What is the derivative of e^{xsinh(x}) ?

The derivative of e^{xsinh(x}) is e^{xsinh(x)}(sinh(x)+xcosh(x))

What is the first derivative of e^{xsinh(x}) ?

The first derivative of e^{xsinh(x}) is e^{xsinh(x)}(sinh(x)+xcosh(x))

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\frac{d}{d x} (e^{x s i n h (x)})

e^{x s i n h (x)} (sinh (x) + x cosh (x))

Solution steps

\frac{d}{d x} (e^{x s i n h (x)})

Apply the chain rule:

e^{x s i n h (x)} \frac{d}{d x} (x sinh (x))

= e^{x s i n h (x)} \frac{d}{d x} (x sinh (x))

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

= e^{x s i n h (x)} (sinh (x) + x cosh (x))

What is the derivative of e^{xsinh(x}) ?
The derivative of e^{xsinh(x}) is e^{xsinh(x)}(sinh(x)+xcosh(x))
What is the first derivative of e^{xsinh(x}) ?
The first derivative of e^{xsinh(x}) is e^{xsinh(x)}(sinh(x)+xcosh(x))