Resolved: "Derivatives question: finds f’(x) given that f(x)=1x2+x+15"

alesterp

Answered question

2021-09-25

Derivatives question: finds f’(x)
given that $f (x) = \frac{1}{\sqrt[5]{x^{2} + x + 1}}$

Answer & Explanation

Sadie Eaton

Skilled2021-09-26Added 104 answers

Step 1
Given function can be written as
$f (x) = \frac{1}{\sqrt[5]{x^{2} + x + 1}}$
$f (x) = \frac{1}{{(x^{2} + x + 1)}^{\frac{1}{5}}}$
$f (x) = {(x^{2} + x + 1)}^{- \frac{1}{5}}$
Step 2
Now, by differentiating with respect to x by using power rule of differentiation which states that derivative of $x^{n} i s n x^{n - 1}$
$f^{'} (x) = - \frac{1}{5} {(x^{2} + x + 1)}^{- \frac{1}{5} - 1} \frac{d}{d x} (x^{2} + x + 1)$
$f^{'} (x) = - \frac{1}{5} {(x^{2} + x + 1)}^{- \frac{6}{5}} (2 x + 1)$
$f^{'} (x) = - \frac{1}{5} \frac{(2 x + 1)}{{(x^{2} + x + 1)}^{\frac{6}{5}}}$
Step 3
Ans:
$f^{'} (x) = - \frac{1}{5} \frac{(2 x + 1)}{{(x^{2} + x + 1)}^{\frac{6}{5}}}$

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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