SOLUTION: Please some help Find f '(a). f(t) = 2t + 4 t + 9

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Question 1153268: Please some help
Find f '(a).
f(t) =
2t + 4
t + 9
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find f '%28a%29.
f%28t%29+=+%282t+%2B+4%29%2F%28t+%2B+9%29

first find f '%28t%29

%28d%2Fdt%29+%282t+%2B+4%29%2F%28t+%2B+9%29

Apply the Quotient Rule:

%28f%2Fg%29' =(f'*g-g'*f)/g%5E2

=
since %28d%2Fdt%29%282t%2B4%29=2 and %28d%2Fdt%29%28t%2B9%29=1, we have
=%282%28t%2B9%29-%282t%2B4%29%29%2F%28t%2B9%29%5E2
=%282t%2B18-2t-4%29%2F%28t%2B9%29%5E2
=14%2F%28t%2B9%29%5E2

f'%28t%29+=+14%2F%28t+%2B+9%29%5E2
then f '%28a%29:
f'%28a%29+=+14%2F%28a+%2B+9%29%5E2