Question

Differentiate the functions. Assume that C is constant.
g(x)=7^x

Answer 1

Derivative of a^x (where a is a constant) is a^x (ln a)

So the derivative of 7^x is 7^x (ln 7)

Answer 2

@Easyaspi314
So is this is the same as (ln7)7^x right?
I don't understand why we have to take ln7?

Answer 3

Yes it is the same.

Answer 4

Keep in mind, that the derivative of e^x would follow the same rule, it will be e^x (ln e)..but ln e = 1 by definition, so the derivative of e^x is just e^x.

It can be shown that the derivative of a^x is a^x (ln a).

Answer 5

If you want a proof, you can check your text or I can help you with it/

Answer 6

@EasyasPi314
My text does not do much of an explanation actually.

Answer 7

Did I answer your question, or do you need more help?

Answer 8

It would be helpful if dont mind explaining.

Answer 9

Consider y= a^x.
Take the log of both sides, you get
ln y = x ln a
Now, take the derivative of both sides, you get

1/y (y ') = ln a

Now multiply both sides by y, you get

y ' = y(ln a)
Therefore, y', the derivative of y, is y(ln a) OR (a^x)(lna)

So you clearly see the poroof that if y = a^x

Then: y ' = a^x (ln a)

Answer 10

Makes sense?????

Answer 11

yes this does makes sense, thanks @ Easaspi314

Answer 12

welcome.