anonymous
  • anonymous
Suppose f(1) = 16 and f '(1) = 9 . Find the derivatives of the following functions a. g(x) = sqrt(f(x)) g prime (1) = b. h(x) = 1/(f(x)) h prime (1) =
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
This is just like taking the derivative of x, but remember that since we have another function of x, we have to include the chain rule. a). \[g(x)=\sqrt{f(x)} \rightarrow g'(x)=\frac{ 1 }{ 2\sqrt{f(x)} }*f'(x)\]\[g'(1)=\frac{ f'(1) }{ 2\sqrt{f(1)} } \rightarrow g'(1)=\frac{ 9 }{ 2\sqrt{16} }\]
anonymous
  • anonymous
b). After rearranging the equation, we can use the power rule\[h(x)=(f(x))^{-1} \rightarrow h'(x)=-1(f(x))^{-2}*f'(x)\] \[h'(1)=\frac{ -f'(1) }{ (f(1))^2 }\] Now just plug in the values that you were given This could also be obtained from the quotient rule if we decided to keep it as 1/f(x).

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