differentiation

[red and white kop!]

im supposed to diffrentiate 10^3x
i figured it was 3(10^(3x-1)) but apparently that is incorrect. why is that?

 

[Deleted member 4993]

im supposed to diffrentiate 10^3x
i figured it was 3(10^(3x-1)) but apparently that is incorrect. why is that?

That rule only applies when the "exponent" (power) is a constant. You can derive it from the fundamentals (limit definition of differentiation).

For your problem - where the exponent is variable - you need to invoke "power of log"

y = 10[sup:1q30v0qh]3x[/sup:1q30v0qh]

ln(y) = (3x) * ln(10)

1/y * dy/dx = 3 * ln(10)

dy/dx = 10[sup:1q30v0qh]3x[/sup:1q30v0qh] * 3 * ln(10)

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