Let f(x, y, z) = x^4 y^3 + z^2 and x = st, y = st^2, and z = st. (a) Calculate t
ID: 2875168 • Letter: L
Question
Let f(x, y, z) = x^4 y^3 + z^2 and x = st, y = st^2, and z = st. (a) Calculate the primary derivatives partial differential f/partial differential x = 4x^3y^3 partial differential f/partial differential y =3y^2x^4 partial differential f/partial differential z = 2z (b) Calculate partial differential x/partial differential s = t partial differential y/partial differential s = t^2 partial differential z/partial differential s = t (c) Use the Chain Rule to compute partial differential f/partial differential s = 4s^9t^10+3t^10s^8+2st^2 In (c) express your answer in terms of the independent variables t, sExplanation / Answer
f(x, y, z) = x4y3 + z2 , x= st , y = st2 , z= st
df/ds = d(x4y3)/ds +d(z2)/ds
= 4x3(dx/ds) *y3 + x4 * 3y2 (dy/ds) +2z(dz/ds)
=4x3(t)*y3 +x4 *3y2(t2) +2z*t
=4t *(st)3 *(st2)3 +3(st2)2 *(t2) +2*(st)*t
=4s6t10 + 3s2t6 +2st2 is the answer
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