Question

why does: y+dy=(x+dx)^-2 equal:
=x^-2(1+dx/x)^-2

Answer 1

put x in evidence

Answer 2

Another way of thinking is divide the expression on R.H.S with x^-2 and then multiply it with x^-2 on the outside

Answer 3

multiplying and dividing Right hand side with x^-2
\[\frac{ x ^{-2}(x+dx)^{-2} }{ x^{-2} }\]
\[x^{-2} (\frac{ x+dx }{ x })^{-2}\]

Answer 4

simplify it to x^-2 (1+dx/x)^-2
I hope it makes sense now

Answer 5

I stiil dont get it
Could someone please explain it step by step?

Answer 6

Ok, do you agree that x+dx could be written as x(1+dx/x)?

Answer 7

\[x+dx=x+\frac{x}{x} dx=x+x \cdot \frac{dx}{x}=x(1+\frac{dx}{x})\]

Answer 8

how can x+dx be written as x(1+dx/x)?

Answer 9

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

Answer 10

Did you see what I said above what you said?