Question

What is the derivative of h(t) = ln(7)7^t

Answer 1

\[\large\rm h(t)=(\ln7)7^t\]Derivative of this guy?

Answer 2

You might be tempted to use product rule, but don't!

ln7 contains no t.
It's just a constant.
It might look like something more,
but it's just a number dressed up in a fancy tuxedo.

Answer 3

So ignore that while differentiating.
Remember how to differentiate an exponential?
Here is our rule,\[\large\rm \frac{d}{dx}a^x=a^x(\ln a)\]

Answer 4

So then,\[\large\rm \frac{d}{dt}7^t=?\]What do you think? :d

Answer 5

Thank you!