# How do you differentiate #g(x) =e^(1-x)sinhx# using the product rule?

the product rule

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To differentiate g(x) = e^(1-x)sinh(x) using the product rule:

- Identify the functions within the expression: f(x) = e^(1-x) and h(x) = sinh(x).
- Apply the product rule: g'(x) = f'(x)h(x) + f(x)h'(x).
- Calculate the derivatives of f(x) and h(x): f'(x) = -e^(1-x) and h'(x) = cosh(x).
- Substitute the derivatives and the original functions into the product rule equation: g'(x) = (-e^(1-x))sinh(x) + (e^(1-x))cosh(x).

Therefore, the derivative of g(x) = e^(1-x)sinh(x) using the product rule is g'(x) = (-e^(1-x))sinh(x) + (e^(1-x))cosh(x).

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