If $y = log (sin (e^{x} + 5 x + 8))$ find $d y / d x$

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Solution

$\begin{matrix} G i v e n y = log sin (e^{x} + 5 x + 8), - - - (1) O n d i f f e r e n t i a t i n g b o t h s i d e o f (1) w . r . t x w e g e t \frac{d y}{d x} = \frac{1}{sin (e^{x} + 5 x + 8)} . cos (e^{x} + 5 x + 8) . \frac{d (e^{x} + 5 x + 8)}{d x} = {cot (e^{x} + 5 x + 8)} (e^{x} + 5) = (e^{x} + 5) . cot (e^{x} + 5 x + 8) . \end{matrix}$

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