CPM Homework Help : APCALC Problem 4-48

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

Step 1

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

Step 2

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

Step 3

Multiply: $f ^\prime\left(x\right)g^\prime\left(x\right) =$ . 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. $h^\prime\left(x\right) ≠ f ^\prime\left(x\right)g^\prime\left(x\right)$