Question

Find from first principles the derivative of f:x maps to (x+2)all squared

Answer 1

Given:

`f(x)=(x+2)^2`

Required:

To find the first principles

Step-by-step explanation:

First principle,

`\lim_(h\to0)(f(x+h)-f(x))/(h)`
`=\lim_(h\to0)((x+h+2)^2-(x+2)^2)/(h)`
`=\lim_(h\to0)(x^2+(h+2)^2+2x(h+2)-x^2-4-4x)/(h)`
`=\lim_(h\to0)(h^2+4+4h+2xh+4x-4-4x)/(h)`
`\begin{gathered} =\lim_(h\to0)(h^2+4h+2xh)/(h) \\ \\ =\lim_(h\to0)(h(h+4+2x))/(h) \\ \\ =\lim_(h\to0)(h+4+2x) \\ =2x+4 \end{gathered}`

Final Answer:

`2x+4`