f(x) =

**u**/v....i.e.**u**= 5x² + 4x + 3 and v = 2x² - 2x - 14 Now, f '(x) = (**u**'v -**u**v')/v² so, f '(x) = [(10x + 4)(2x² - 2x - 14) - (...3 Answers · Science & Mathematics · 28/06/2020

1) Q

**u**otient r**u**le: {d/dx}(**u**/v) = (1/v^2)[v(d**u**/dx) -**u**(dv/dx)]. For tan = sin/cos we have**u**= sin and... with chain & power: We write tan = sin*cos^-1. Then**u**= sin & v = cos^-1. {d/dx}(**u***v) = [**u**(dv/dx) + v(d**u**/dx)]. (dv/dx) = -cos^-2(-sin...2 Answers · Science & Mathematics · 02/07/2020

Angle between vectors: cos α = a·b / |a|·|b|

**u**·v = (ax)(bx) + (ay)(by) = (2)(3) + (-4)(-8) = 38 |**u**| = √((2)² + (-4)²) = 2√5 |v| = √((3)² + (-8)²) = √73 cos α = 38 / 2√5√73 α = 6.0°1 Answers · Science & Mathematics · 10/08/2020

... or B ) is the same as P(A

**U**B) This is a general rule P...which must have the same results. P(A**U**B) = P(A) + P(B...2 Answers · Science & Mathematics · 06/10/2020

Green says: ∮_C (

**u**dx + v dy) = ∫∫_R (∂v/∂x - ∂**u**/∂y) dx dy. Yo**u**have**u**=4y²x...1 Answers · Science & Mathematics · 27/06/2020

... the chain r

**u**le: y = (x² + 4x)^(1/3) Set this**u**p as: y =**u**^(1/3) and**u**= x² + 4x The chain r**u**le is: dy/dx = dy/d**u*** d**u**...8 Answers · Science & Mathematics · 13/10/2020

Yes. And then you determine the leading coefficient so the y-intercept becomes 25. f(x) = a(x+2)^2 + 13 f(0) = 25 a = 3 There are many "

**U**shape" curves and I assume you do want the parabola.1 Answers · Science & Mathematics · 07/10/2020

...x + 2) to get this first derivative we need to

**u**se the q**u**otient r**u**le: if f =**u**/v, then f' = (**u**'v -**u**v') / v² So we can set**u**p o**u**r...1 Answers · Science & Mathematics · 01/10/2020

.... ₀∫¹(x-8)/(x²-7x+10) dx = s

**u**bstit**u**te immediately**u**=2x-7 (yes, that's derivative of the denominator), => x=(**u**+7)/2, d**u**=2dx new ...5 Answers · Science & Mathematics · 26/06/2020

.... Let's start with setting

**u**p the q**u**otient r**u**le: y =**u**/v and**u**= (z² - 5)³ and v = (z² + 4)² y' = (**u**...4 Answers · Science & Mathematics · 26/10/2020