Find the Derivative - d/dx (4x-x^2)^100

Problem

d(4*x−x2)/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is u100 and the inner function is u=4*x−x2

2. Apply the Power Rule to the outer function by bringing the exponent down and subtracting one from the exponent.

d(u100)/d(u)=100*u99

3. Differentiate the inner function 4*x−x2 with respect to x

d(4*x−x2)/d(x)=4−2*x

4. Combine the results using the Chain Rule formula d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

d(4*x−x2)/d(x)=100*(4*x−x2)99⋅(4−2*x)

5. Simplify the expression by factoring out a 2 from the term (4−2*x) and multiplying it by 100.

100*(2)*(2−x)*(4*x−x2)99

200*(2−x)*(4*x−x2)99

Final Answer

d(4*x−x2)/d(x)=200*(2−x)*(4*x−x2)99

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