Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69201	Evaluate the Limit	limit as x approaches 0 of x^(1/x)	$lim_{x \to 0} x^{\frac{1}{x}}$
69202	Find the Absolute Max and Min over the Interval	y=sin(x) , 0<=x<=2pi	$y = \sin (x)$ , $0 \leq x \leq 2 π$
69203	Find the Derivative - d/dx	(-x^2)/2	$\frac{- x^{2}}{2}$
69204	Evaluate the Integral	integral from 0 to 3 of (3-x) with respect to x	$\int_{0}^{3} (3 - x) d x$
69205	Find the Turning Points	h(x)=x^4-x^3-6x^2	$h (x) = x^{4} - x^{3} - 6 x^{2}$
69206	Find the Maximum/Minimum Value	y=1/x	$y = \frac{1}{x}$
69207	Find the Derivative - d/dx	e^x+xe^x	$e^{x} + x e^{x}$
69208	Find dy/dx	y=e^(x+y)	$y = e^{x + y}$
69209	Use Logarithmic Differentiation to Find the Derivative	y=sin(x)^( natural log of x)	$y = {\sin (x)}^{\ln (x)}$
69210	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (-8x)^2e^(-3x)	$lim_{x \to \infty} {(- 8 x)}^{2} e^{- 3 x}$
69211	Evaluate the Limit	limit as x approaches 0 of (3(2)^x-1)/2	$lim_{x \to 0} \frac{3 {(2)}^{x} - 1}{2}$
69212	Find dy/dx	(2x+9y)^2=-8x^2-10y^2	${(2 x + 9 y)}^{2} = - 8 x^{2} - 10 y^{2}$
69213	Find the Derivative - d/da	y=2a-bx	$y = 2 a - b x$
69214	Find dy/dx	y=arcsin(x)	$y = \arcsin (x)$
69215	Find the Derivative - d/dx	square root of x^2+x+1	$\sqrt{x^{2} + x + 1}$
69216	Find the Derivative - d/dx	y = square root of (1+x)/(1-x)	$y = \sqrt{\frac{1 + x}{1 - x}}$
69217	Find the Derivative - d/dx	(x^2-2x)/(1-x)	$\frac{x^{2} - 2 x}{1 - x}$
69218	Find the Derivative - d/dx	x/(1-4x^3)	$\frac{x}{1 - 4 x^{3}}$
69219	Evaluate the Integral	integral from 0 to pi/4 of sin(x)^5 with respect to x	$\int_{0}^{\frac{π}{4}} \sin^{5} (x) d x$
69220	Find the Derivative - d/dx	y natural log of x	$y \ln (x)$
69221	Evaluate the Limit	limit as x approaches -1 of (-x^2+x+3)/(4x)	$lim_{x \to - 1} \frac{- x^{2} + x + 3}{4 x}$
69222	Find the Derivative - d/dy	-y/(x^2+y^2)	$- \frac{y}{x^{2} + y^{2}}$
69223	Find the Derivative - d/dx	y=1/(2x^2)+4/( square root of x)	$y = \frac{1}{2 x^{2}} + \frac{4}{\sqrt{x}}$
69224	Integrate Using u-Substitution	integral of xe^(-x^2) with respect to x	$\int x e^{- x^{2}} d x$
69225	Find the Derivative - d/dx	d/(dx)(x^(3/2))	$\frac{d}{d x} (x^{\frac{3}{2}})$
69226	Find dy/dx	(xy)^x=e	${(x y)}^{x} = e$
69227	Evaluate the Integral	integral from 0 to infinity of 1/(1+x^2) with respect to x	$\int_{0}^{\infty} \frac{1}{1 + x^{2}} d x$
69228	Find dy/dx	y=arctan(cos(x))	$y = \arctan (\cos (x))$
69229	Find the Derivative - d/dθ	csc(theta)^2	$\csc^{2} (θ)$
69230	Find the Derivative - d/dx	1/(1+cos(x))	$\frac{1}{1 + \cos (x)}$
69231	Evaluate the Limit	limit as x approaches infinity of (x^2+6)/(x^2+3)	$lim_{x \to \infty} \frac{x^{2} + 6}{x^{2} + 3}$
69232	Evaluate the Limit	limit as x approaches infinity of (2x^4+3)/(5x^3-x^2-3)	$lim_{x \to \infty} \frac{2 x^{4} + 3}{5 x^{3} - x^{2} - 3}$
