Find the Derivative - d/dx y=e^(-8x)

Problem

d()/d(x)*e(−8*x)

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 eu which states d(eu)/d(x)=eu⋅d(u)/d(x)

3. Define the inner function as u=−8*x

4. Differentiate the inner function to find d(u)/d(x)=−8

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

Final Answer

d(e(−8*x))/d(x)=−8*e(−8*x)

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