Find the Derivative - d/dy xe^(y/z)

Problem

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

Solution

1. Identify the variable of differentiation, which is y

2. Treat the variables x and z as constants, as they do not depend on y

3. Apply the constant multiple rule by pulling the constant factor x out of the derivative.

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

4. Apply the chain rule to the exponential function eu where u=y/z

d(e(y/z))/d(y)=e(y/z)d()/d(y)y/z

5. Differentiate the inner function y/z with respect to y noting that 1/z is a constant.

d()/d(y)y/z=1/z

6. Combine the results to find the final derivative.

(d(x)*e(y/z))/d(y)=x*e(y/z)1/z

Final Answer

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

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