How do you differentiate #f(x) = 4(x^2 + x - 1)^10# using the chain rule?

1 Answer
Edric Y.
Nov 9, 2015

#f'(x) = 40(x^2 + x -1)^9 * (2x + 1)#

Explanation:

let #u = x^2 + x -1#
now #f(x) = 4u^10#

differentiate:
remember, chain rule requires you to multiply by the derivative of the inside function (or #u'#)
#f'(x) = 4 * 10u^9 * u'#

#f'(x) = 4 * 10(x^2 + x -1)^9 * (x^2 + x -1)'#

#f'(x) = 4 * 10(x^2 + x -1)^9 * (2x + 1)#

#f'(x) = 40(x^2 + x -1)^9 * (2x + 1)#

you might rewrite this as:
#f'(x) = (80x+40)(x^2 + x -1)^9#

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