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differentiate wrtx

1)log(a+ bsinx)/(a-bsinx)

2)log₇(log₇x)

3)(e^x+e^-x)/(e^x-e^-x)

$y = \log (\frac{a + b \sin x}{a - b \sin x}) = \log (a + b \sin x) - \log (a - b \sin x) \frac{d y}{d x} = \frac{1}{a + b \sin x} (b \cos x) - \frac{1}{a - b \sin x} (- b \cos x) \frac{d y}{d x} = \frac{b \cos x}{a + b \sin x} + \frac{b \cos x}{a - b \sin x} = \frac{2 a b \cos x}{a^{2} - b^{2} \sin^{2} x} y = \log_{7} \log_{7} x \Rightarrow \frac{d y}{d x} = \frac{1}{\log_{7} x} \times (\frac{1}{x}) y = \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} \frac{d y}{d x} = \frac{(e^{x} - e^{- x}) (e^{x} - e^{- x}) - (e^{x} + e^{- x}) (e^{x} + e^{- x})}{(e^{x} - e^{- x})^{2}} = - \frac{4}{(e^{x} - e^{- x})^{2}}$

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