Calculus questions - page 641

Questions

Rank	Topic	Problem	Formatted Problem
64001	Find the Derivative - d/d@VAR	h(t)=(t^4-1)^9(t^3+1)^4	$h (t) = {(t^{4} - 1)}^{9} {(t^{3} + 1)}^{4}$
64002	Find the Derivative - d/d@VAR	h(t) = fourth root of t-4e^t	$h (t) = \sqrt[4]{t} - 4 e^{t}$
64003	Evaluate the Summation	sum from n=1 to 100 of 2n-6	$\sum_{n = 1}^{100} 2 n - 6$
64004	Evaluate the Summation	sum from n=1 to 100 of 3+n^2	$\sum_{n = 1}^{100} 3 + n^{2}$
64005	Evaluate the Summation	sum from k=1 to 6 of 8k	$\sum_{k = 1}^{6} 8 k$
64006	Evaluate the Summation	sum from k=1 to 6 of 2k	$\sum_{k = 1}^{6} 2 k$
64007	Find dy/dx	(dy)/(dx)=x-10	$\frac{d y}{d x} = x - 10$
64008	Find dy/dx	x^3y^2-e^(3y)=5	$x^{3} y^{2} - e^{3 y} = 5$
64009	Find dy/dx	x^3-xy^2+y^3=1	$x^{3} - x y^{2} + y^{3} = 1$
64010	Find dy/dx	x^2y+4y=8	$x^{2} y + 4 y = 8$
64011	Find dy/dx	4x^2+3xy+7y^3+4y^2=2	$4 x^{2} + 3 x y + 7 y^{3} + 4 y^{2} = 2$
64012	Find dy/dx	4x^2-2y^2=9	$4 x^{2} - 2 y^{2} = 9$
64013	Find dy/dx	y=(3x^2-9)^-10	$y = {(3 x^{2} - 9)}^{- 10}$
64014	Find Where Increasing/Decreasing Using Derivatives	3(x-4)^(2/3)+6	$3 {(x - 4)}^{\frac{2}{3}} + 6$
64015	Find the Integral	integral of e^(4x) with respect to x	$\int e^{4 x} d x$
64016	Find the Integral	integral of cos(x^2) with respect to x	$\int \cos (x^{2}) d x$
64017	Find the Integral	integral of cube root of x with respect to x	$\int \sqrt[3]{x} d x$
64018	Find the Integral	((x^3-3x^2+2x-1)dx)/(x^2-4x+4)	$\frac{(x^{3} - 3 x^{2} + 2 x - 1) d x}{x^{2} - 4 x + 4}$
64019	Find the Integral	4^x	$4^{x}$
64020	Find the Derivative - d/dt	2te^(3t)	$2 t e^{3 t}$
64021	Find the Derivative - d/dy	cos(2y)	$\cos (2 y)$
64022	Find the Derivative - d/d@VAR	f(x)=0.005x(300-x)	$f (x) = 0.005 x (300 - x)$
64023	Find the Derivative - d/d@VAR	f(x) = sixth root of (x^2+1)^5	$f (x) = \sqrt[6]{{(x^{2} + 1)}^{5}}$
64024	Find the Derivative - d/d@VAR	f(x)=(e^(-3x) square root of 2x-5)/((6-5x)^4)	$f (x) = \frac{e^{- 3 x} \sqrt{2 x - 5}}{{(6 - 5 x)}^{4}}$
64025	Find the Derivative - d/d@VAR	f(x)=(5x-5)(4x^3-x^2+1)	$f (x) = (5 x - 5) (4 x^{3} - x^{2} + 1)$
64026	Find the Derivative - d/d@VAR	f(x)=6/(x^4)	$f (x) = \frac{6}{x^{4}}$
64027	Find the Derivative - d/d@VAR	f(x)=arcsin(8x)+arccos(8x)	$f (x) = \arcsin (8 x) + \arccos (8 x)$
64028	Find the Derivative - d/d@VAR	f(x)=e^(18x)	$f (x) = e^{18 x}$
64029	Find the Derivative - d/d@VAR	f(x)=e^x-x^e	$f (x) = e^{x} - x^{e}$
64030	Find the Derivative - d/d@VAR	f(x)=2^70	$f (x) = 2^{70}$
64031	Find the Derivative - d/d@VAR	f(x)=19e^x	$f (x) = 19 e^{x}$
64032	Find the Derivative - d/d@VAR	f(x)=5x+1	$f (x) = 5 x + 1$
