How do you differentiate #f(x)=(4x-x^2)^100#?

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How do you differentiate #f(x)=(4x-x^2)^100#?

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Answer 1 · 2016-10-24T22:46:20

#f'(x) = 100(4x-x^2)^99 (4-2x) #

Explanation:

Let # u=4x-x^2 # and then # f(x)=u^100 #

# (du)/dx = 4-2x #

Then, # f'(x)=d/dx(f(x)) #
# :. f'(x) = d/dx u^100 #
# :. f'(x) = d/(du) u^100 (du)/dx # (the chain rule)
# :. f'(x) = 100u^99 (4-2x) #
# :. f'(x) = 100(4x-x^2)^99 (4-2x) #

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How do you differentiate #f(x)=(4x-x^2)^100#?

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