27 Dec 2021
Problem 62
Page 182
Section: 3.1 Derivatives of Polynomials and Exponential Functions
Chapter 3: Differentiation Rules
Textbook ExpertVerified Tutor
27 Dec 2021
Given information
Given function is
Step-by-step explanation
Step 1.
Given the general form for , we know that its derivatives must be:
Plugging these into the given equation, we have that
Re-arranging the terms on the right hand side, this implies that
Since the coefficients on must be equal on both sides, we have . Meaning that
Also, since the coefficients on $x$ must be equal, we have that
Which gives us also.
Finally, since the constant terms on both sides of the equation must be equal, we have that
Therefore, , meaning that
Hence, we can conclude that