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

1 Answer
Dec 1, 2017

Answer:

#d/dx(f(g(x)))=-e^sqrtx/(2sqrtx)#

Explanation:

Given #f(x)=-e^x# and #g(x)=sqrtx#

So,

#f(g(x))=-e^(g(x))#

As #g(x)=sqrtx#

Therefore,

#f(g(x))=-e^(sqrtx)#

Now differentiate both sides with respect to #x# using the chain rule.

The chain rule says that #->#

#(U(V(x)))'=U'(V(x)) xx V'(x)#

Now back to the question #->#

#f(g(x))=-e^(sqrtx)#

#d/dx(f(g(x)))=d/dx-e^sqrt(x)#

#d/dx(f(g(x)))=-e^sqrt(x) xx d/dx sqrtx#

#d/dx(f(g(x)))=-e^sqrtx xx 1/(2sqrtx)#

Therefore,

#d/dx(f(g(x)))=-e^sqrtx/(2sqrtx)#