If $f ( r , \theta ) = r \sin \theta + r ^ { 2 } \tan ^ { 2 } \theta$ , find the partial derivative of $f$ with respect to $r$ and the partial derivative with respect to $\theta$ , both at the point $\left( - 4 , \frac { \pi } { 6 } \right)$ .

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The Answer of If $f ( r , \theta ) = r \sin \theta + r ^ { 2 } \tan ^ { 2 } \theta$ , find the partial derivative of $f$ with respect to $r$ and the partial derivative with respect to $\theta$ , both at the point $\left( - 4 , \frac { \pi } { 6 } \right)$ .

If f(r,θ)=rsin⁡θ+r2tan⁡2θf ( r , \theta ) = r \sin \theta + r ^ { 2 } \tan ^ { 2 } \thetaf(r,θ)=rsinθ+r2tan2θ

If $f ( r , \theta ) = r \sin \theta + r ^ { 2 } \tan ^ { 2 } \theta$