Chapter 2: Differentiation

Section 2.9: The Hyperbolic Functions and Their Derivatives

	Example 2.9.1
	$$ Verify the differentiation rule for $\sinh \left(x\right)$. $$ Solution $$ Write $\sinh \left(x\right)$ in terms of its exponential definition, then differentiate. The details are follows.   $\frac{d}{\mathrm{dx}}\sinh \left(x\right)$ $\=\frac{d}{\mathrm{dx}}\left(\frac{e^x-e^{-x}}{2}\right)$ $$ $\=\frac{e^x\+e^{-x}}{2}$ $$ $\equiv \cosh \left(x\right)$ $$

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