why? (1 Viewer)

[pip88]

i don't know the answer to this question
consider the graphs of y=loge x, y= loge 2x and y=loge3x. the first derivative for these three functions is the sme. the second derivative for the three functions is the same. why is this? how do the first and the second derivatives relate to the original functions.

i have no idea help please

 

[rama_v]

log (2x) = log 2 + log x
log 2 is just a number so its derivative is zero. The rest follows quickly.

 

[Riviet]

You can also think of it as the graph of log x shifted up/down log a units, shifting a graph doesn't change the gradient at a point on the curve. This means when you differentiate each, your gradient at each x value will be the same.

 

[pip88]

thank you so much.... i was struggling with that!!!!!!