Question

Find the derivative of $y=e^{\sin \theta }$ with respect to $\theta$

• A. $e^{\cos \theta }\left(\sin \theta \right)$
• B. $e^{\sin \theta }\left(\cos \theta \right)$
• C. $e^{\tan \theta }\left(\sin \theta \right)$
• D. $e^{\cos \theta }\left(\cot \theta \right)$

Answer 1

The correct option is B $e^{\sin \theta }\left(\cos \theta \right)$

Given: $y=e^{\sin \theta }$
Using chain rule we have
$y^{{}^{\prime }}=\frac{d{e}^{\sin \theta }}{d\sin \theta }\times \frac{d\sin \theta }{d\theta }$
$\Rightarrow y^{{}^{\prime }}=e^{\sin \theta }\left(\cos \theta \right)$