Find the Derivative - d/dy e^xsin(y)

Problem

d(e(x*sin(y)))/d(y)

Solution

1. Identify the variable of differentiation, which is y Since x is not the variable of differentiation, it is treated as a constant.

2. Apply the chain rule for the exponential function eu where u=x*sin(y) The derivative is eu⋅d(u)/d(y)

3. Differentiate the exponent with respect to y The derivative of x*sin(y) is x*cos(y)

4. Combine the results to find the final derivative.

Final Answer

d(e(x*sin(y)))/d(y)=x*cos(y)*e(x*sin(y))

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