Check the solution to "Find the derivatives. f(x)=4x3+x3−6xx12"

College
Calculus and Analysis
Differential Calculus
Derivatives

Elleanor Mckenzie

Answered question

2021-09-23

Find the derivatives.
$f (x) = \frac{4 x^{3} + \sqrt[3]{x} - 6 x}{x^{\frac{1}{2}}}$

Answer & Explanation

BleabyinfibiaG

Skilled2021-09-24Added 118 answers

$f (x) = \frac{4 x^{3} + \sqrt[3]{x} - 6 x}{x^{\frac{1}{2}}}$
$\Rightarrow f (x) = 4 x^{\frac{5}{2}} + x^{- \frac{1}{6}} - 6 x^{\frac{1}{2}}$
Finding derivative of the function:
$\Rightarrow f^{'} (x) = \frac{d}{d x} (4 x^{\frac{5}{2}} + x^{- \frac{1}{6}} - 6 x^{\frac{1}{2}})$
$\Rightarrow f^{'} (x) = 4 \times \frac{5}{2} x^{\frac{3}{2}} - \frac{1}{6} x^{- \frac{7}{6}} - 6 \times \frac{1}{2} x^{- \frac{1}{2}}$
$\Rightarrow f^{'} (x) = 10 x^{\frac{3}{2}} - \frac{1}{6} x^{- \frac{7}{6}} - 3 x^{- \frac{1}{2}}$

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