What is the derivative of xsinh(x) ?

The derivative of xsinh(x) is sinh(x)+xcosh(x)

What is the first derivative of xsinh(x) ?

The first derivative of xsinh(x) is sinh(x)+xcosh(x)

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

sinh (x) + x cosh (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sinh (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sinh (x) + cosh (x) x

Simplify

= sinh (x) + x cosh (x)

What is the derivative of xsinh(x) ?
The derivative of xsinh(x) is sinh(x)+xcosh(x)
What is the first derivative of xsinh(x) ?
The first derivative of xsinh(x) is sinh(x)+xcosh(x)