Find the Derivative - d/dx 5e^(-4x)

Problem

(d(5)*e(−4*x))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 5 to be moved outside the derivative.

(d(5)*e(−4*x))/d(x)=5⋅d(e(−4*x))/d(x)

2. Apply the chain rule for the exponential function, where the derivative of eu is eu⋅d(u)/d(x)

d(e(−4*x))/d(x)=e(−4*x)⋅(d(−)*4*x)/d(x)

3. Differentiate the exponent −4*x with respect to x

(d(−)*4*x)/d(x)=−4

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

5⋅e(−4*x)⋅(−4)=−20*e(−4*x)

Final Answer

(d(5)*e(−4*x))/d(x)=−20*e(−4*x)

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