Question #3df2a

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Jun 1, 2017

Answer: #d/(dx)sqrt(x^2+4)=x/sqrt(x^2+4)#

Explanation:

Assuming the question meant "differentiate" using the chain rule rather than "derive" the chain rule.

Differentiate #sqrt(x^2+4)#

Note that the chain rule states that for a composition of functions:
#h(x)=f(g(x))#
The derivative of #h(x)# would be:
#h'(x)=f'(g(x))*g'(x)#

First, we note that:
#sqrt(x^2+4)=(x^2+4)^(1/2)#

In this problem, we apply the chain rule.
We notice that in this case, #f(x)=sqrt(x)# and #g(x)=x^2+4#, so:
#d/(dx)(x^2+4)^(1/2)=1/2(x^2+4)^(-1/2)(2x)#
#d/(dx)(x^2+4)^(1/2)=x/sqrt(x^2+4)#

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