Let f(x, y, z) = xy^3 + z^2 and x = s^3t^3, y = st^3, and z = s^2t^2 Calculate t
ID: 2876956 • Letter: L
Question
Let f(x, y, z) = xy^3 + z^2 and x = s^3t^3, y = st^3, and z = s^2t^2 Calculate the primary derivatives partial differential f/partial differential z = partial differential f/partial differential y = partial differential f/partial differential z = Calculate partial differential x/partial differential s = partial differential y/partial differential s = partial differential z/partial differential s = Use the Chain Rule to compute partial differential f/partial differential s = In (c) express your answer in terms of the independent variables t, sExplanation / Answer
given f(x,y,z)=xy3+z2
a)
f/x=y3
f/y=3xy2
f/z=2z
x=s3t3,y=st3,z=s2t2
b)
x/s=3s2t3
y/s=t3
z/s=2st2
c)f/s =(f/x *x/s)+(f/y *y/s)+(f/z *z/s)
f/s =((y3)*(3s2t3))+((3xy2)*(t3))+((2z)*(2st2))
f/s =(((st3)3)*(3s2t3))+((3(s3t3)(st3)2)*(t3))+((2(s2t2))*(2st2))
f/s =(s3t9 *3s2t3)+(3(s3t3)(s2t6)*t3)+(2(s2t2)*2st2)
f/s =(3s5t12)+(3s5t12)+(4s3t4)
f/s =(6s5t12)+(4s3t4)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.