Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84101	Find dy/dx	y=sin(8-9x)	$y = \sin (8 - 9 x)$
84102	Find Where Increasing/Decreasing	Let h(x)=-x^3+3x^2+9	Let $h (x) = - x^{3} + 3 x^{2} + 9$
84103	Find the Antiderivative	square root of x^2+4	$\sqrt{x^{2} + 4}$
84104	Find dy/dx	y = natural log of x+y	$y = \ln (x + y)$
84105	Find the Derivative - d/dx	d/(dx)x/2	$\frac{d}{d x} \cdot \frac{x}{2}$
84106	Find the Second Derivative	y=-1/5x^-4+1/10+3/2x^2+2/3x^6	$y = - \frac{1}{5} x^{- 4} + \frac{1}{10} + \frac{3}{2} x^{2} + \frac{2}{3} x^{6}$
84107	Evaluate the Limit	limit as t approaches infinity of 1/(sin(x))-(x)^-1	$lim_{t \to \infty} \frac{1}{\sin (x)} - {(x)}^{- 1}$
84108	Find the Slope	2x+3	$2 x + 3$
84109	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (3 natural log of 4-x)/(x-3)	$lim_{x \to 3} \frac{3 \ln (4 - x)}{x - 3}$
84110	Evaluate Using L'Hospital's Rule	limit as x approaches -2 of ( natural log of -1-x)/(e^(x+2)-1)	$lim_{x \to - 2} \frac{\ln (- 1 - x)}{e^{x + 2} - 1}$
84111	Evaluate the Integral	integral from -4 to -1 of pi/2 with respect to theta	$\int_{- 4}^{- 1} \frac{π}{2} d θ$
84112	Find the Second Derivative	f(x)=3/20x^-4+x^5+1/3x^3+x^2	$f (x) = \frac{3}{20} x^{- 4} + x^{5} + \frac{1}{3} x^{3} + x^{2}$
84113	Find the Antiderivative	g(x)=x^6-5x^4+9x^2-10	$g (x) = x^{6} - 5 x^{4} + 9 x^{2} - 10$
84114	Find the Antiderivative	1/(cos(x)^3)	$\frac{1}{\cos^{3} (x)}$
84115	Find the Third Derivative	y=1/6x^-3-1/6x^3-1/3	$y = \frac{1}{6} x^{- 3} - \frac{1}{6} x^{3} - \frac{1}{3}$
84116	Evaluate the Integral	integral from 0 to a of 10x square root of a^2-x^2 with respect to x	$\int_{0}^{a} 10 x \sqrt{a^{2} - x^{2}} d x$
84117	Find the Derivative - d/dx	- square root of 4-x	$- \sqrt{4 - x}$
84118	Evaluate the Integral	integral of (6x+x) with respect to x	$\int (6 x + x) d x$
84119	Evaluate the Integral	integral of [5x+2/(3x^5)] with respect to x	$\int [5 x + \frac{2}{3 x^{5}}] d x$
84120	Evaluate the Integral	integral from 1 to infinity of (x^2)/((x^3+2)^2) with respect to x	$\int_{1}^{\infty} \frac{x^{2}}{{(x^{3} + 2)}^{2}} d x$
84121	Find the Derivative - d/dx	(1+e^x)^2	${(1 + e^{x})}^{2}$
84122	Find dy/dx	y^3+2x=x^2-2+y^2	$y^{3} + 2 x = x^{2} - 2 + y^{2}$
84123	Find the Derivative - d/dh	limit as h approaches 0 of ((8+h)^(1/3)-2)/h	$lim_{h \to 0} \frac{{(8 + h)}^{\frac{1}{3}} - 2}{h}$
84124	Find the Derivative - d/dx	y=sin(sin(pix))^2	$y = \sin^{2} (\sin (π x))$
84125	Integrate Using u-Substitution	integral of x^3 square root of 1-x^2 with respect to x	$\int x^{3} \sqrt{1 - x^{2}} d x$
84126	Find the Derivative - d/dx	x^2* square root of x	$x^{2} \cdot \sqrt{x}$
84127	Find the Derivative - d/dx	( square root of x^2+1)/x	$\frac{\sqrt{x^{2} + 1}}{x}$
84128	Evaluate the Limit	limit as x approaches 0 of (x^3-2x^2+x)/(2x^3+x^2-2x)	$lim_{x \to 0} \frac{x^{3} - 2 x^{2} + x}{2 x^{3} + x^{2} - 2 x}$
84129	Find the Derivative - d/dx	square root of xe^x	$\sqrt{x e^{x}}$
84130	Find the Derivative - d/dx	(-cos(x-1))	$(- \cos (x - 1))$
84131	Evaluate the Integral	integral of (4x)/(5(6x^2-7)^(2/3)) with respect to x	$\int \frac{4 x}{5 {(6 x^{2} - 7)}^{\frac{2}{3}}} d x$
84132	Evaluate the Integral	integral from 1 to 8 of cube root of x-1/x with respect to x	$\int_{1}^{8} \sqrt[3]{x} - \frac{1}{x} d x$
