Usando a regra da potência, faça a derivada parcial da função: \( F(x, y, z, w) = e^x - \text{cossec}(y) + 2\text{ln}(z) + \text{ln}(w) \) Escol...

Usando a regra da potência, faça a derivada parcial da função: \( F(x, y, z, w) = e^x - \text{cossec}(y) + 2\text{ln}(z) + \text{ln}(w) \) Escolha uma opção: a. \( \dfrac{df}{dx} = 2xe^x\,\,\,\, \dfrac{df}{dy} = \text{xcossec}(y)\text{xcotg}(y)\,\,\,\,\dfrac{df}{dz} = \dfrac{2}{z}\,\,\,\,\dfrac{df}{dw} = \dfrac{1}{w} \) b. \( \dfrac{df}{dx} = e^x\,\,\,\, \dfrac{df}{dy} = \text{cossec}(y)\text{cotg}(y)\,\,\,\,\dfrac{df}{dz} = \dfrac{2}{z}\,\,\,\,\dfrac{df}{dw} = \dfrac{1}{w} \) c. \( \dfrac{df}{dx} = e^x\,\,\,\, \dfrac{df}{dy} = \text{- cossec}(y)\text{cotg}(y)\,\,\,\,\dfrac{df}{dz} = \dfrac{2}{z}\,\,\,\,\dfrac{df}{dw} = \dfrac{1}{w} \) d. \( \dfrac{df}{dx} = e^y\,\,\,\, \dfrac{df}{dy} = \text{cossec}(x)\text{cotg}(x)\,\,\,\,\dfrac{df}{dz} = \dfrac{2}{w}\,\,\,\,\dfrac{df}{dw} = \dfrac{1}{z} \)