Get the solution to "Find the derivatives of the functions. f(x)=(x+1)0.5ln⁡x" - Plainmath

nitraiddQ

Answered question

2021-05-11

Find the derivatives of the functions.

f (x) = {(x + 1)}^{0.5} \ln x

Answer & Explanation

svartmaleJ

Skilled2021-05-12Added 92 answers

First, using the product rule, we get

f^{'} (x) = {[{(x + 1)}^{0.5}]}^{'} \ln x + {(x + 1)}^{0.5} {(\ln x)}^{'}

Recall that

{(\ln x)}^{'} = \frac{1}{x}

[{(x + 1)}^{0.5}] = 0.5 {(x + 1)}^{- 0.5} {(x + 1)}^{'} = 0.5 {(x + 1)}^{- 0.5}

Thus

f^{'} (x) = 0.5 {(x + 1)}^{- 0.5} \ln x + \frac{{(x + 1)}^{0.5}}{x}

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