Partial derivative with constant

Question

Given

$$c = 0.03 + 0.08a$$

What is $\dfrac{\partial c}{\partial a}$?

I'm guessing $\dfrac{\partial c}{\partial a} = 0.03 + 0.08 = 0.11$? The constant is confusing me. Thanks.

Answer 1

Think of $c$ as $c(a)$, as in $c$ is a function in terms of the independent variable $a$. (This means $c$ is not a constant.) Hopefully this will help clear that confusion you had with the $c$.

Given $c = 0.03 + 0.08a$

Then \begin{align}\frac{\partial c}{\partial a} &= \frac{\partial}{\partial a} (0.03 + 0.08a) \\ &=\frac{\partial}{\partial a}(0.03) + \frac{\partial}{\partial a}(0.08a) \\ &= 0 + 0.08 \\ &=\boxed{0.08}\end{align}