Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68101	Find the Derivative - d/dx	d/(dx)(3 natural log of x-12sin(x))	$\frac{d}{d x} (3 \ln (x) - 12 \sin (x))$
68102	Find the Derivative - d/dh	limit as h approaches 0 of ( square root of 9+h-3)/h	$lim_{h \to 0} \frac{\sqrt{9 + h} - 3}{h}$
68103	Find the Derivative - d/dθ	(sin(theta))/(1+cos(theta))	$\frac{\sin (θ)}{1 + \cos (θ)}$
68104	Find the Derivative - d/dx	y=6/((5x)^3)	$y = \frac{6}{{(5 x)}^{3}}$
68105	Evaluate the Integral	integral of (5x^3+3x^2+x)/(x^2) with respect to x	$\int \frac{5 x^{3} + 3 x^{2} + x}{x^{2}} d x$
68106	Find dy/dx	y=cos(2x)	$y = \cos (2 x)$
68107	Evaluate the Integral	integral from 1 to 3 of (x^2+2x-4) with respect to x	$\int_{1}^{3} (x^{2} + 2 x - 4) d x$
68108	Find Where Increasing/Decreasing	f(x)=e^(2x)+e^(-x)	$f (x) = e^{2 x} + e^{- x}$
68109	Find the Derivative - d/dx	log base a of 2x^3+7	$\log_{a} (2 x^{3} + 7)$
68110	Evaluate the Limit	limit as x approaches infinity of (4x^2-2x+6)/(-6x^4+8x^3+x^2+7x+4)	$lim_{x \to \infty} \frac{4 x^{2} - 2 x + 6}{- 6 x^{4} + 8 x^{3} + x^{2} + 7 x + 4}$
68111	Evaluate the Integral	integral of (x^2-3x+5) with respect to x	$\int (x^{2} - 3 x + 5) d x$
68112	Evaluate the Summation	sum from i=1 to 7 of (3i-2)^3	$\sum_{i = 1}^{7} {(3 i - 2)}^{3}$
68113	Find dy/dx	y=(2x+3)/(3x+2)	$y = \frac{2 x + 3}{3 x + 2}$
68114	Integrate By Parts	integral of xcos(2x) with respect to x	$\int x \cos (2 x) d x$
68115	Find the Maximum/Minimum Value	k(x)=6x^4+16x^3	$k (x) = 6 x^{4} + 16 x^{3}$
68116	Evaluate the Integral	integral from 1/( square root of 3) to square root of 3 of 5/(1+x^2) with respect to x	$\int_{\frac{1}{\sqrt{3}}}^{\sqrt{3}} \frac{5}{1 + x^{2}} d x$
68117	Find dy/dx	x^2y+3xy^3-x=3	$x^{2} y + 3 x y^{3} - x = 3$
68118	Find the Derivative - d/dx	d/(dx)((2x^2+x-3)/(2x+7))	$\frac{d}{d x} (\frac{2 x^{2} + x - 3}{2 x + 7})$
68119	Find the Inflection Points	F(x)=x square root of 9-x	$F (x) = x \sqrt{9 - x}$
68120	Find dy/dx	xsin(y)+ysin(x)=4	$x \sin (y) + y \sin (x) = 4$
68121	Find the Derivative - d/dx	square root of 9	$\sqrt{9}$
68122	Find the Derivative - d/dx	y=(2-x)/(3x+1)	$y = \frac{2 - x}{3 x + 1}$
68123	Evaluate the Integral	integral of x/(x^2+y^2) with respect to x	$\int \frac{x}{x^{2} + y^{2}} d x$
68124	Evaluate the Limit	limit as x approaches 0 of ((-4x-3)^2-9)/(-5x)	$lim_{x \to 0} \frac{{(- 4 x - 3)}^{2} - 9}{- 5 x}$
68125	Integrate Using u-Substitution	integral of (1+2x)^4(2) with respect to x	$\int {(1 + 2 x)}^{4} (2) d x$
68126	Evaluate the Integral	integral from square root of pi/2 to square root of pi of theta^3cos(theta^2) with respect to theta	$\int_{\sqrt{\frac{π}{2}}}^{\sqrt{π}} θ^{3} \cos (θ^{2}) d θ$
68127	Evaluate the Integral	integral of fourth root of x^4 with respect to x	$\int \sqrt[4]{x^{4}} d x$
68128	Find the Derivative - d/da	(ax+b)/(cx+d)	$\frac{a x + b}{c x + d}$
68129	Evaluate the Limit	limit as x approaches 0.1 from the left of (10x-1)/(\|10x^3-x^2\|)	$lim_{x \to {0.1}^{-}} \frac{10 x - 1}{\| 10 x^{3} - x^{2} \|}$
68130	Find dx/dy	x^2+y^2=36	$x^{2} + y^{2} = 36$
