Natural logarithmic derivative trick Hi chaps and chapesses, I was wondering if someone could just explain something. If I have a function which is dependent on x, the familiar f(x). Now, if I take the derivative of this, and multiple by x and divide through by f(x). How does this then become true: (x)/(f(x))(d(f(x)))/(dx)=(d ln(f(x)))/(d ln(x)) I'm thinking I'm either a.) tired, b.) stupud or c.) both

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

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A) No
B) 0
C) Yes
D) 6

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

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