Respuesta :
we are given
[tex]f(x)=x^3[/tex]
Firstly, we will find f(x+delta x)
[tex]f(x+\delta x)=(x+\delta x)^3[/tex]
now, we can plug this in formula
[tex]\frac{f(x+\delta x)-f(x)}{\delta x}[/tex]
[tex]\frac{f(x+\delta x)-f(x)}{\delta x}=\frac{(x+\delta x)^3-(x)^3}{\delta x}[/tex]
now, we can simplify it
[tex]=\frac{x^3+(\delta x)^3+3x^2\delta x+3(\delta x)^2x-x^3}{\delta x}[/tex]
now, we can simplify it
[tex]=\frac{(\delta x)^3+3x^2\delta x+3(\delta x)^2x}{\delta x}[/tex]
[tex]=\frac{\delta x ((\delta x)^2+3x^2+3(\delta x)x)}{\delta x}[/tex]
we can cancel it
[tex]=(\delta x)^2+3x^2+3(\delta x)x[/tex]...........Answer
