Suppose F(G(x))=x2 and G'(1)=6. Find F'(G(1)).

Question

Need help please!!!!

Answer 1

F(G(x)) = x². Take derivative from both sides, we have:

 

G'(x) * F'(G(x)) = 2 * x.

 

So, we have: F'(G(x)) = 2*x/G'(x).

 

Replacing x = 1, we have:

 

F'(G(1)) = 2 * 1/ G'(1) = 2/6 = 1/3.

Answer 2

F(G(X))=X² ....... GIVEN FUNCTION

Differentiating both sides w.r.t x,

F'(G(x)).G'(x)=2x ..... since when u=f(v) and v=f(z) then du/dz= (du/dv).(dv/dz)=u'.v'

substituting x=1,

F'(G(1)).G'(1)=2.1 

=>F'(G(1)).6=2 ............. as given that G'(1)=6

=>F'(G(1)) .6/6= 2/6.....dividing both sides by 6

=>F'(G(1))=1/3 ... Answer