Science:Math Exam Resources/Courses/MATH110/April 2017/Question 01 (f)

MATH110 April 2017

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Question 01 (f)
If $F(x)=f(f(x))$ and $f(2)=3$, $f'(2)=4$, $f'(3)={\frac {1}{2}}$, evaluate $F'(2)$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Using the chain rule for derivative: Suppose that we have two functions $f(x)$ and $g(x)$ and they are both differentiable, If we define $F(x)=(f\circ g)(x)$, then the derivative of $F(x)$ is $f'(g(x))g'(x)$.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Followed the hint, $F'(x)=f'(f(x))f'(x)$, $F'(2)=f'(f(2))f'(2)=f'(3)4=1/2*4=2$ answer: $\color {blue}2$