question about calculus notation
slope at a point is f'(a)
what is d/dx (f(lnx))?

Question

question about calculus notation
slope at a point is f'(a)
what is d/dx (f(lnx))?

precal · Answer

Isn't the second one to take the derivative of the composition function f(lnx)?

anonymous · Answer

Chain rule applies
$$\frac{ d(f(\ln  x))}{ dx } = f \prime(\ln x) \times \frac{f(\ln x) }{ x }$$

precal · Answer

ok I will take another look at it but I was working from inside out
ie I sub lnx then took the derivative of the function

anonymous · Answer

Maybe the reason the problem mentions
$$f \prime (a)$$
is to let you know that f(x) is a differentiable function.
Therefore $$f \prime (\ln (x))$$  exists.

precal · Answer

no actually f'(a) is not mentioned at all.  Someone I was tutoring did not understand the difference in notation.  I just wanted another point of view.