Test 8: Fluid Dynamics

Instruction: Create a pdf file with all the solutions, upload file on Google Drive and share the link in the form shared at the bottom of the page

Total Marks: 75

1) Find the directional derivative of $\varphi (x,y,z)=x^{2}yz+4x{z}^2$ at the point (1,-2,-1) in the direction of the vector $2\overrightarrow{i}-\overrightarrow{j}-2\overrightarrow{k}$.

a) ${\displaystyle \frac{37}{9}}$
b) ${\displaystyle \frac{37}{3}}$
c) ${\displaystyle \frac{37}{6}}$
d) ${\displaystyle \frac{37}{7}}$