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

1 Answer
Sep 4, 2016

Answer:

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

Explanation:

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#