I hope you?ve enjoyed attempting the exercise lectures
but now I'm here to guide you through so you can check your solutions.
Let's start with the first one we have the function y equals to 3x plus 7 to the power of 15.
Have a look at what kind of function this is before you decide how to differentiate it.
I hope you spotted that this is a function inside of a function,
so we can use our fast away when we differentiate the outside function first.
So you bring the power down, leave the inside exactly as it is
and you decrease the power by one and then you look at the inside function
and we're now looking at the differential of 3x plus 7.
Remember any constants just disappear so the differential of this will just be 3.
Bring it all together our gradient will be 45, 3x plus 7 to the power of 14.