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

Problem

d(e^(−1/x))/d(x)

Solution

1. Identify the outer function as the exponential function e^u and the inner function as u=−x^(−1)

2. Apply the chain rule, which states that the derivative of e^ƒ(x) is e^ƒ(x)⋅d(ƒ(x))/d(x)

3. Differentiate the inner function −x^(−1) using the power rule.

4. Calculate the derivative of the exponent:

(d(−)*x^(−1))/d(x)=−(−1)*x^(−2)

5. Simplify the resulting expression:

(d(−)*x^(−1))/d(x)=1/(x^2)

6. Combine the parts to find the final derivative:

d(e^(−1/x))/d(x)=e^(−1/x)⋅1/(x^2)

Final Answer

d(e^(−1/x))/d(x)=(e^(−1/x))/(x^2)

Want more problems? Check here!