SOLUTION: Obtain derivative of f(t) = In(5 – 2/3t)

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Question 99082: Obtain derivative of f(t) = In(5 – 2/3t)
Answer by Adam(64) About Me  (Show Source):
You can put this solution on YOUR website!
derivative of ln(x) is 1/x
you cannot apply this directly to ln(5-2/3t),because it is composition of two functions f(t) = ln(t) and g(t)=5-2/3t
there is a rule for differentiation of theese compositions : f'(g(x))= f'(x)*g(x) - derivative of composition is product of derivatives of outter and inner functions. If you apply this rule you get d%2Fdt ln%285-%282%2F3%29t%29 = d%2Fdt ln%28t%29*d%2Fdt%285-%282%2F3%29t%29
= %281%2F%285-%282%2F3%29t%29%2A%28-2%2F3%29%29 which gives us common formula for derivative of ln(x) which is d%2Fdxln%28x%29= %28dx%2Fx%29%2Fx - which means that derivative of natural of x can be represented as derivative of x over x.
once again for clarity your solution : %28%28-2%2F3%29%2F%285-%282%2F3%29t%29%29