If $f ( x , y ) = \ln ( y )$ , then $\nabla f ( x , y ) = \frac { 1 } { y }$ .

Name: If $f ( x , y ) = \ln ( y )$ , then $\nabla f ( x , y ) = \frac { 1 } { y }$ .
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The gradient of $f(x, y) = \ln(y)$ is $\nabla f(x, y) = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) = (0, \frac{1}{y})$, because the partial derivative with respect to $x$ is $0$ since $f$ does not depend on $x$, and the partial derivative with respect to $y$ is $\frac{1}{y}$.

If f(x,y)=ln⁡(y)f ( x , y ) = \ln ( y )f(x,y)=ln(y)

If $f ( x , y ) = \ln ( y )$