Find f'(a). f(t)= frac{3t+3}{t+2}

Question
Functions
asked 2021-02-25
Find f'(a).
\(f(t)= \frac{3t+3}{t+2}\)

Answers (1)

2021-02-26
The easiest approach will be to use the quotient rule which says that the derivative of the function f(x)=\frac{g(x)}{h(x)} at any point where h(x) does not equal 00 is
\(f′(x)=(g′(x)h(x)−g(x)h′(x))/[h(x)]2\)
In this case, \(g(t)=3t+3\) \ and \ \(h(t)=t+2\). The derivatives of these functions are \(g′(t)=3\) and \(h′(t)=1\) respectively. So substituting them in we get
\(f′(a)=\frac{3(a+2)−(3a+3)(1)}{a+2^{2}}=\frac{3}{a+2^{2}}\)
0

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