Question 2.9.1: Computing the Derivative of a Hyperbolic Function Compute th...
Computing the Derivative of a Hyperbolic Function
Compute the derivative of f(x)=\sinh ^2(3 x).
From the chain rule, we have
f^{\prime}(x)=\frac{d}{d x} \sinh ^2(3 x)=\frac{d}{d x}[\sinh (3 x)]^2=2 \sinh (3 x) \frac{d}{d x}[\sinh (3 x)]
=2 \sinh (3 x) \cosh (3 x) \frac{d}{d x}(3 x)
=2 \sinh (3 x) \cosh (3 x)(3)
=6 \sinh (3 x) \cosh (3 x).
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