Question

Q6. Find the gradient of the following functions

f(x, y, z) = x2y3z4.

f(x, y, z) = exsin(y) ln(z).

Answer 1

$\text{grad }f_1=2xy^3z^4\vec i+3x^2y^2z^4\vec j+4x^2y^3z^3\vec k,$

$\text{grad}f_2=e^x\sin y\ln z\vec i+e^x\cos y\ln z\vec j+\frac{e^x\sin y}z\vec k.$