Math, asked by abhisharma21, 9 months ago

derivative of logx???

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Answered by Anonymous

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logx=1/x

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Answered by manasi12391

Step-by-step explanation:

We want to find the derivative of log(x). To do this, we first need to examine the expression log(x). In general, a logarithm has the form loga (x). That is, we call a the base of the logarithm. Also, loga (x) represents the number we raise a to in order to get x.

Now, notice that log(x) doesn't have a base shown. When this is the case, the implied base is 10. Therefore, log(x) = log10 (x).

derlogx1

Alright, now we can get to the derivative of log(x). This derivative is fairly simple to find, because we have a formula for finding the derivative of loga (x), in general.

derlogx2

We have that the derivative of loga (x) is 1 / (xln(a)). Wait! What the heck is a natural log of a, notated in our formula as ln(a)? No worries, ln(a) is simply another logarithm with implied base e, where e is the irrational number with approximate value 2.71828. That is, ln(x) = loge (x).

Okay, so let's use this formula to find the derivative of log(x). We have that the base of log(x) is 10, so we plug this into the derivative formula for loga (x).

derlogx3

hope it's help

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