Mathematics, 10.07.2019 13:20 lilly198o
Find the gradient of the function at the given point. function point f(x, y, z) = x2 + y2 + z2 (3, 9, 8)
Answers: 1
![\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)](/tpl/images/0073/3795/c3356.png)
![\displaystyle \nabla \big[ \alpha f(x) \big] = \alpha \nabla f(x)](/tpl/images/0073/3795/6e823.png)
[Gradient] Rewrite [Gradient Property - Addition/Subtraction]: ![\displaystyle \nabla f = \bigg[ \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial x}(y^2) + \frac{\partial}{\partial x}(z^2) \bigg] \hat{\i} + \bigg[ \frac{\partial}{\partial y}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial y}(z^2) \bigg] \hat{\j} + \bigg[ \frac{\partial}{\partial z}(x^2) + \frac{\partial}{\partial z}(y^2) + \frac{\partial}{\partial z}(z^2) \bigg] \hat{\text{k}}](/tpl/images/0073/3795/593c4.png)
[Gradient] Differentiate [Derivative Rule - Basic Power Rule]: 
[Gradient] Substitute in point: 
[Gradient] Evaluate: 
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Find the gradient of the function at the given point. function point f(x, y, z) = x2 + y2 + z2 (3, 9...
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