What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?
By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x).
Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)).
Then by the power rule, g'(x)=(1/2)x^(-1/2)=1/(2x^(1/2)). Evidently, h'(x)=3.
So, by the chain rule, f'(x)=g'(h(x))h'(x)=3/(2(3x+2)^(1/2)).
LP
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