If #f(x)= - x^2 + x # and #g(x) = sqrtx #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2016-09-04T08:20:48

#(1) / (2 sqrt(x)) - 1#

We have: #f(x) = -x^(2) + x# and #g(x)= sqrt(x)#

First, let's evaluate #f(g(x))#:

#=> f(g(x)) = f(sqrt(x))#

#=> f(g(x)) = -(sqrt(x))^(2) + (sqrt(x))#

#=> f(g(x)) = sqrt(x) - x#

Now, let's differentiate this expression:

#=> (d) / (dx) (sqrt(x) - x) = (1) / (2) x^(- (1) / (2)) - x^(0)#

#=> (d) / (dx) (sqrt(x) - x) = (1) / (2 sqrt(x)) - 1#