Question

-Find a derivative formula for $\frac{d}{dx}[x*f(x)]$ in terms of x, f, and f'. Prove your formula is correct.

Answer 1

Answer:

x*f'(x)+f(x)

Step-by-step explanation:

By using the product rule ie. d/dx[f(x)*g(x)]=f'(x)g(x)+f(x)g'(x)

=>d/dx[x*f(x)]=x*f'(x)+x'*f(x)

Since, x'=1

=>x*f'(x)+f(x)