84133	Evaluate the Limit	limit as x approaches -1 of ((2x+3)^2-1)/(x^2+x)	$lim_{x \to - 1} \frac{{(2 x + 3)}^{2} - 1}{x^{2} + x}$
84134	Find the Derivative - d/dx	(1/(x^2))	$(\frac{1}{x^{2}})$
84135	Evaluate the Limit	limit as h approaches 0 of ( square root of (x+h)^3+2- square root of x^3+2)/h	$lim_{h \to 0} \frac{\sqrt{{(x + h)}^{3} + 2} - \sqrt{x^{3} + 2}}{h}$
84136	Find the Derivative - d/dx	pi/2x	$\frac{π}{2} x$
84137	Find the Derivative - d/dx	2^(5x-3x^2)	$2^{5 x - 3 x^{2}}$
84138	Integrate Using u-Substitution	integral of (4x)/(2x^2+6) with respect to x	$\int \frac{4 x}{2 x^{2} + 6} d x$
84139	Find the Derivative - d/dx	( square root of x+1-2)/(x-3)	$\frac{\sqrt{x + 1} - 2}{x - 3}$
84140	Find the Antiderivative	6 cube root of x-2/x+3e^x	$6 \sqrt[3]{x} - \frac{2}{x} + 3 e^{x}$
84141	Find the Relative Extrema	f(x)=3x^5-x^3+4x-2	$f (x) = 3 x^{5} - x^{3} + 4 x - 2$
84142	Find dy/dx	xy^2-y^3=x^2-5	$x y^{2} - y^{3} = x^{2} - 5$
84143	Evaluate the Integral	integral of (x^pi+x^3) with respect to x	$\int (x^{π} + x^{3}) d x$
84144	Find the Center and Radius	x^2-6x+y^2+8y+c=0	$x^{2} - 6 x + y^{2} + 8 y + c = 0$
84145	Find dy/dx	y=5(5x^2+3)^4	$y = 5 {(5 x^{2} + 3)}^{4}$
84146	Find dy/dx	(x^2+y)^4=2y	${(x^{2} + y)}^{4} = 2 y$
84147	Find the Center and Radius	x^2+y^2+4y+4=9	$x^{2} + y^{2} + 4 y + 4 = 9$
84148	Find the Derivative - d/dx	y=cot(1-sin(x))^2	$y = \cot^{2} (1 - \sin (x))$
84149	Find the Antiderivative	x^3+x+102	$x^{3} + x + 102$
84150	Find the Antiderivative	1/( cube root of x)-2x^(2/5)+3	$\frac{1}{\sqrt[3]{x}} - 2 x^{\frac{2}{5}} + 3$
84151	Evaluate the Limit	limit as x approaches negative infinity of (x^2)/(e^(1-x))	$lim_{x \to - \infty} \frac{x^{2}}{e^{1 - x}}$
84152	Find the Integral	(e^x)/(e^x+1)	$\frac{e^{x}}{e^{x} + 1}$
84153	Find the Integral	(dx)/(cos(x)^2)	$\frac{d x}{\cos^{2} (x)}$
84154	Find the Integral	2^(2x)	$2^{2 x}$
84155	Find the Antiderivative	f(x)=1/3cos(6x)-4sin(4x)	$f (x) = \frac{1}{3} \cos (6 x) - 4 \sin (4 x)$
84156	Find the Derivative - d/dx	square root of \|x\|	$\sqrt{\| x \|}$
84157	Evaluate the Limit	limit as x approaches 1 of (3-2x-x^2)/(-4+3x+x^2)	$lim_{x \to 1} \frac{3 - 2 x - x^{2}}{- 4 + 3 x + x^{2}}$
84158	Find dy/dx	2y^3-x^2+2y=-4y^2-x^3	$2 y^{3} - x^{2} + 2 y = - 4 y^{2} - x^{3}$
84159	Find the Antiderivative	4*3x^2	$4 \cdot 3 x^{2}$
84160	Find the Derivative - d/dx	y=2sin(3x^3+5x^2-5)	$y = 2 \sin (3 x^{3} + 5 x^{2} - 5)$
84161	Find the Maximum/Minimum Value	( natural log of x)/(x^2)	$\frac{\ln (x)}{x^{2}}$
84162	Find Where Increasing/Decreasing	3/4x^4-x^3-84x^2-2	$\frac{3}{4} x^{4} - x^{3} - 84 x^{2} - 2$
84163	Evaluate the Summation	5 sum from i=1 to 14 of i^2+14*13	$5 \sum_{i = 1}^{14} i^{2} + 14 \cdot 13$
84164	Evaluate the Integral	integral of (x^2-3x-5)/x with respect to x	$\int \frac{x^{2} - 3 x - 5}{x} d x$
84165	Find the Derivative - d/dx	3e^(x-3)	$3 e^{x - 3}$
84166	Evaluate the Integral	integral from 0 to 2 of (x-x^2)^3(1-2x) with respect to x	$\int_{0}^{2} {(x - x^{2})}^{3} (1 - 2 x) d x$
84167	Find the Derivative - d/dx	square root of 1+sin(x)	$\sqrt{1 + \sin (x)}$
84168	Evaluate the Limit	limit as x approaches 2 of (x-2)/(h(x+4)-3)	$lim_{x \to 2} \frac{x - 2}{h (x + 4) - 3}$
