Get the answer to "Find the derivatives. y=(x2+6x+2)(2x4+x53+3)"

glasskerfu

Answered question

2021-05-03

Find the derivatives.
$y = (x^{2} + 6 x + 2) (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3)$

Answer & Explanation

Alara Mccarthy

Skilled2021-05-05Added 85 answers

Use Product rule of derivative and find the derivative of above function.
$\frac{d}{d x} (f (x) g (x)) = f^{'} (x) g (x) + g^{'} (x) f (x)$ [Product rule]
$f (x) = (x^{2} + 6 x + 2) (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3)$
$f^{'} (x) = (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3) \frac{d}{d x} (x^{2} + 6 x + 2) + (x^{2} + 6 x + 2) \frac{d}{d x} (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3)$
$= (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3) (2 x + 6) + (x^{2} + 6 x + 2) (\frac{(- 4) 2}{x^{5}} + \frac{5}{3} x^{\frac{2}{3}} + 0)$
$= (\frac{2}{x^{4}} + \sqrt[3]{x^{5}} + 3) (2 x + 6) + (x^{2} + 6 x + 2) (\frac{- 8}{x^{5}} + \frac{5}{3} x^{\frac{2}{3}})$
$= \frac{4}{x^{3}} + 2 x^{3} \sqrt[3]{x^{5}} + 6 x + \frac{12}{x^{4}} + 6 \sqrt[3]{x^{5}} + 18 - \frac{8}{x^{3}} + \frac{5}{3} x^{\frac{8}{3}} - \frac{48}{x^{4}} + 10 x^{\frac{5}{3}} - \frac{16}{x^{5}} + \frac{10}{3} x^{\frac{2}{3}}$

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