64033	Find the Derivative - d/d@VAR	f(t)=(cos(t))/t	$f (t) = \frac{\cos (t)}{t}$
64034	Find the Derivative - d/d@VAR	f(s)=arccot(e^s)	$f (s) = arccot (e^{s})$
64035	Find the Derivative - d/d@VAR	f(x)=1/(2x^(1/3))	$f (x) = \frac{1}{2 x^{\frac{1}{3}}}$
64036	Find the Derivative - d/d@VAR	f(x)=144/x	$f (x) = \frac{144}{x}$
64037	Find the Derivative - d/d@VAR	B(y)=cy^-7	$B (y) = c y^{- 7}$
64038	Find the Local Maxima and Minima	f(x)=(x-7)(x^2-14x-98)	$f (x) = (x - 7) (x^{2} - 14 x - 98)$
64039	Find the Second Derivative	x^(1/2)	$x^{\frac{1}{2}}$
64040	Evaluate the Summation	sum from i=1 to 6 of 9i	$\sum_{i = 1}^{6} 9 i$
64041	Evaluate the Summation	sum from i=4 to 12 of -4-7i	$\sum_{i = 4}^{12} - 4 - 7 i$
64042	Evaluate the Summation	sum from i=1 to 4 of (i+1)^i	$\sum_{i = 1}^{4} {(i + 1)}^{i}$
64043	Find dy/dx	y = square root of 4-x^2	$y = \sqrt{4 - x^{2}}$
64044	Find dy/dx	y = cube root of x	$y = \sqrt[3]{x}$
64045	Find dy/dx	y=-4x^3	$y = - 4 x^{3}$
64046	Find dy/dx	8x^2+4xy+4y^2=0	$8 x^{2} + 4 x y + 4 y^{2} = 0$
64047	Find dy/dx	e^(2x)=sin(x+2y)	$e^{2 x} = \sin (x + 2 y)$
64048	Find dy/dx	cos(xy)+x^4=y^4	$\cos (x y) + x^{4} = y^{4}$
64049	Find dy/dx	x^2-y^2=80	$x^{2} - y^{2} = 80$
64050	Find dy/dx	x^2y^2-2x=4-4y	$x^{2} y^{2} - 2 x = 4 - 4 y$
64051	Find dy/dx	tan(x-y)=y/(9+x^2)	$\tan (x - y) = \frac{y}{9 + x^{2}}$
64052	Find dy/dx	x^10-5x^2y^2=4	$x^{10} - 5 x^{2} y^{2} = 4$
64053	Find dy/dx	square root of xy=4x+2y	$\sqrt{x y} = 4 x + 2 y$
64054	Find dy/dx	2y^2+7x^2-13=0	$2 y^{2} + 7 x^{2} - 13 = 0$
64055	Evaluate the Summation	sum from k=1 to 2 of (72k)/(k+7)	$\sum_{k = 1}^{2} \frac{72 k}{k + 7}$
64056	Evaluate the Summation	sum from k=8 to 47 of 3.5	$\sum_{k = 8}^{47} 3.5$
64057	Evaluate the Summation	sum from n=1 to 100 of 2n-4	$\sum_{n = 1}^{100} 2 n - 4$
64058	Evaluate the Summation	sum from n=1 to 120 of 2n-8	$\sum_{n = 1}^{120} 2 n - 8$
64059	Evaluate the Summation	sum from n=1 to 120 of 6-1/2n	$\sum_{n = 1}^{120} 6 - \frac{1}{2} n$
64060	Find the Second Derivative	x^2+y^2=7	$x^{2} + y^{2} = 7$
64061	Find the Derivative - d/d@VAR	f(x)=(1-2x)^-8	$f (x) = {(1 - 2 x)}^{- 8}$
64062	Find the Derivative - d/d@VAR	f(x)=(10-7x^2)(10x^3+6x^-2+8)	$f (x) = (10 - 7 x^{2}) (10 x^{3} + 6 x^{- 2} + 8)$
64063	Find the Derivative - d/d@VAR	f(x)=2/(3x^(1/3))	$f (x) = \frac{2}{3 x^{\frac{1}{3}}}$
64064	Find the Derivative - d/d@VAR	f(x)=3/5x^10	$f (x) = \frac{3}{5} x^{10}$
64065	Find the Derivative - d/d@VAR	f(r)=5/(r^3)	$f (r) = \frac{5}{r^{3}}$
64066	Find the Derivative - d/d@VAR	f(theta)=7/5sin(2theta)^2	$f (θ) = \frac{7}{5} \sin^{2} (2 θ)$
64067	Find the Derivative - d/d@VAR	f(t)=1/4(t^4+8)	$f (t) = \frac{1}{4} (t^{4} + 8)$
