Find the Derivative - d/dx 4e^(-x)

Problem

d()/d(x)*4*e(−x)

Solution

1. Identify the constant multiple rule, which allows the constant 4 to be moved outside the derivative.

d()/d(x)*4*e(−x)=4d(e(−x))/d(x)

2. Apply the chain rule to the exponential function eu where u=−x

d(eu)/d(x)=eud(u)/d(x)

3. Differentiate the exponent −x with respect to x

(d(−)*x)/d(x)=−1

4. Multiply the results together to find the final derivative.

4⋅e(−x)⋅(−1)=−4*e(−x)

Final Answer

d()/d(x)*4*e(−x)=−4*e(−x)

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