Find the Derivative - d/dx 1/(e^x)

Problem

d()/d(x)1/(ex)

Solution

1. Rewrite the expression using negative exponents to make differentiation easier.

1/(ex)=e(−x)

2. Apply the chain rule for the exponential function, where the derivative of eu is eu⋅d(u)/d(x)

d(e(−x))/d(x)=e(−x)⋅(d(−)*x)/d(x)

3. Differentiate the exponent −x with respect to x

(d(−)*x)/d(x)=−1

4. Multiply the results to find the final derivative.

e(−x)⋅(−1)=−e(−x)

5. Simplify the expression by moving the term back to the denominator.

−e(−x)=−1/(ex)

Final Answer

d()/d(x)1/(ex)=−1/(ex)

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