calculate derivative of f(x)=5x (x-1)^4

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We have to find the derivative of f(x) = 5x * (x-1)^4

We can use the product rule here:

f(x) = 5x * (x-1)^4

f'(x) = (5x)' * (x-1)^4 + 5x * [(x-1)^4]'

=> f'(x) = 5* ( x - 1)^4 + 5x * 4*(x - 1)^3

=> f'(x) = 5(x - 1)^4 + 20x(x - 1)^3

The required derivative is f'(x) = 5*(x - 1)^4 + 20*x*(x - 1)^3

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