Expert answers to "Differentiate the function.G(x)=x6+6x5G′(x)="

Cheyanne Leigh

Answered question

2021-09-30

Differentiate the function.
$G (x) = \sqrt[5]{x^{6} + 6 x}$
$G^{'} (x) =$

Answer & Explanation

curwyrm

Skilled2021-10-01Added 87 answers

Step 1
We have to differentiate the given function:
$G (x) = \sqrt[5]{x^{6} + 6 x}$
Rewriting the given function,
$G (x) = \sqrt[5]{x^{6} + 6 x}$
$= {(x^{6} + 6 x)}^{\frac{1}{5}}$
We know the formula of derivatives,
$\frac{{d x}^{n}}{d x} = n x^{n - 1}$
$\frac{d {(f (x))}^{n}}{d x} = n {(f (x))}^{n - 1} \frac{d f (x)}{d x}$
Step 2
Applying above formula for the given function, we get
$\frac{d G (x)}{d x} = \frac{d {(x^{6} + 6 x)}^{\frac{1}{5}}}{d x}$
$G^{'} (x) = \frac{1}{5} {(x^{6} + 6 x)}^{\frac{1}{5} - 1} \frac{d (x^{6} + 6 x)}{d x}$
$= \frac{1}{5} {(x^{6} + 6 x)}^{\frac{1 - 5}{5}} (6 x^{6 - 1} + 6 \frac{d x}{d x})$
$= \frac{1}{5} {(x^{6} + 6 x)}^{\frac{- 4}{5}} (6 x^{5} + 6)$
$= \frac{(6 x^{5} + 6)}{5 {(x^{6} + 6 x)}^{\frac{4}{5}}}$
Hence,
$G^{'} (x) = \frac{(6 x^{5} + 6)}{5 {(x^{6} + 6 x)}^{\frac{4}{5}}}$ .

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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