64068	Find the Derivative - d/d@VAR	f(t)=5tsin(pit)	$f (t) = 5 t \sin (π t)$
64069	Find the Derivative - d/d@VAR	f(t)=e^(5tsin(2t))	$f (t) = e^{5 t \sin (2 t)}$
64070	Find the Derivative - d/d@VAR	f(t)=t- cube root of t	$f (t) = t - \sqrt[3]{t}$
64071	Find the Derivative - d/d@VAR	f(x)=(x+1)/(x-1)	$f (x) = \frac{(x + 1)}{(x - 1)}$
64072	Find the Derivative - d/d@VAR	f(x)=3x-8	$f (x) = 3 x - 8$
64073	Find the Derivative - d/d@VAR	f(x)=-4x-2	$f (x) = - 4 x - 2$
64074	Find the Derivative - d/d@VAR	f(x)=4x^2-2x+3	$f (x) = 4 x^{2} - 2 x + 3$
64075	Find the Derivative - d/d@VAR	f(x)=-7x^3	$f (x) = - 7 x^{3}$
64076	Find the Derivative - d/d@VAR	f(x)=-6x^3	$f (x) = - 6 x^{3}$
64077	Find the Derivative - d/d@VAR	f(x)=3e^(2x-5)	$f (x) = 3 e^{2 x - 5}$
64078	Find the Derivative - d/d@VAR	f(x)=3^(2x)	$f (x) = 3^{2 x}$
64079	Find the Derivative - d/d@VAR	f(x)=2^80	$f (x) = 2^{80}$
64080	Find the Derivative - d/d@VAR	f'(x)=cos(x)	$f' (x) = \cos (x)$
64081	Find the Derivative - d/d@VAR	f(x)=x^( natural log of x)	$f (x) = x^{\ln (x)}$
64082	Find the Derivative - d/d@VAR	f(x)=x square root of x+4	$f (x) = x \sqrt{x + 4}$
64083	Find the Derivative - d/d@VAR	f(x)=tan(2x)	$f (x) = \tan (2 x)$
64084	Find the Derivative - d/d@VAR	f(x)=sin(2x)e^(3x+1)	$f (x) = \sin (2 x) e^{3 x + 1}$
64085	Find the Derivative - d/d@VAR	F(x)=(5x+8)^2	$F (x) = {(5 x + 8)}^{2}$
64086	Find the Derivative - d/d@VAR	f(x)=7/2x^2	$f (x) = \frac{7}{2} x^{2}$
64087	Find the Derivative - d/d@VAR	f(x)=6/x+1/(x^2)	$f (x) = \frac{6}{x} + \frac{1}{x^{2}}$
64088	Find the Derivative - d/d@VAR	f(x) = log of cos(x)	$f (x) = \log (\cos (x))$
64089	Find the Derivative - d/d@VAR	f(x) = square root of x natural log of x	$f (x) = \sqrt{x} \ln (x)$
64090	Find the Derivative - d/d@VAR	f(x) = natural log of 4x	$f (x) = \ln (4 x)$
64091	Find the Derivative - d/d@VAR	f(x)=(x^3)/9	$f (x) = \frac{x^{3}}{9}$
64092	Find the Derivative - d/d@VAR	g(theta)=cos(theta)^2	$g (θ) = \cos^{2} (θ)$
64093	Find the Derivative - d/d@VAR	f(x)=xe^(x^2+1)	$f (x) = x e^{x^{2} + 1}$
64094	Find the Derivative - d/d@VAR	f(x)=x^4-17x^2+16	$f (x) = x^{4} - 17 x^{2} + 16$
64095	Find the Derivative - d/d@VAR	f(x)=x^2(x-2)^4	$f (x) = x^{2} {(x - 2)}^{4}$
64096	Find the Derivative - d/d@VAR	f(x)=x^2+7x-2	$f (x) = x^{2} + 7 x - 2$
64097	Find the Derivative - d/d@VAR	g(x)=1/(x^2)	$g (x) = \frac{1}{x^{2}}$
64098	Find the Derivative - d/d@VAR	s(t)=(7t)/(sin(t))	$s (t) = \frac{7 t}{\sin (t)}$
64099	Find the Derivative - d/d@VAR	s(t)=19t^2	$s (t) = 19 t^{2}$
64100	Find the Derivative - d/dT	(89T)/(99T-89)	$\frac{89 T}{99 T - 89}$

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