CPM Homework Help : CALC Problem 4-48

If $h(x) = f(x) · g(x)$ , then does $h^\prime(x) = f^\prime(x) · g^\prime(x)$ ? Test this idea on $h(x) = (x^2 + 1)(x − 4)$ using your results from problem 4-47. Thoroughly record your results.

Step 1

Let $h(x) = (x^² + 1)(x − 4)$ and note its derivative (you found the derivative in problem 4-47).

Step 2

If $h(x) = f(x)g(x)$ , then $f(x) = x^² + 1$ and $g(x) = x − 4$ . Find the $f^\prime(x)$ and $g^\prime(x)$ .

Step 3

Multiply: $f^\prime(x)g^\prime(x) =$ . Is this the same derivative you found in problem 4-47?

Hint

During this course, you will discover many shortcuts to finding derivatives, but this is not one of them. $h^\prime(x) ≠ f^\prime(x)g^\prime(x)$