What is the derivative of the following?

[avito009]

In the book that I am reading the derivative of y = bp^x is bp^xxlog_ep. How?

 

[Thewindyfan]

In the book that I am reading the derivative of y = bp^x is bp^xxlog_ep. How?

Well the b and p in this case I'm assuming is a constant. Is it?

Also the general rule of thumb for the derivative of some number K^x is K^x times Ln(K). For a general proof of this, I highly recommend checking out khan academy's video over this general derivative. I'm not sure what it was exactly called, but it might've been an example for the chain rule.

Also the product rule may be involved in this as well. State what the letters represent.

Also for future notice, post this in the calculus section of the homework sub-forum.

 

[Mark44]

Edit: Fixed an error I made.

In the book that I am reading the derivative of y = bp^x is bp^xxlog_ep. How?

Assuming that b and p are constants,
1. Take the natural log of both sides.
ln(y) = ln(bp^x) = ln(b) + xln(p)
2. Differentiate both sides with respect to x.
3. Solve algebraically for y'.

I leave it to you to fill in the details.

 

[Thewindyfan]

And if you're still wondering as to how the shortcut I mentioned earlier makes sense, here's the video I mentioned. It explains it well in terms of the chain rule, so I'm assuming you are already aware of what the chain rule is:

 

[Svein]

Assuming that b and p are constants,
1. Take the natural log of both sides.
ln(y) = ln(bpx) = ln(b) + pln(x)

Er... ln(y) = ln(b) + x⋅ln(p)...

 

[Mark44]

Er... ln(y) = ln(b) + x⋅ln(p)...

I edited my post to fix my error...