69233	Evaluate the Limit	limit as x approaches infinity of (-3x^2+7)/x	$lim_{x \to \infty} \frac{- 3 x^{2} + 7}{x}$
69234	Find dy/dx	x^2+xy+y^2=100	$x^{2} + x y + y^{2} = 100$
69235	Find the Derivative - d/dx	( square root of x)/(cos(x))	$\frac{\sqrt{x}}{\cos (x)}$
69236	Find the Derivative - d/dx	y=x^2(2x^2-3x)	$y = x^{2} (2 x^{2} - 3 x)$
69237	Find dy/dx	9x^2-y^2=1	$9 x^{2} - y^{2} = 1$
69238	Find the Derivative - d/dx	-x^2e^(-x)+2xe^(-x)	$- x^{2} e^{- x} + 2 x e^{- x}$
69239	Find dy/dx	y=(x^3)/3	$y = \frac{x^{3}}{3}$
69240	Evaluate the Integral	integral of (2/( cube root of w)- cube root of w) with respect to w	$\int (\frac{2}{\sqrt[3]{w}} - \sqrt[3]{w}) d w$
69241	Find the Derivative - d/dx	(f(x))/x	$\frac{f (x)}{x}$
69242	Find dy/dx	4 square root of y-y=2x	$4 \sqrt{y} - y = 2 x$
69243	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^2 natural log of x	$lim_{x \to 0^{+}} x^{2} \ln (x)$
69244	Integrate Using u-Substitution	integral of x^3e^(x^4) with respect to x	$\int x^{3} e^{x^{4}} d x$
69245	Find the Maximum/Minimum Value	3x^4+4x^3	$3 x^{4} + 4 x^{3}$
69246	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+1/x)^(x^2)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{x^{2}}$
69247	Find dy/dx	y = natural log of sec(x)+tan(x)	$y = \ln (\sec (x) + \tan (x))$
69248	Find the Derivative - d/dx	4/x+5x-1	$\frac{4}{x} + 5 x - 1$
69249	Find the Derivative - d/dx	-y/(x^2+y^2)	$- \frac{y}{x^{2} + y^{2}}$
69250	Find dy/dx	y=8x	$y = 8 x$
69251	Find the Derivative - d/dx	y=3/x+2/( cube root of x^2)	$y = \frac{3}{x} + \frac{2}{\sqrt[3]{x^{2}}}$
69252	Find the Maximum/Minimum Value	f(x)=16 natural log of x^2-x^2	$f (x) = 16 \ln (x^{2}) - x^{2}$
69253	Find the Derivative - d/dt	s=t^3-12t	$s = t^{3} - 12 t$
69254	Find the Derivative - d/dx	cot(6x-x^2)	$\cot (6 x - x^{2})$
69255	Find the Maximum/Minimum Value	f(x)=x^6e^(-x)	$f (x) = x^{6} e^{- x}$
69256	Find dx/dy	3x^2+4xy+2y^2=2x+15	$3 x^{2} + 4 x y + 2 y^{2} = 2 x + 15$
69257	Evaluate the Integral	integral from 2 to 8 of 1/((x^2-1)^(3/2)) with respect to x	$\int_{2}^{8} \frac{1}{{(x^{2} - 1)}^{\frac{3}{2}}} d x$
69258	Evaluate the Integral	integral from negative infinity to 0 of xe^(-x) with respect to x	$\int_{- \infty}^{0} x e^{- x} d x$
69259	Find the Derivative - d/dx	y=cot(x)^2	$y = \cot^{2} (x)$
69260	Find the Derivative - d/dx	(e^x(x-1))/(x^2)	$\frac{e^{x} (x - 1)}{x^{2}}$
69261	Evaluate the Limit	limit as x approaches 0 from the right of x/(\|x\|)	$lim_{x \to 0^{+}} \frac{x}{\| x \|}$
69262	Evaluate the Integral	integral from -2 to 0 of (8x^2+8x) with respect to x	$\int_{- 2}^{0} (8 x^{2} + 8 x) d x$
69263	Find dy/dx	y=cos(x)^4	$y = \cos^{4} (x)$
69264	Evaluate the Integral	integral from 0 to infinity of 9e^(-9x) with respect to x	$\int_{0}^{\infty} 9 e^{- 9 x} d x$
