I have to prove that, given $ f\in C^{1, \frac{\alpha}{2}}([a, b])$ , then there exists a constant $ K$ such that $ $ \|e^f\|_{1, \frac{\alpha}{2}}\leq K\|f\|_{1, \frac{\alpha}{2}}. $ $ I do not undestand how to prove it. Can someone help me?

Thank You