求函数f = ln(x² + y²+ z²)在点M(1,2,-2)处的梯度gradf|M.

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求函数f=ln(x²+y²+z²)在点M(1,2,-2)处的梯度gradf|M.求函数f=ln(x²+y²+z²)在点M(1,2,-2)处的

求函数f = ln(x² + y²+ z²)在点M(1,2,-2)处的梯度gradf|M.
求函数f = ln(x² + y²+ z²)在点M(1,2,-2)处的梯度gradf|M.

求函数f = ln(x² + y²+ z²)在点M(1,2,-2)处的梯度gradf|M.
先求偏导
af/ax=2x/(x^2+y^2+z^2)将点代入=2/9
af/ay=2y/(x^2+y^2+z^2)将点代入=4/9
af/az=2z/(x^2+y^2+z^2)将点代入=-4/9
gradf|M=(2/9)i+(4/9)j+(-4/9)k