### Home > CALC > Chapter 4 > Lesson 4.2.1 > Problem 4-48

4-48.

If *h*(*x*) = *f*(*x*) · *g*(*x*), then does *h *′(*x*) = *f *′(*x*) · *g *′(*x*)? Test this idea on *h*(*x*) = (*x*^{2} + 1)(*x* − 4) using your results from problem 4-47. Thoroughly record your results. Homework Help ✎

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

If *h*(*x*) = *f*(*x*)*g*(*x*), then *f*(*x*) = *x*² + 1 and *g*(*x*) = *x* − 4. Find the *f* '(*x*) and *g*'(*x*).

Multiply: *f* '(*x*)*g*'(*x*) = . Is this the same derivative you found in problem 4-47?

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