How do you differentiate f(x)=e^(sin(2/x) using the chain rule.?

Apr 17, 2017

first differentiate ${e}^{\sin} \left(\frac{2}{x}\right)$ then differentiate $\sin \left(\frac{2}{x}\right)$ and finally differentiate $\left(\frac{2}{x}\right)$ .
so , differentiation of ${e}^{x}$ is ${e}^{x}$ ,
differentiation of $\sin x$ is $\cos x$ ,
differentiation of $\frac{2}{x}$ is $- \frac{2}{x} ^ 2$ ,
$f ' \left(x\right) = {e}^{\sin} \left(\frac{2}{x}\right) \cdot \cos \left(\frac{2}{x}\right) \cdot \left(- \frac{2}{x} ^ 2\right)$