What is the derivative of x(cosh((200/x)-1)-100) ?

The derivative of x(cosh((200/x)-1)-100) is cosh((200)/x)-(200sinh((200)/x))/(x)-1

What is the first derivative of x(cosh((200/x)-1)-100) ?

The first derivative of x(cosh((200/x)-1)-100) is cosh((200)/x)-(200sinh((200)/x))/(x)-1

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\frac{d}{d x} (x (cosh (\frac{200}{x}) - 1) - 100)

cosh (\frac{200}{x}) - \frac{200 sinh ( \frac{200}{x} )}{x} - 1

Solution steps

\frac{d}{d x} (x (cosh (\frac{200}{x}) - 1) - 100)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x (cosh (\frac{200}{x}) - 1)) - \frac{d}{d x} (100)

\frac{d}{d x} (x (cosh (\frac{200}{x}) - 1)) = cosh (\frac{200}{x}) - 1 - \frac{200 sinh ( \frac{200}{x} )}{x}

\frac{d}{d x} (100) = 0

= cosh (\frac{200}{x}) - 1 - \frac{200 sinh ( \frac{200}{x} )}{x} - 0

Simplify

= cosh (\frac{200}{x}) - \frac{200 sinh ( \frac{200}{x} )}{x} - 1

What is the derivative of x(cosh((200/x)-1)-100) ?
The derivative of x(cosh((200/x)-1)-100) is cosh((200)/x)-(200sinh((200)/x))/(x)-1
What is the first derivative of x(cosh((200/x)-1)-100) ?
The first derivative of x(cosh((200/x)-1)-100) is cosh((200)/x)-(200sinh((200)/x))/(x)-1