Question

find f'(x) f(x)=x/(1+x) using f(x+h)-f(x) / h

Answer 1

\[f(x+h)=\frac{x+h}{1+x+h}\]

Answer 2

\[\lim_{h \rightarrow 0}\frac{\frac{x+h}{1+x+h}-\frac{x}{1+x}}{h}\]

Answer 3

\[\lim_{h \rightarrow 0}\frac{(1+x+h)(1+x)}{(1+x+h)(1+x)} \cdot \frac{\frac{x+h}{1+x+h}-\frac{x}{1+x}}{h}\]

Answer 4

\[\lim_{h \rightarrow 0}\frac{(x+h)(1+x)-x(1+x+h)}{(1+x+h)(1+x)h}\]

Answer 5

\[\lim_{h \rightarrow 0}\frac{x+x^2+h+xh-x-x^2-xh}{(1+x+h)(1+x)h}\]

Answer 6

\[\lim_{h \rightarrow 0}\frac{h}{(1+x+h)(1+x)h}=\lim_{h \rightarrow 0}\frac{1}{(1+x+h)(1+x)}\]

Answer 7

\[\frac{1}{(1+x+0)(1+x)}=\frac{1}{(1+x)^2}\]

Answer 8

wow thx myininaya!

Answer 9

i don't get it could you write it again?

Answer 10

don't mind satellite
hes always out to punish me

Answer 11

lol