Jack L. answered • 03/14/20
Princeton PhD Student, Yale Graduate, and Experienced Tutor
This is an instance of the chain rule for the expression (4x + 5)2. We first want to take the derivative of the outside expression which is something squared. Applying the power rule we get that the derivative of the outside is just
(1) 2(4x + 5)
As the power rule says to bring down the coefficient and then decrease the exponent by 1. Then we want to multiply by the derivative of the inside expression (4x + 5). We know that the derivative of x is just 1 and the derivative of 5 is 0; as such, this derivative equals 4. Multiplying by 4 yields
(2) 8(4x + 5)
Finally, we have to muliply by our leading coefficient of 12 to yield a final solution of
(3) 96(4x + 5)
I hope this helps!
