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Is the calculation below valid?

\begin{align} f(x)=ax+b+g(f(x))\\ \frac{df(x)}{dx}=a+\frac{dg(f(x))}{df(x)}\frac{df(x)}{dx}\\ \frac{df(x)}{dx}-\frac{dg(f(x))}{df(x)}\frac{df(x)}{dx}=a\\ \frac{df(x)}{dx}=\frac{a}{1-\frac{dg(f(x))}{df(x)}}\\ \end{align} assuming $\frac{dg(f(x))}{df(x)} \neq 1$

Thanks a lot.

marvinthemartian
  • 644

1 Answers1

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i have the same: $$f'(x)=a+g'(f(x))f'(x)$$ thus we obtain $$f'(x)(1-g'(f(x))=a$$

Dr. Sonnhard Graubner
  • 95,283