what is the derivative of log

what is the derivative of log The answer is y log 10 e 1 x Solution Suppose we have log a b we want to change it on exponential e base then it can be written as log a b log a e log e b Similarly function log 10 x can be written as y log 10 e log e x Let s say we have y c f x where c is a constant then y c f x Now this is quite straightforward to differentiate as log 10 e is

1 Answer That depends on what base you intend logx is sometimes used for log10x logex and log2x d dx logbx 1 x 1 logex Using lnx logex we write d dx logbx 1 x 1 lnb The derivative is f x 1 logx x 2 This is an example of the the Quotient Rule Quotient Rule The quotient rule states that the derivative of a function f x u x v x is f x v x u x u x v x v x 2 To put it more concisely f x vu uv v 2 where u and v are functions specifically the numerator and denominator of the original function f x For this

what is the derivative of log

what is the derivative of log
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Derivative Of Log Base 5 Acetolarge
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Derivative Of General Logarithmic Function YouTube
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What is the derivative of f x log 6 x 2 See all questions in Differentiating Logarithmic Functions without Base e Impact of this question Log7x lnx ln7 This is simple to differentiate The only tricky thing is to remember that 1 ln7 is a constant so it can be brought outside when differentiating d dx lnx ln7 1 ln7 d dx lnx Since d dx lnx 1 x d dx lnx ln7 1 ln7 1 x 1 xln7 Rewrite the expression using the change of base formula log 7x lnx ln7 This is

Assuming you mean xlog 10 x the derivative of lnx is 1 x so using the change of base law d dx log x d dx logx log 10 d dx lnx ln10 Finding the derivative of a logarithm with a base other than e is not difficult simply change the logarithm base using identities If given a function log a b change the base to e by writing it as frac ln b ln a

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Thus log2x logx log2 Now to derivate it we must remember that there is no need to use the quotient rule as the denominator can be understood as a constant there s no variable in log2 it s just a number you can calculate promptly Thus dy dx 1 x log2 dy dx 1 xlog2 By changing its base and solving it then as follows By log The derivative of h x ln x is h x 1 x Michael B 3 Sep 24 2014 What is the derivative of log e x

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