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  1. Consider the function z=(x+y)e^y and x= u ^2+v^2 and y= u ^2−v^2. Recollect the chain rule: ∂z/∂ u = ∂z/∂x...y*e^y + e^y*∂/∂y*(x+y)= (x + y)e^y + e^y *1 =  = (x + y + 1)e^y x = u ^2 + v^2 ∂z/∂ u = ∂/∂ u *( u ^2+v^2) = 2u + 0 =  2u.  Treat v as constant...

    2 Answers · Science & Mathematics · 03/10/2020

  2. The first instruction, in bold, implies that you should enter square roots in the format "a^0.5". So try replacing (sqrt(3)) with 3^0.5 and replacing (sqrt(2)) with 2^0.5 For information,  you omitted a minus sign in a basis vector in your...

    1 Answers · Science & Mathematics · 18/08/2020

  3. x * ln(x) * dx = y * (1 + sqrt(15 + y^2)) * dy u = 15 + y^2 du = 2y * dy x * ln(x) * dx = (1/2) * (1 + sqrt( u )) * du x * ln(x) * dx...2/3) * u ^(3/2) + C (1/2) * x^2 * ln(x) - (1/2) * int(x^2 * dx/x) = (1/2) * u + (1/3) * u ^(3/2) + C x^2 * ln(x) - int(x * dx) = u + (2/3) * u ^(3/2) + ...

    2 Answers · Science & Mathematics · 23/06/2020

  4. ...5) / arcsin(x^2) We have 0/0, so we can use L'hopital's rule u = arctan(x/5) tan( u ) = x/5 sec( u )^2 * u ' = 1/5 u ' = (1/5) / sec( u )^2 u '...

    3 Answers · Science & Mathematics · 07/11/2019

  5. .... Let's try to break this down: y = ln|(1 - x)e^(-3x)| if we say: u = |(1 - x)e^(-3x)| then we have: y = ln( u ) This derivative is simple...

    4 Answers · Science & Mathematics · 18/06/2020

  6. ... POSITIVE, //      the parabola is CONCAVE UP ( U -shaped) so //      it won't have any maximum, but it will have a...

    4 Answers · Science & Mathematics · 09/09/2020

  7. a) III. is an identity because sin(2u) = 2sin( u )cos( u ) None of the others are identities which can...

    2 Answers · Science & Mathematics · 27/07/2020

  8. ... are kC2 ways to choose two different integers U ,V ( U <V) from S. Let a pair of...

    1 Answers · Science & Mathematics · 09/02/2020

  9. ... perpendicular to the plane. determinate of i  j  k 2 2 1 2 -2 -4 is u = <-6, 10, -8>, and that's a normal to the plane. The...

    2 Answers · Science & Mathematics · 12/06/2020

  10. ... k' = 6x⁵ m = (x - 1)¹⁰ for the chain rule, if we set: u = x - 1 and m = u¹⁰ We can get the first derivative of u in...

    1 Answers · Science & Mathematics · 30/06/2020

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