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$$\begin{array}{l}{\text { Let } r(x)=f(g(h(x))), \text { where } h(1)=2, g(2)=3} \\ {h^{\prime}(1)=4, g^{\prime}(2)=5, \text { and } f^{\prime}(3)=6 . \text { Find } r^{\prime}(1)}\end{array}$$

120

Calculus 1 / AB

Chapter 2

DERIVATIVES

Section 5

The Chain Rule

Derivatives

Differentiation

Applications of the Derivative

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Okay. This question wants us to find the derivative of this function at X equals one. So to start, we'll take that derivatives. And we have to use the chain rule here. So we have f prime of everything inside. Then times the derivative of everything inside which reacts. Here's another chain rule on So we get the derivative of G leaving H the same times the derivative of age. So now our prime of one would be F crime of G of h of one times g prime of h of one times h crime of one. So now inserting values in here it says the h of one is to so we can plug that in and then h prime of one is four then g of to is three g prime of to is five and now we just need f prime of three, which it says is six. So are derivative is just six times five times for which is 30 times for or 120

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