Question 26.2: If Φ = Φ (x, y, z) = 4x³y sin z, find ∇Φ....
If \phi=\phi(x,y,z)=4x^{3}y\,\mathrm{sin}\,z,, find ∇Φ.
Step-by-Step
\phi(x,y,z)=4x^{3}y\sin z
so that by partial differentiation we obtain
{\frac{\partial\phi}{\partial x}}=12x^{2}y\sin z\\ {\frac{\partial\phi}{\partial y}}=4x^{3}\sin z\\ {\frac{\partial\phi}{\partial z}}=4x^{3}y\cos zTherefore
\nabla\phi=12x^{2}y\sin z\mathbf{i}+4x^{3}\sin z\mathbf{j}+4x^{3}y\cos z\mathbf{k}Related Answered Questions
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