68131	Find dy/dx	1-xy=x-y	$1 - x y = x - y$
68132	Find the Derivative - d/dx	log base a of x	$\log_{a} (x)$
68133	Integrate By Parts	integral of x^4 natural log of x with respect to x	$\int x^{4} \ln (x) d x$
68134	Find dy/dx	y=arcsin(5x)	$y = \arcsin (5 x)$
68135	Find dy/dx	y=x^3 natural log of x	$y = x^{3} \ln (x)$
68136	Find the Derivative - d/dx	y=(x^3)/3+1/(4x)	$y = \frac{x^{3}}{3} + \frac{1}{4 x}$
68137	Find the Maximum/Minimum Value	f(x)=(x^2)/(x^2+3)	$f (x) = \frac{x^{2}}{x^{2} + 3}$
68138	Evaluate the Integral	integral of (u^2+u+1) with respect to u	$\int (u^{2} + u + 1) d u$
68139	Find the Derivative - d/dx	2/x-x^2+1	$\frac{2}{x} - x^{2} + 1$
68140	Evaluate the Integral	integral of (6x^2+12x^3-2x) with respect to x	$\int (6 x^{2} + 12 x^{3} - 2 x) d x$
68141	Find the Concavity	f(x)=6x^5+x^4-5x-6	$f (x) = 6 x^{5} + x^{4} - 5 x - 6$
68142	Find the Derivative - d/dx	y=(cos(x))/(x^3)	$y = \frac{\cos (x)}{x^{3}}$
68143	Find the Second Derivative	y=x square root of x	$y = x \sqrt{x}$
68144	Evaluate the Integral	integral of (sech(1/x)^2)/(x^2) with respect to x	$\int \frac{{sech}^{2} (\frac{1}{x})}{x^{2}} d x$
68145	Find the Derivative - d/dx	cos(xdx)	$\cos (x d x)$
68146	Find Where Increasing/Decreasing	f(x)=2(x+1)^3-5	$f (x) = 2 {(x + 1)}^{3} - 5$
68147	Find the Derivative - d/dx	y=(5x-3)(4x-3/x)	$y = (5 x - 3) (4 x - \frac{3}{x})$
68148	Evaluate the Integral	integral of (x^2+x) with respect to x	$\int (x^{2} + x) d x$
68149	Use Logarithmic Differentiation to Find the Derivative	y=x^(4cos(x))	$y = x^{4 \cos (x)}$
68150	Find the Slope	A	$A$
68151	Find dy/dx	y = cube root of 1+8x	$y = \sqrt[3]{1 + 8 x}$
68152	Find dy/dx	y = natural log of 2x^2-3y^2	$y = \ln (2 x^{2} - 3 y^{2})$
68153	Find the Antiderivative	square root of x^2+1	$\sqrt{x^{2} + 1}$
68154	Find the Tangent Line at (2,-7)	f(x)=-2x^2+1 ; at (2,-7)	$f (x) = - 2 x^{2} + 1$ ; at $(2, - 7)$
68155	Find the Derivative - d/dx	(y^2)/x	$\frac{y^{2}}{x}$
68156	Find Where Increasing/Decreasing	f(x)=x^3-3/2x^2	$f (x) = x^{3} - \frac{3}{2} x^{2}$
68157	Find dy/dx	e^(xy)-y^2=e-4	$e^{x y} - y^{2} = e - 4$
68158	Integrate Using u-Substitution	integral of x/(x^2+1) with respect to x	$\int \frac{x}{x^{2} + 1} d x$
68159	Find Where Increasing/Decreasing	f(x)=-(x+1)^3+12x	$f (x) = - {(x + 1)}^{3} + 12 x$
68160	Find the Derivative - d/dx	y=(x-1)(x^2+x+1)	$y = (x - 1) (x^{2} + x + 1)$
68161	Evaluate the Integral	integral from 0 to 7 of 3 square root of x+9 with respect to x	$\int_{0}^{7} 3 \sqrt{x + 9} d x$
68162	Find dx/dy	x^2y+xy^2=6	$x^{2} y + x y^{2} = 6$
68163	Evaluate the Limit	limit as x approaches 0 of (x+tan(x))/(sin(x))	$lim_{x \to 0} \frac{x + \tan (x)}{\sin (x)}$
68164	Evaluate the Limit	limit as x approaches negative infinity of (x+2)/(x^2+x+1)	$lim_{x \to - \infty} \frac{x + 2}{x^{2} + x + 1}$
68165	Evaluate the Limit	limit as x approaches negative infinity of (6x^4+4x^2-5x+6)/(-5x^3-5x^2-7x+7)	$lim_{x \to - \infty} \frac{6 x^{4} + 4 x^{2} - 5 x + 6}{- 5 x^{3} - 5 x^{2} - 7 x + 7}$
68166	Find dy/dx	y=arctan(x)	$y = \arctan (x)$
68167	Find dy/dx	(x+y)/(x-y)=x	$\frac{x + y}{x - y} = x$
