From Rogawski ET 2e section 14.6, exercise 1. (a) Calculate the primary derivati
ID: 2835844 • Letter: F
Question
From Rogawski ET 2e section 14.6, exercise 1.
(a) Calculate the primary derivatives
(b) Calculate
(c) Use the Chain Rule to compute
From Rogawski ET 2e section 14.6, exercise 1. Let f(x,y,z)=x^{3}y^{2}+z^{4} and x=s^{3}t^{2}, y=st^{3}, and z=st. Calculate the primary derivatives rac{partial{f}}{partial{x}}= 3x^2y^2 Calculate rac{partial{x}}{partial{s}}= Use the Chain Rule to compute (9s^10t^12)+(2s^10t^11)+(4s^3t^4) In (c) express your answer in terms of the independent variables t,s Help please !!!Explanation / Answer
c) use chain rule
df/ds = df/dx *dx/ds + df/dy*dy/ds +df/dz *dz/ds
df/dx = 3x^2 y^2 = 3(s^3 t^2)^2 (st^3)^2 = 3 *s^8 t^10
df/dy = 2yx^3 = 2(st^3)(s^3 t^2)^3 = 2s^10 t^9
df/dz = 4z^3 = 4s^3 t^3
dx/ds = 3s^2 t^2
dy/ds = t^3
dz/ds = t
df/ds = 3s^8 t^10 * 3s^2 t^2 + 2s^10 t^9 * t^3 + 4s^3 t^3 * t
= 9 s^10 t^12 + 2 s^10 t^12 + 4 s^3 t^4