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Consider the f

**u**nction z=(x+y)e^y and x=**u**^2+v^2 and y=**u**^2−v^2. Recollect the chain r**u**le: ∂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) = 2**u**+ 0 = 2**u**. Treat v as constant...2 Answers · Science & Mathematics · 03/10/2020

The first instr

**u**ction, in bold, implies that yo**u**sho**u**ld enter sq**u**are roots in the format &q**u**ot;a^0.5&q**u**ot;. So try replacing (sqrt(3)) with 3^0.5 and replacing (sqrt(2)) with 2^0.5 For information, yo**u**omitted a min**u**s sign in a basis vector in yo**u**r...1 Answers · Science & Mathematics · 18/08/2020

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

...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

.... 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

... POSITIVE, // the parabola is CONCAVE

**U**P (**U**-shaped) so // it won't have any maximum, but it will have a...4 Answers · Science & Mathematics · 09/09/2020

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

... 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

... perpendic

**u**lar 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

... k' = 6x⁵ m = (x - 1)¹⁰ for the chain r

**u**le, if we set:**u**= x - 1 and m =**u**¹⁰ We can get the first derivative of**u**in...1 Answers · Science & Mathematics · 30/06/2020

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