrt{y^{2} + 7 x^{2}}$
69081	Find dy/dx	y=1/(x^8)	$y = \frac{1}{x^{8}}$
69082	Evaluate the Limit	limit as x approaches infinity of (-x^3+4x)/(4x^3-2x^2+4)	$lim_{x \to \infty} \frac{- x^{3} + 4 x}{4 x^{3} - 2 x^{2} + 4}$
69083	Find the Derivative - d/dx	sin(x)csc(x)	$\sin (x) \csc (x)$
69084	Find the Second Derivative	f(x)=x	$f (x) = x$
69085	Integrate Using u-Substitution	integral of cos(x^2)*2x with respect to x , u=x^2	$\int \cos (x^{2}) \cdot 2 x d x$ , $u = x^{2}$
69086	Evaluate the Integral	integral of (-7 cube root of x-9 fourth root of x+2x^4) with respect to x	$\int (- 7 \sqrt[3]{x} - 9 \sqrt[4]{x} + 2 x^{4}) d x$
69087	Determine if Continuous	f(x)=cx^2+6x if x<5; x^3-cx if x>=5	$f (x) = {\begin{cases} c x^{2} + 6 x & x < 5 \\ x^{3} - c x & x \geq 5 \end{cases}$
69088	Integrate Using Trig Substitution	integral of (x^2)/( square root of 1-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{1 - x^{2}}} d x$
69089	Find dy/dx	y=(cos(x))/(sin(x)^2)	$y = \frac{\cos (x)}{\sin^{2} (x)}$
69090	Find the Tangent Line at (0,2)	y=2e^x+x , (0,2)	$y = 2 e^{x} + x$ , $(0, 2)$
69091	Evaluate the Limit	limit as x approaches 0 of x^2sin(1/(x^2))	$lim_{x \to 0} x^{2} \sin (\frac{1}{x^{2}})$
69092	Find dy/dx	x/y+y/x=3y	$\frac{x}{y} + \frac{y}{x} = 3 y$
69093	Evaluate the Integral	integral from -2 to 1 of (x+1) square root of x+3 with respect to x	$\int_{- 2}^{1} (x + 1) \sqrt{x + 3} d x$
69094	Find Where Increasing/Decreasing	f(x)=5/2 square root of -(x-6)	$f (x) = \frac{5}{2} \sqrt{- (x - 6)}$
69095	Find the Derivative - d/dx	y = square root of e^x	$y = \sqrt{e^{x}}$
69096	Evaluate the Integral	integral of (5cos(x)+4sin(x)) with respect to x	$\int (5 \cos (x) + 4 \sin (x)) d x$
69097	Evaluate from the Left	limit as x approaches -3 of F(x)	$lim_{x \to - 3} F (x)$
69098	Evaluate the Limit	limit as x approaches infinity of (-3x^2+7)/(5x+1)	$lim_{x \to \infty} \frac{- 3 x^{2} + 7}{5 x + 1}$
69099	Evaluate the Limit	limit as x approaches 4 of 2^x+ square root of x-x	$lim_{x \to 4} 2^{x} + \sqrt{x} - x$
69100	Evaluate the Limit	limit as x approaches infinity of (2x^2-3x-4)/( square root of x^4+1)	$lim_{x \to \infty} \frac{2 x^{2} - 3 x - 4}{\sqrt{x^{4} + 1}}$