Find the Derivative - d/dx -20e^(1-4x)+20

Problem

d()/d(x)*(−20*e(1−4*x)+20)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

d()/d(x)*(−20*e(1−4*x)+20)=(d(−)*20*e(1−4*x))/d(x)+d(20)/d(x)

2. Apply the constant rule to the second term, noting that the derivative of any constant is zero.

d(20)/d(x)=0

3. Apply the constant multiple rule to the first term by moving the coefficient outside the derivative.

−20⋅d(e(1−4*x))/d(x)

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

−20⋅e(1−4*x)⋅d(1−4*x)/d(x)

5. Differentiate the inner function 1−4*x with respect to x

d(1−4*x)/d(x)=−4

6. Multiply the results to find the final derivative.

−20⋅e(1−4*x)⋅(−4)=80*e(1−4*x)

Final Answer

d()/d(x)*(−20*e(1−4*x)+20)=80*e(1−4*x)

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