68168	Find dy/dx	x^2y^2+xy=2	$x^{2} y^{2} + x y = 2$
68169	Evaluate the Limit	limit as x approaches pi/6 of 4tan(-x)+4sin(-2x)	$lim_{x \to \frac{π}{6}} 4 \tan (- x) + 4 \sin (- 2 x)$
68170	Find Where Increasing/Decreasing	f(x)=3x	$f (x) = 3 x$
68171	Integrate Using u-Substitution	integral of (x^2+2x)(x+1) with respect to x	$\int (x^{2} + 2 x) (x + 1) d x$
68172	Find dy/dx	x^3+y^3=2xy	$x^{3} + y^{3} = 2 x y$
68173	Find the Derivative - d/dx	d/(dx)(( natural log of x)/(e^x))	$\frac{d}{d x} (\frac{\ln (x)}{e^{x}})$
68174	Find the Derivative - d/da	2a	$2 a$
68175	Solve the Differential Equation	(2x-1)dx+(3y+7)dy=0	$(2 x - 1) d x + (3 y + 7) d y = 0$
68176	Evaluate the Limit	limit as x approaches a of (x^5-a^5)/(x-a)	$lim_{x \to a} \frac{x^{5} - a^{5}}{x - a}$
68177	Find dy/dx	y=arctan( square root of (1+x)/(1-x))	$y = \arctan (\sqrt{\frac{1 + x}{1 - x}})$
68178	Evaluate the Integral	integral of (2/(x^3)+3/(x^2)+5) with respect to x	$\int (\frac{2}{x^{3}} + \frac{3}{x^{2}} + 5) d x$
68179	Find the Derivative - d/dx	y=(4x^2-3)/(x-1)	$y = \frac{4 x^{2} - 3}{x - 1}$
68180	Integrate Using u-Substitution	integral of x/( square root of 1-x^2) with respect to x	$\int \frac{x}{\sqrt{1 - x^{2}}} d x$
68181	Evaluate the Limit	limit as x approaches -2 of (x^3+3x^2+2x)/(x^2-x-6)	$lim_{x \to - 2} \frac{x^{3} + 3 x^{2} + 2 x}{x^{2} - x - 6}$
68182	Find dy/dx	y^x=x^y	$y^{x} = x^{y}$
68183	Maximize the Equation given the Constraints	F=2x+y 3x+5y<=45 , x>=0 and y>=0 2x+4y<=32	$F = 2 x + y$ $3 x + 5 y \leq 45$ , $x \geq 0$ and $y \geq 0$ $2 x + 4 y \leq 32$
68184	Evaluate the Limit	limit as x approaches 8 of (x-8)/( cube root of x-2)	$lim_{x \to 8} \frac{x - 8}{\sqrt[3]{x} - 2}$
68185	Find the Derivative - d/dx	1÷x	$1 \div x$
68186	Find the Derivative - d/dx	y=(4x^2-1/2x)(9x+8)	$y = (4 x^{2} - \frac{1}{2} x) (9 x + 8)$
68187	Find dy/dx	ycos(2x-4y)=-2xy-4	$y \cos (2 x - 4 y) = - 2 x y - 4$
68188	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^3)/(9e^(x/5))	$lim_{x \to \infty} \frac{x^{3}}{9 e^{\frac{x}{5}}}$
68189	Evaluate the Integral	integral from pi/2 to 0 of cos(theta) with respect to theta	$\int_{\frac{π}{2}}^{0} \cos (θ) d θ$
68190	Find Where Increasing/Decreasing	f(x)=-4	$f (x) = - 4$
68191	Evaluate the Limit	limit as x approaches 3 of (x-3)/(x^2+x-12)	$lim_{x \to 3} \frac{x - 3}{x^{2} + x - 12}$
68192	Find dx/dy	y=5x^2e^(3x)	$y = 5 x^{2} e^{3 x}$
68193	Find the Derivative - d/dx	y=x/(cos(x))	$y = \frac{x}{\cos (x)}$
68194	Find the Maximum/Minimum Value	y=(x-3)^2+2	$y = {(x - 3)}^{2} + 2$
68195	Find the Maximum/Minimum Value	h(t)=20-16t^2+32t	$h (t) = 20 - 16 t^{2} + 32 t$
68196	Integrate Using Trig Substitution	integral of 1/(x^2 square root of x^2+4) with respect to x	$\int \frac{1}{x^{2} \sqrt{x^{2} + 4}} d x$
68197	Find the Derivative - d/dx	(2x+1)	$(2 x + 1)$
68198	Find dy/dx	x^2y-xy^2+x^2+y^2=0	$x^{2} y - x y^{2} + x^{2} + y^{2} = 0$
68199	Find dy/dx	sin(xy)=cos(x+y)	$\sin (x y) = \cos (x + y)$
68200	Find the Tangent Line at (0,1)	y=e^xcos(x)+sin(x) , (0,1)	$y = e^{x} \cos (x) + \sin (x)$ , $(0, 1)$