Question

If f(x, y, z) = 3x^2y + 2 y -3z then del f is​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ f(x, y, z) = 3 {x}^{2}y + 2y - 3z }$

TO DETERMINE

The value of $\sf{ \nabla f}$

EVALUATION

Here it is given that

$\displaystyle \sf{ f(x, y, z) = 3 {x}^{2}y + 2y - 3z }$

Now

$\displaystyle \sf{ \nabla f }$

$\displaystyle \sf{ = \nabla f(x, y, z) }$

$\displaystyle \sf{ = \bigg(\hat{i} \frac{ \partial}{ \partial x} + \hat{j} \frac{ \partial}{ \partial y} +\hat{k} \frac{ \partial}{ \partial z} \bigg)(3 {x}^{2}y + 2y - 3z) }$

$\displaystyle \sf{ = \hat{i} \frac{ \partial}{ \partial x} (3 {x}^{2}y + 2y - 3z) + \hat{j} \frac{ \partial}{ \partial y}(3 {x}^{2}y + 2y - 3z) +\hat{k} \frac{ \partial}{ \partial z} (3 {x}^{2}y + 2y - 3z)}$

$\displaystyle \sf{ = 6xy\hat{i} +(3 {x}^{2} + 2) \hat{j} - 3\hat{k} }$

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