Question

quyz i need a prove for derivative of the sum or difference of two function

Answer 1

d(u + v) /dx = du/dx + dv /dx

??

Answer 2

We know derivative is defined as
\[f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{x+h-x}=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\]

Answer 3

suppose f(x)=g(x)+r(x)
so
\[f'(x)=\lim_{h \to 0} \frac{g(x+h)+r(x+h)-g(x)-r(x)}{x+h-x}\]
let's rearrange a little
\[f'(x)=\lim_{h \to 0} \frac{g(x+h)-g(x)+r(x+h)-r(x)}{h}\]\[=\lim_{h \to 0} \frac{g(x+h)-g(x)}{h}+\frac{r(x+h)-r(x)}{h}=g'(x)+r'(x)\]
Hence proved

Answer 4

thx too much @ash2326

Answer 5

you're welcome:D