69265	Find dy/dx	y=2x+1	$y = 2 x + 1$
69266	Find dx/dy	1/x+1/y=1	$\frac{1}{x} + \frac{1}{y} = 1$
69267	Find dy/dx	x^2+xy-y^2=11	$x^{2} + x y - y^{2} = 11$
69268	Find dy/dx	2xy^3-x^2y=2	$2 x y^{3} - x^{2} y = 2$
69269	Find the Derivative - d/dx	tan(x)^2+1	$\tan^{2} (x) + 1$
69270	Find the Fourth Derivative	f(x)=1/x	$f (x) = \frac{1}{x}$
69271	Find the Derivative - d/dx	x^2-1/x	$x^{2} - \frac{1}{x}$
69272	Find dy/dx	y=x^(1/x)	$y = x^{\frac{1}{x}}$
69273	Find dy/dx	y=x^(tan(x))	$y = x^{\tan (x)}$
69274	Find dy/dx	x-3x^4y^5=-2	$x - 3 x^{4} y^{5} = - 2$
69275	Find dy/dx	ycos(3x-y)=6xy-2	$y \cos (3 x - y) = 6 x y - 2$
69276	Find dy/dx	y = natural log of e^(-x)+xe^(-x)	$y = \ln (e^{- x} + x e^{- x})$
69277	Find Where Increasing/Decreasing	x/(x^2+1)	$\frac{x}{x^{2} + 1}$
69278	Evaluate the Limit	limit as x approaches infinity of (x+7)/( square root of 4x^2+3x)	$lim_{x \to \infty} \frac{x + 7}{\sqrt{4 x^{2} + 3 x}}$
69279	Find dy/dx	square root of xy+3=y	$\sqrt{x y} + 3 = y$
69280	Find the Maximum/Minimum Value	f(x)=25 natural log of x^2-x^2	$f (x) = 25 \ln (x^{2}) - x^{2}$
69281	Find the Second Derivative	f(x)=cos(x)^2	$f (x) = \cos^{2} (x)$
69282	Evaluate the Integral	integral from 0 to 2 of (2x-x^2) with respect to x	$\int_{0}^{2} (2 x - x^{2}) d x$
69283	Find the Derivative - d/dx	-cot(x)csc(x)	$- \cot (x) \csc (x)$
69284	Find dy/dx	y=x+ square root of x	$y = x + \sqrt{x}$
69285	Find the Derivative - d/dx	tan(x-y)=y/(1+x^2)	$\tan (x - y) = \frac{y}{1 + x^{2}}$
69286	Integrate Using Trig Substitution	integral of cos(x)^3 with respect to x	$\int \cos^{3} (x) d x$
69287	Integrate By Parts	integral of x^2 with respect to x	$\int x^{2} d x$
69288	Find the Derivative - d/dx	sin(x)x^-2	$\sin (x) x^{- 2}$
69289	Find the Derivative - d/da	log base a of 2x^3+7	$\log_{a} (2 x^{3} + 7)$
69290	Find the Tangent Line at (1,3)	y=4x-x^2 , (1,3)	$y = 4 x - x^{2}$ , $(1, 3)$
69291	Evaluate the Limit	limit as x approaches -3 of (-3x-9)/(x^2+3x)	$lim_{x \to - 3} \frac{- 3 x - 9}{x^{2} + 3 x}$
69292	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ( square root of 9+19x- square root of 9+15x)/(3x)	$lim_{x \to 0} \frac{\sqrt{9 + 19 x} - \sqrt{9 + 15 x}}{3 x}$
69293	Evaluate the Summation	sum from i=6 to 14 of 9i^2	$\sum_{i = 6}^{14} 9 i^{2}$
69294	Find dv/dr	v=1/3pir^2h	$v = \frac{1}{3} π r^{2} h$
69295	Find dy/du	y=e^(-u)cos(u)	$y = e^{- u} \cos (u)$
69296	Find the Derivative - d/dθ	e^(2theta)	$e^{2 θ}$
69297	Solve the Differential Equation	(dy)/(dx)-x=x^2 , (-2,2)	$\frac{d y}{d x} - x = x^{2}$ , $(- 2, 2)$
69298	Find the Tangent Line at (0,0)	y=xe^(-x^2) , (0,0)	$y = x e^{- x^{2}}$ , $(0, 0)$
69299	Find dy/dx	y=sin(x)tan(x)	$y = \sin (x) \tan (x)$
69300	Evaluate the Derivative at a=16	h(x)=x^( square root of x) , a=16	$h (x) = x^{\sqrt{x}}$ , $a = 16$