A function is defined in `(0,oo)` by
`f(x)={{:(,1-x^(2)," for ",0ltxle1),(In ,x," for ",1ltxle2),(In, 2-1+0.5x," for ",2ltxltoo):}`
Which one of the following is correct in respect of the derivative of the function, i.e., f'(x)?

Options

A. `f'(x)=2x" for "0ltxle1`
B. `f'(x)=-2x" for "0ltxle1`
C. `f'(x)=-2x" for "0ltxlt1`
D. `f'(x)=0" for "0ltxltoo`

Answer

C

Explanation

`f(x)={{:(1-x^(2)," for ",0ltxle1),(lnx," for ",1ltxle2),(ln2-1+0.5x," for ",2ltxltoo):}`
`f'(x)=-2x" for "0ltxlt1`