### Home > CALC > Chapter 4 > Lesson 4.2.1 > Problem4-48

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.

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 $f^\prime(x)$ and $g^\prime(x)$.

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