Find the Derivative - d/dt e^(-2t)

Problem

d(e^(−2*t))/d(t)

Solution

1. Identify the rule needed for the derivative of an exponential function with a composite exponent, which is the Chain Rule.

2. Apply the formula for the derivative of e^u which states that d(e^u)/d(t)=e^u⋅d(u)/d(t)

3. Define the inner function as u=−2*t

4. Differentiate the inner function with respect to t to find d(u)/d(t)=−2

5. Multiply the original exponential function by the derivative of the inner function.

6. Simplify the resulting expression.

Final Answer

d(e^(−2*t))/d(t)=−2*e^(−2*t)

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