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

The derivative of cosh(xsinh(x)) is sinh^2(x)+cosh^2(x)

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

The first derivative of cosh(xsinh(x)) is sinh^2(x)+cosh^2(x)

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

sinh^{2} (x) + cosh^{2} (x)

Solution steps

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

Apply the Product Rule:

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

f = cosh (x), g = sinh (x)

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

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

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

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

Simplify

sinh (x) sinh (x) + cosh (x) cosh (x) : sinh^{2} (x) + cosh^{2} (x)

= sinh^{2} (x) + cosh^{2} (x)

What is the derivative of cosh(xsinh(x)) ?
The derivative of cosh(xsinh(x)) is sinh^2(x)+cosh^2(x)
What is the first derivative of cosh(xsinh(x)) ?
The first derivative of cosh(xsinh(x)) is sinh^2(x)+cosh^2(x)