Answer :
The composite function in the form of f(g(x)) = [tex]\sqrt{1+5x}[/tex]
Derivative dy / dx = [tex]\frac{5}{2\sqrt{1+5x} }[/tex]
Given,
Inner function, u = g(x)
Outer function, y = f(u)
y = 3 [tex]\sqrt{1+5x}[/tex]
we have to find f(g(x))
we know,
u = g(x) = 1 + 5x
f(x) = [tex]\sqrt{x}[/tex]
then,
y = f(g(x)) = f(1+5x) =[tex]\sqrt{u}[/tex] = [tex]\sqrt{1+5x}[/tex]
next we have to find derivative.
dy/dx = (dy/du) (du/dx) = ½ u^-1/2(5) = 5/2[tex]\sqrt{u}[/tex] = 5/2[tex]\sqrt{1+5x}[/tex]
that is,
f(g(x)) = [tex]\sqrt{1+5x}[/tex]
dy / dx = 5/2[tex]\sqrt{1+5x}[/tex]
learn more about composite function here: https://brainly.com/question/24260286
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The question is incomplete. Completed question is given below.
Write the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 underroot 1 + 5x. find the derivative dy/dx.
