Find the Derivative - d/dx e^(x/10)

Problem

d(e(x/10))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is eu and the inner function is u=x/10

2. Apply the Chain Rule by multiplying the derivative of the outer function with respect to u by the derivative of the inner function with respect to x

d(e(x/10))/d(x)=e(x/10)⋅d()/d(x)x/10

3. Differentiate the inner function x/10 which is a linear term with a constant coefficient of 1/10

d()/d(x)x/10=1/10

4. Multiply the results to find the final derivative.

d(e(x/10))/d(x)=e(x/10)⋅1/10

Final Answer

d(e(x/10))/d(x)=(e(x/10))/10

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