Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68401	Find the Derivative - d/dx	y = cube root of x^3+2	$y = \sqrt[3]{x^{3} + 2}$
68402	Find dy/dx	x^2+2y^2=9	$x^{2} + 2 y^{2} = 9$
68403	Find the Tangent Line at (1,6)	y=7x^2-x^3 , (1,6)	$y = 7 x^{2} - x^{3}$ , $(1, 6)$
68404	Evaluate the Integral	integral from 0 to 8 of 6 square root of x+1 with respect to x	$\int_{0}^{8} 6 \sqrt{x + 1} d x$
68405	Find the Antiderivative	x natural log of x	$x \ln (x)$
68406	Find the Relative Extrema	f(x)=x^3-12x	$f (x) = x^{3} - 12 x$
68407	Find the Derivative - d/dx	-4sin(x)-9 natural log of x+11	$- 4 \sin (x) - 9 \ln (x) + 11$
68408	Find dy/dx	2sin(x)cos(y)=1	$2 \sin (x) \cos (y) = 1$
68409	Find Where Increasing/Decreasing	f(x)=1/3x^3-1/2x^2	$f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2}$
68410	Find the Derivative - d/dx	d/(dx)(x^3sin(x))	$\frac{d}{d x} (x^{3} \sin (x))$
68411	Evaluate the Integral	integral from -2 to 1 of (4x^2-2x+3) with respect to x	$\int_{- 2}^{1} (4 x^{2} - 2 x + 3) d x$
68412	Find dy/dx	y=e^(7 square root of x)	$y = e^{7 \sqrt{x}}$
68413	Evaluate the Limit	limit as x approaches negative infinity of (2x^2-x+4)/(2x+3)	$lim_{x \to - \infty} \frac{2 x^{2} - x + 4}{2 x + 3}$
68414	Evaluate the Integral	integral of (x^2-3x+4) with respect to x	$\int (x^{2} - 3 x + 4) d x$
68415	Find the Derivative - d/dx	x root of x	$\sqrt[x]{x}$
68416	Find the Derivative - d/da	a+b	$a + b$
68417	Find the Linearization at a=64	f(x) = cube root of x , a=64	$f (x) = \sqrt[3]{x}$ , $a = 64$
68418	Evaluate the Integral	integral of 1/(x square root of 9+4x^2) with respect to x	$\int \frac{1}{x \sqrt{9 + 4 x^{2}}} d x$
68419	Find dy/dx	x^3-xy^2+y^3=1	$x^{3} - x y^{2} + y^{3} = 1$
68420	Find dy/dx	y=arccsc(x^2+1)	$y = arccsc (x^{2} + 1)$
68421	Find the Derivative - d/dx	ycos(xy)	$y \cos (x y)$
68422	Evaluate the Integral	integral of (x^3+2) with respect to x	$\int (x^{3} + 2) d x$
68423	Evaluate the Integral	integral from 0 to pi of 5sin(t)^2cos(t)^4 with respect to t	$\int_{0}^{π} 5 \sin^{2} (t) \cos^{4} (t) d t$
68424	Find the Derivative - d/dx	-3/(2 square root of x)	$- \frac{3}{2 \sqrt{x}}$
68425	Integrate By Parts	integral of x with respect to x	$\int x d x$
68426	Find dy/dx	xy^4+x^2y=x+3y	$x y^{4} + x^{2} y = x + 3 y$
68427	Find the Tangent Line at (2,-11)	f(x)=-3x^2+1 ; at (2,-11)	$f (x) = - 3 x^{2} + 1$ ; at $(2, - 11)$
68428	Find the Derivative - d/dx	d/(dx)(2x)	$\frac{d}{d x} (2 x)$
68429	Evaluate the Limit	limit as t approaches 0 of ( square root of t^2+3^2-3)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t^{2} + 3^{2}} - 3}{t^{2}}$
68430	Find the Area Between the Curves	y=4x-x^2	$y = 4 x - x^{2}$
68431	Find dy/dx	e^x-y=xy^3+e^2-18	$e^{x} - y = x y^{3} + e^{2} - 18$
68432	Find dy/dx	(3xy+7)^2=6y	${(3 x y + 7)}^{2} = 6 y$
68433	Evaluate the Limit	limit as x approaches 0 of ( square root of 5^2+x-5)/x	$lim_{x \to 0} \frac{\sqrt{5^{2} + x} - 5}{x}$
68434	Integrate Using u-Substitution	integral from 0 to 1 of cube root of 1+7x with respect to x	$\int_{0}^{1} \sqrt[3]{1 + 7 x} d x$
