Question

Determine 𝜕3𝑈 over 𝜕𝑥𝜕𝑦𝜕𝑧 , if 𝑈(𝑥, 𝑦, 𝑧) = 𝑒 power 𝑥𝑦z

Answer 1

u(x,y,z) = e^(xyz)

𝜕u/𝜕x = yz e^(xyz)
𝜕2/u/𝜕d𝜕y = (z + xyz^2)e^(xyz)
𝜕3u/𝜕x𝜕y𝜕z = [(1+2xyz) + (z + xyz^2)*xy]e^(xyz)