Find the Derivative - d/dy e^(xy)

Problem

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

Solution

1. Identify the variable of differentiation, which is y This means x is treated as a constant.

2. Apply the chain rule for exponential functions, which states that d(eu)/d(y)=eu⋅d(u)/d(y)

3. Differentiate the exponent with respect to y Since x is a constant, the derivative of x*y is x

(d(x)*y)/d(y)=x

4. Multiply the original exponential function by the derivative of the exponent.

e(x*y)⋅x

Final Answer

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

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