What is the first differential of $y=10^(3x-4)$ ?

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Answer 1 · 2017-04-30T04:17:05

$dy/dx= 3ln10*10^(3x-4)$

$y=10^(3x-4)$

$lny = (3x-4)*ln10$

$1/y dy/dx = ln10*d/dx(3x-4)$ [Implicit differentiation and standard differential]

$1/y dy/dx= ln10*(3-0)$ [Power rule]

$dy/dx = 3ln10*y$

$= 3ln10*10^(3x-4)$

Answer 2 · 2017-04-30T15:27:50

A few additional observations

Notice that $10^(3x-4) = 10^(3x)/10^4$
So that $10^(3x-4) = 1000^(x)/10000$
Therefore if $y = 10^(3x-4)$ then $y = 1000^(x)/10000$

This gives us $dy/dx = (1/10000)1000^x*ln(1000)$ .
If we wish to simplify ln(1000), we have
$dy/dx = ((3ln10)/10000)1000^x$ .

This answer is equal to the one given in the original response.

What is the first differential of y=10^(3x-4)y=10^(3x-4) ?