I have been starting to learn derivatives and finding the equation of the tangent of a curve. However, I am a bit confused as to how to solve this question:
Let $f$ be a differentiable function such that $f(0)=7$ and let $g(x) = x f'(x)$. Evaluate $g′(0)$.
For context, I understand the basics of differentiation(finding the derivative) and how to find the equation of the tangent. However, what I am not clear on is: what is the relationship between f(x) and its derivative? I feel like the question above requires some manipulation of f(x) and f'(x) and using tangent equations to solve this. If anyone can please explain the solution to the above question, that'll be greatly appreciated. Thank you.