Find the Derivative - d/dx y=e^(-16x)

Problem

d()/d(x)*e(−16*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 that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Define the inner function as u=−16*x

4. Calculate the derivative of the inner function, which is (d(−)*16*x)/d(x)=−16

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

d(e(−16*x))/d(x)=e(−16*x)⋅(−16)

6. Simplify the expression by placing the constant coefficient in front.

d(e(−16*x))/d(x)=−16*e(−16*x)

Final Answer

d(e(−16*x))/d(x)=−16*e(−16*x)

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