So I hope you've enjoyed the challenge of attempting this question in the exercise lecture.
Let's go through them together and just check our solutions together.
So our first question states that y equals to e to the 15x, plus 3.
Now remember that we're having to differentiate this
and we're going to have to think of lots of different things, what kind of function this is,
whether it's a function of a function or whether you,
it's a product of the function or why the things are dividing
and then we have to decide what rule to use to differentiate
and then we also have to incorporate the differentials of e's and ln's and sine's, cos', and tan's.
So let's have a look at this question now.
If you look at this closely, we have e to the power of 15x, so it's not just e to the power of x,
it's e to the power of another function. So we're going to treat this as a function
within another function and we're going to use the chain rule.
When we do have dy/dx, remember e to the power of anything,
just differentiates to e to the power of the same thing, so it doesn't change.
So this stays as e to the 15x, but then you also multiply it with the differential of the inside function,
so the differential of this function, the differential of 15x is just 15,
and you can multiply that here. So that becomes 15e to the 15x.
And any constant at the end just disappears,
so the derivative of e to the 15x plus 3 is just 15e to the 15x.