68435	Integrate By Parts	integral of sin( natural log of x) with respect to x	$\int \sin (\ln (x)) d x$
68436	Evaluate the Integral	integral of ( square root of x+1/(8 square root of x)) with respect to x	$\int (\sqrt{x} + \frac{1}{8 \sqrt{x}}) d x$
68437	Find dy/dx	y=tan(pix)	$y = \tan (π x)$
68438	Find the Derivative - d/dx	y=(x/(x+1))^5	$y = {(\frac{x}{x + 1})}^{5}$
68439	Evaluate the Integral	integral of (x^2+x^3) with respect to x	$\int (x^{2} + x^{3}) d x$
68440	Find the Fourth Derivative	f(x)=x square root of x^2+1	$f (x) = x \sqrt{x^{2} + 1}$
68441	Evaluate the Integral	integral from 0 to 2 of (4-x^2) with respect to x	$\int_{0}^{2} (4 - x^{2}) d x$
68442	Solve the Differential Equation	(dy)/(dx)=(3x^2)/(e^(2y))	$\frac{d y}{d x} = \frac{3 x^{2}}{e^{2 y}}$
68443	Find the Derivative - d/dx	y=x/( square root of x^4+4)	$y = \frac{x}{\sqrt{x^{4} + 4}}$
68444	Find the Domain and Range	f(x)=x+3 if -2<=x<1; 8 if x=1; -x+2 if x>1	$f (x) = {\begin{cases} x + 3 & - 2 \leq x < 1 \\ 8 & x = 1 \\ - x + 2 & x > 1 \end{cases}$
68445	Find dy/dx	3x^2+y^2=1	$3 x^{2} + y^{2} = 1$
68446	Find the Derivative - d/dx	e^xtan(x)	$e^{x} \tan (x)$
68447	Find the Maximum/Minimum Value	y=-x^2	$y = - x^{2}$
68448	Find dy/dx	y=5x^3	$y = 5 x^{3}$
68449	Find dy/dx	x+3y=y^2+4	$x + 3 y = y^{2} + 4$
68450	Evaluate the Integral	integral of (x^2+x^-2) with respect to x	$\int (x^{2} + x^{- 2}) d x$
68451	Find dp/dq	p=(sin(q)-cos(q))/(sin(q))	$p = \frac{\sin (q) - \cos (q)}{\sin (q)}$
68452	Find the Derivative - d/dx	d/(dx)(4x-3/x+1/(x^2))	$\frac{d}{d x} (4 x - \frac{3}{x} + \frac{1}{x^{2}})$
68453	Evaluate the Limit	limit as x approaches 0 of ( square root of 2^2+x-2)/x	$lim_{x \to 0} \frac{\sqrt{2^{2} + x} - 2}{x}$
68454	Evaluate the Integral	integral of ((1-x)/x)^2 with respect to x	$\int {(\frac{1 - x}{x})}^{2} d x$
68455	Solve the Differential Equation	(dy)/(dx)=e^(-11x) , (0,13)	$\frac{d y}{d x} = e^{- 11 x}$ , $(0, 13)$
68456	Find the Derivative - d/dx	(2x-1)	$(2 x - 1)$
68457	Find the Derivative - d/dx	( square root of x+h- square root of x)/h	$\frac{\sqrt{x + h} - \sqrt{x}}{h}$
68458	Use Logarithmic Differentiation to Find the Derivative	y=sin(5x)^( natural log of x)	$y = {\sin (5 x)}^{\ln (x)}$
68459	Find the Antiderivative	x^e	$x^{e}$
68460	Integrate By Parts	integral of ( natural log of x)/(x^3) with respect to x	$\int \frac{\ln (x)}{x^{3}} d x$
68461	Evaluate the Integral	integral from 0 to 3 of (3-2x+x^2) with respect to x=9	$\int_{0}^{3} (3 - 2 x + x^{2}) d x = 9$
68462	Find the Derivative - d/dx	d/(dx)(3cos(x)+4x^2)	$\frac{d}{d x} (3 \cos (x) + 4 x^{2})$
68463	Find the Slope	f(x)=3x-2	$f (x) = 3 x - 2$
68464	Find dx/dy	y=x	$y = x$
68465	Evaluate the Limit	limit as t approaches 0 of ( square root of t^2+5^2-5)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t^{2} + 5^{2}} - 5}{t^{2}}$
68466	Evaluate the Integral	integral of 4tan(x)^3sec(x) with respect to x	$\int 4 \tan^{3} (x) \sec (x) d x$
68467	Evaluate the Limit	limit as x approaches 3 of (1/(x^2)-1/9)/(x-3)	$lim_{x \to 3} \frac{\frac{1}{x^{2}} - \frac{1}{9}}{x - 3}$
