Question

Find the derivative. Simplify where possible

35. \(f\left( x \right) = {\bf{cosh}}\,{\bf{3}}x\)

Short answer

The derivative of \(f\left( x \right)\) is \(3\sinh 3x\).

Step-by-step solution

Step 1:Differentiate the equation \(f\left( x \right) = {\bf{cosh}}\,{\bf{3}}x\)

Differentiate the equation \(f\left( x \right) = \cosh 3x\) using the chain rule.

\(\begin{aligned}f'\left( x \right) &= \frac{{\rm{d}}}{{{\rm{d}}x}}\left( {\cosh 3x} \right)\\ &= \left( {\sinh 3x} \right)\frac{{\rm{d}}}{{{\rm{d}}x}}\left( {3x} \right)\end{aligned}\)

Differentiate the equation in step 1

The equation \(f'\left( x \right) = \left( {\sinh 3x} \right)\frac{{\rm{d}}}{{{\rm{d}}x}}\left( {3x} \right)\) can be simplified as,

\(\begin{aligned}f'\left( x \right) &= \left( {\sinh 3x} \right)\frac{{\rm{d}}}{{{\rm{d}}x}}\left( {3x} \right)\\ &= 3\sinh 3x\end{aligned}\)

So, the derivative of \(f\left( x \right)\) is \(3\sinh 3x\).