Question

8. Suppose f and g are differentiable functions on R with values in R$^n$. a. Show that $(f \cdot g)' = f' \cdot g + f \cdot g'.$ b. Suppose also that $n = 3$, and show that $(f \times g)' = f' \times g + f \times g'$.

          8. Suppose f and g are differentiable functions on R with values in R$^n$.
a. Show that $(f \cdot g)' = f' \cdot g + f \cdot g'.$
b. Suppose also that $n = 3$, and show that $(f \times g)' = f' \times g + f \times g'$.

8. Suppose f and g are differentiable functions on R with values in R^n.
a. Show that (f · g)' = f' · g + f · g'.
b. Suppose also that n = 3, and show that (f × g)' = f' × g + f × g'.

Added by Nieves E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Eric Mockensturm

08/01/2021

Step 1

The product rule states that if h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x). Show more…

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8. Suppose f and g are differentiable functions on R with values in R^n. a. Show that (f g)' = f g + f g'. b. Suppose also that n = 3, and show that (f' g)' = f' g + f g'.