If $f (x) = cos 3 x$ $f(x) =cos3x$ and $g (x) = {(2 x - 1)}^{2}$ $g(x) = (2x-1)^2$ , what is $f'(g(x))$ ?

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Answer 1 · 2016-03-21T16:40:16

$(df)/(dg)=(-3sin3x)/(4(2x-1))$

As per chain formula $(df)/(dx)=(df)/(dg)xx(dg)/(dx)$ . hence

$(df)/(dg)=((df)/(dx))/((dg)/(dx))$

As $f(x)=sin3x$ and $g(x)=(2x-1)^2$

$(df)/(dx)=-sin3x xx3$ and $(dg)/(dx)=2(2x-1)xx2$

Hence $(df)/(dg)=(-3sin3x)/(4(2x-1))$

If f(x) =cos3x f(x)=cos3xf(x) =cos3x and g(x) = (2x-1)^2 g(x)=(2x−1)2g(x) = (2x-1)^2 , what is f'(g(x)) f'(g(x)) ?