Question

How do you get this: (uv)'=u'v+uv'?

Answer 1

Besides the fact that is IS the "Product Rule"?

Answer 2

ok , so you are trying to prove product rule ?

Answer 3

The product rule of derivative.

Answer 4

Given \(\dfrac{d}{dx}f(x) = f'(x)\)

and \(\dfrac{d}{dx}g(x) = g'(x)\)

What is \(\dfrac{d}{dx}\left(f(x)\cdot g(x)\right)\)

One might pursue the definition of a derivative...

\(\lim\limits_{h\rightarrow 0}\dfrac{f(x+h)g(x+h) - f(x)g(x)}{h}\)

It's kind of a funny thing. Pull this out of the air: \(f(x+h)g(x)\) and add it to the mix.

\(\lim\limits_{h\rightarrow 0}\dfrac{f(x+h)g(x+h) - f(x+h)g(x) + f(x+h)g(x) - f(x)g(x)}{h}\)

Now, you can split it up and make some progress.