SOLUTION: Find the derivative of log base 6 (x^2-7x)

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Question 1189549: Find the derivative of log base 6 (x^2-7x)
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative of log%286%2C%28x%5E2-7x%29%29
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f(x) = log%286%2C%28x%5E2-7x%29%29+=+ln%28x%5E2-7x%29%2Fln%286%29
f'(x) = %282x-7%29%2F%28%28x%5E2-7x%29%2Aln%286%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the derivative of log+%286%2C+%28x%5E2-7x%29%29

%28d%2Fdx%29%28log+%286%2C+%28x%5E2-7x%29%29%29

apply log rule: log%28a%2C%28b%29%29=ln%28b%29%2Fln%28a%29

=%28d%2Fdx%29%28%28ln%28x%5E2-7x%29%29%2Fln%286%29%29

take the constant out: %28a%2Af%29'=a*f’

=%281%2Fln%286%29%29%28d%2Fdx%29%28ln%28x%5E2-7x%29%29

apply the chain rule: %281%2F%28x%5E2-7x%29%29%28d%2Fdx%29%28x%5E2-7x%29

and since %28d%2Fdx%29%28x%5E2-7x%29=2x-7

you have

=%281%2Fln%286%29%29%281%2F%28x%5E2-7x%29%29%282x-7%29.............simplify

=%282x-7%29%2F%28ln%286%29%28x%5E2-7x%29%29 -> your answer