Respuesta :

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[tex] \frac{dw}{dt} = \frac{dx}{dt} \times \frac{dw}{dx} + \frac{dy}{dt} \times \frac{dw}{dy} + \frac{dz}{dt} \times \frac{dw}{dz} \\ \frac{dw}{dt} = 3t ^{2} \times {e}^{ \frac{y}{z} } + - t \times \frac{x {e}^{ \frac{y}{z} } }{z} + 4 \times - \frac{xy {e}^{ \frac{y}{z} } }{ {z}^{2} } \\ \frac{dw}{dt} = \frac{ {e}^{ \frac{y}{z} } (3 {t}^{2} {z}^{2} - tzx - 4xy)}{ {z}^{2} } [/tex]