84169	Evaluate the Integral	integral of ((x^3)/4+(2x^2)/3-1) with respect to x	$\int (\frac{x^{3}}{4} + \frac{2 x^{2}}{3} - 1) d x$
84170	Evaluate the Integral	integral of (3x^2)/(2 square root of 5-3x^3) with respect to x	$\int \frac{3 x^{2}}{2 \sqrt{5 - 3 x^{3}}} d x$
84171	Evaluate the Integral	integral of r/( square root of r^2-x^2) with respect to r	$\int \frac{r}{\sqrt{r^{2} - x^{2}}} d r$
84172	Find the Antiderivative	square root of x/5	$\sqrt{\frac{x}{5}}$
84173	Evaluate the Limit	limit as x approaches 0 of (1-sec(x))/(cos(x)-1)	$lim_{x \to 0} \frac{1 - \sec (x)}{\cos (x) - 1}$
84174	Evaluate the Integral	integral of (2x-x square root of x)/( square root of x) with respect to x	$\int \frac{2 x - x \sqrt{x}}{\sqrt{x}} d x$
84175	Find the Domain and Range	f(x)=(x+3)^2-2 , x<=-3	$f (x) = {(x + 3)}^{2} - 2$ , $x \leq - 3$
84176	Find the Derivative - d/dx	(2 square root of x)/5	$\frac{2 \sqrt{x}}{5}$
84177	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (2 natural log of -x)/(e^(3x+3)-1)	$lim_{x \to - 1} \frac{2 \ln (- x)}{e^{3 x + 3} - 1}$
84178	Find the Antiderivative	e^x(1+e^(-x))	$e^{x} (1 + e^{- x})$
84179	Evaluate the Limit	limit as x approaches 0 from the right of x log of x	$lim_{x \to 0^{+}} x \log (x)$
84180	Find the Derivative - d/dx	(2 square root of x)/x	$\frac{2 \sqrt{x}}{x}$
84181	Find the Derivative - d/dx	y=tanh((3x+2)^2)^2	$y = \tanh^{2} ({(3 x + 2)}^{2})$
84182	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x^2-1+ natural log of x)/(e^x-e)	$lim_{x \to 1} \frac{x^{2} - 1 + \ln (x)}{e^{x} - e}$
84183	Find the Derivative - d/dx	cot(e^(2x))	$\cot (e^{2 x})$
84184	Find the Integral	x/(x+2)	$\frac{x}{x + 2}$
84185	Find the Antiderivative	f(x)=2+sin(x)	$f (x) = 2 + \sin (x)$
84186	Find the Derivative - d/dx	(6x)/pi-4sin(x)^2	$\frac{6 x}{π} - 4 \sin^{2} (x)$
84187	Find dy/dx	y=x^2y^3+x^3y^2	$y = x^{2} y^{3} + x^{3} y^{2}$
84188	Find dx/dy	y=2sin(x)	$y = 2 \sin (x)$
84189	Evaluate the Integral	integral of xcos(4pix^2) with respect to x	$\int x \cos (4 π x^{2}) d x$
84190	Evaluate the Summation	sum from i=4 to 7 of 2^(i-7)	$\sum_{i = 4}^{7} 2^{i - 7}$
84191	Evaluate the Limit	limit as x approaches 2 of (3- square root of 2x+5)/(x-2)	$lim_{x \to 2} \frac{3 - \sqrt{2 x + 5}}{x - 2}$
84192	Evaluate the Limit	limit as x approaches infinity of ((k^2+2)x^3+k^2x-2k square root of 2x^3+2)/(x^2-5)	$lim_{x \to \infty} \frac{(k^{2} + 2) x^{3} + k^{2} x - 2 k \sqrt{2} x^{3} + 2}{x^{2} - 5}$
84193	Evaluate the Integral	integral of (5 square root of y-3/( square root of 7)) with respect to x	$\int (5 \sqrt{y} - \frac{3}{\sqrt{7}}) d x$
84194	Find the Derivative - d/dA	cos(A)^2	$\cos^{2} (A)$
84195	Find the Maximum/Minimum Value	f(x)=x^4+x+2	$f (x) = x^{4} + x + 2$
84196	Find the Third Derivative	1/6x^-3-1/6x^3-1/3	$\frac{1}{6} x^{- 3} - \frac{1}{6} x^{3} - \frac{1}{3}$
84197	Find the Derivative - d/dx	y=e^x-e^(-x)	$y = e^{x} - e^{- x}$
84198	Find the Derivative - d/dx	( natural log of 2x)/x	$\frac{\ln (2 x)}{x}$
84199	Evaluate the Limit	limit as x approaches 0 of (3sin(3x))/(4sin(4x))	$lim_{x \to 0} \frac{3 \sin (3 x)}{4 \sin (4 x)}$
84200	Evaluate the Integral	integral of (4 cube root of x)/3 with respect to x	$\int \frac{4 \sqrt[3]{x}}{3} d x$