Answer:
Step-by-step explanation:
For this problem, we will need to use the product rule:
[tex]h(x) = f(x)g(x)[/tex]
[tex]h'(x) = f'(x)g(x) + f(x)g'(x)[/tex]
In this problem, [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \sqrt{2x + 3}[/tex]
Finding the derivative of each gives us the following:
[tex]f'(x) = 3x^{2}[/tex]
[tex]g'(x) = \frac{1}{\sqrt{2x + 3}}[/tex]
Plugging these values into the product rule gives us the final derivative:
[tex]y'(x) = 3x^{2}\sqrt{2x + 3} + \frac{x^{3}}{\sqrt{2x + 3}}[/tex]
