zainejude41236 zainejude41236
  • 03-03-2020
  • Mathematics
contestada

Find the value of the given function's derivative at x=3

f(x)=k(g(x))
g(x)=2x-x^2
k'(-3)=2
f'(3)=[]

Find the value of the given functions derivative at x3 fxkgx gx2xx2 k32 f3 class=

Respuesta :

danielmaduroh
danielmaduroh danielmaduroh
  • 11-03-2020

Explanation:

According to the chain rule, if we have a function:

[tex]f(x)=k(g(x))[/tex]

The derivative at a point [tex]a[/tex] will be:

[tex]f'(a)=k'(g(a))g'(a)[/tex]

We know that:

[tex]f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}[/tex]

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