Question

For a submarine cable, the range of signalling is governed by the function

f(r) = r^2 ln⁡(1/r)

where 0
Find df/dr.

Answer 1

`(df)/(dr) = (-r) + log((1)/(r) )( 2 r)`

Explanation:

Explanation

Given function f(r) = r² log r ....(i)

Apply derivatives formula

`(d)/(dx) UV = U^(l) V + V^(l) U`

`(d)/(dx)x^(n) = nx^(n-1)`

`(d)/(dx)log x = (1)/(x)`

Differentiating equation (i) with respective to 'r' , we get

`(df)/(dr) = r^(2) ((1)/((1)/(r) ) )(d)/(dr) ((1)/(r ) )+ log((1)/(r) ) 2 r`

`(df)/(dr) = r^(2) ((1)/((1)/(r) ) )((-1)/(r^(2) ) )+ log((1)/(r) ) 2 r`

Final answer:-

`(df)/(dr) = (-r) + log((1)/(r) )( 2 r)`