Question
Step 1 Recall the Chain Rule in terms of the functions \( h(x) \) and \( g(x) \), which states that if \( g \) is differentiable at \( x \) and \( h \) is differentiable at \( g(x) \), then the composite function \( F=h \) o \( g \) defined by \( F(x)=h(g(x)) \) is differentiable at \( x \) and \( F^{\prime} \) is given by the following. \[ F^{\prime}(x)=h^{\prime}(g(x)) \cdot g^{\prime}(x) \] We are given the function \( f(x)=\sin (8 \ln (x)) \) To write this is the form \( F(x)=h(g(x)) \) we can let \( g(x)=8 \ln (x) \) and \( h(x)= \) SUBMI SUB (YOU CANNOT COME BACK) Need Help? Read It SUBMIT ANSWER SKI
Ask by Johnson Parry. in the United States
Mar 16,2025
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Answer
\( h(x) = \sin(x) \)
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Beyond the Answer
To express \( f(x)=\sin(8 \ln(x)) \) in the form \( F(x)=h(g(x)) \), we define \( g(x)=8 \ln(x) \) and \( h(x)=\sin(x) \). This means \( F(x)=h(g(x))=\sin(8 \ln(x)) \), perfectly aligning with the given function. If you’re diving into derivatives involving the chain rule, remember to stay vigilant about the inner and outer functions! It’s common to mix them up, leading to errors. Always label your functions clearly, ensuring you differentiate each part correctly methodically. Happy differentiating!
