Chain, Product and Quotient Rule: Exercise 1

00:00 I hope you've enjoyed attempting the exercise like yours. But now I'm here to guide you through so you can check your solutions. Let's start with the first one.

00:09 We have the function y equals to 3x plus 7 to the power of 15. How to 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 faster way 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 1. 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 altogether, our gradient will be 45 3x plus 7 to the power of 14.