What is the derivative of xsinh(x-cosh(x)) ?

The derivative of xsinh(x-cosh(x)) is xcosh(x)

What is the first derivative of xsinh(x-cosh(x)) ?

The first derivative of xsinh(x-cosh(x)) is xcosh(x)

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\frac{d}{d x} (x sinh (x) - cosh (x))

x cosh (x)

Solution steps

\frac{d}{d x} (x sinh (x) - cosh (x))

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x sinh (x)) = sinh (x) + x cosh (x)

\frac{d}{d x} (cosh (x)) = sinh (x)

= sinh (x) + x cosh (x) - sinh (x)

Simplify

= x cosh (x)

What is the derivative of xsinh(x-cosh(x)) ?
The derivative of xsinh(x-cosh(x)) is xcosh(x)
What is the first derivative of xsinh(x-cosh(x)) ?
The first derivative of xsinh(x-cosh(x)) is xcosh(x)