68468	Find dy/dx	sin(x+y)=y^2cos(x)	$\sin (x + y) = y^{2} \cos (x)$
68469	Find the Maximum/Minimum Value	f(x)=-3x^5+5x^3	$f (x) = - 3 x^{5} + 5 x^{3}$
68470	Evaluate the Summation	sum from i=1 to 4 of (x_i)^2	$\sum_{i = 1}^{4} {(x_{i})}^{2}$
68471	Find dy/dx	(10-x)y^2=x^3	$(10 - x) y^{2} = x^{3}$
68472	Use Logarithmic Differentiation to Find the Derivative	y = square root of (x-1)/(x^4+1)	$y = \sqrt{\frac{x - 1}{x^{4} + 1}}$
68473	Evaluate the Limit	limit as x approaches 0 of (5x)/(3- square root of 9+x)	$lim_{x \to 0} \frac{5 x}{3 - \sqrt{9 + x}}$
68474	Find dy/dx	xy=cot(xy)	$x y = \cot (x y)$
68475	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of tan(8x)^x	$lim_{x \to 0^{+}} {\tan (8 x)}^{x}$
68476	Integrate Using u-Substitution	integral of 1/(2x+2) with respect to x	$\int \frac{1}{(2 x + 2)} d x$
68477	Find the Maximum/Minimum Value	f(x)=(x^2)/(x^2-9)	$f (x) = \frac{x^{2}}{x^{2} - 9}$
68478	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2-25)	$f (x) = \frac{x^{2}}{x^{2} - 25}$
68479	Evaluate the Integral	integral from 0 to 1 of (x-x^2) with respect to x	$\int_{0}^{1} (x - x^{2}) d x$
68480	Use Logarithmic Differentiation to Find the Derivative	y=(x^2+2)^2(x^4+4)^4	$y = {(x^{2} + 2)}^{2} {(x^{4} + 4)}^{4}$
68481	Evaluate from the Right	limit as x approaches 0 of x/(\|x\|)	$lim_{x \to 0} \frac{x}{\| x \|}$
68482	Find dy/dx	xy-2x^2=10	$x y - 2 x^{2} = 10$
68483	Find dy/dx	y=x^2(e^x-1)	$y = x^{2} (e^{x} - 1)$
68484	Integrate By Parts	integral of x^2e^(-3x) with respect to x	$\int x^{2} e^{- 3 x} d x$
68485	Integrate Using u-Substitution	integral of (cos( square root of x))/( square root of x) with respect to x	$\int \frac{\cos (\sqrt{x})}{\sqrt{x}} d x$
68486	Find the Derivative - d/dx	y=5/4x^(2/3)	$y = \frac{5}{4} x^{\frac{2}{3}}$
68487	Find the Derivative - d/dx	y=sin(x^3-2x)	$y = \sin (x^{3} - 2 x)$
68488	Find dy/dx	xy-cos(xy)=1	$x y - \cos (x y) = 1$
68489	Evaluate the Integral	integral from 0 to 1 of 2x^2(x^3-1)^3 with respect to x	$\int_{0}^{1} 2 x^{2} {(x^{3} - 1)}^{3} d x$
68490	Evaluate the Integral	integral of 1/( square root of a-bx) with respect to x	$\int \frac{1}{\sqrt{a - b x}} d x$
68491	Find dy/dx	y^2-x^3=8	$y^{2} - x^{3} = 8$
68492	Find dy/dx	y=e^(9 square root of x)	$y = e^{9 \sqrt{x}}$
68493	Find dy/dx	y=x^13	$y = x^{13}$
68494	Evaluate the Integral	integral from 1 to infinity of x^(-p) with respect to x	$\int_{1}^{\infty} x^{- p} d x$
68495	Evaluate the Integral	integral from 0 to pi of 3sin(t)^2cos(t)^4 with respect to t	$\int_{0}^{π} 3 \sin^{2} (t) \cos^{4} (t) d t$
68496	Find the Derivative - d/dx	d/(dx)(csc(x))=-csc(x)cot(x)	$\frac{d}{d x} (\csc (x)) = - \csc (x) \cot (x)$
68497	Find the Derivative - d/dx	(xy)^(1/2)	${(x y)}^{\frac{1}{2}}$
68498	Find dp/dq	p=(cos(q)-sin(q))/(cos(q))	$p = \frac{\cos (q) - \sin (q)}{\cos (q)}$
68499	Find dy/dx	4y^2=(5x-3)/(5x+3)	$4 y^{2} = \frac{5 x - 3}{5 x + 3}$
68500	Evaluate the Limit	limit as t approaches 0 of (sin(kt))/t	$lim_{t \to 0} \frac{\sin (k t)}{t}$