Question

Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx.

y=√sinx

√ is square root.

Answer 1

g(x) = sinx
f(x) = √x

then f(g(x))
= f(sinx)
= √sinx

if y = fg(x)) = √sinx = (sinx)^(1/2)
dy/dx = (1/2)(sinx)^(-1/2) (cosx
= cosx/(2√sinx)